From a451dca961efe0e26c44829f78712a44f6d73eac Mon Sep 17 00:00:00 2001 From: Frank14f <1515444314@qq.com> Date: Sun, 9 Aug 2026 21:04:54 +0800 Subject: [PATCH] feat(theory): publish steady cloak result package Freeze the bounded steady-flow evidence, reader documentation, lattice-exact plotting package, and reproducible diagnostics for writing and review. 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It defines the inviscid problem; it does not validate the existing numerical solver or establish the later circulation-cancellation mechanism. Every substantive statement below has exactly one registry label. + +## 0. Statement registry and audit rule + +Labels have these exact meanings: + +- **proved mathematical result**: derived here from stated hypotheses. +- **primary-literature-supported result**: taken from or directly corroborated by the cited primary source. +- **numerical observation**: measured in this project; no numerical observation is promoted to a theorem. +- **modeling assumption**: an input, closure, convention, or extrapolation not implied by Euler. + +| ID | Exact label | Auditable statement | +|---|---|---| +| S1 | modeling assumption | Stage 1 studies a steady, two-dimensional, incompressible outer field around three fixed circles, either in a free-slip strip or its unbounded-plane limit. | +| S2 | proved mathematical result | Subject to the regularity, far-field, compatibility, and function-space hypotheses in §3, an irrotational Euler/Neumann solution is unique after all body circulations are fixed. | +| S3 | proved mathematical result | Rigid rotation of a circle about its center contributes no normal wall velocity. | +| S4 | primary-literature-supported result | A multiply connected irrotational outer flow contains independent circulation periods not selected by impermeability; Crowdy (2006), especially (16), (18), (20), and (34), supplies an exact zero-circulation construction. | +| S5 | proved mathematical result | For one circle, the exact uniform-flow-plus-circulation family has wall velocity `u_theta(a,theta)=-2U sin(theta)+Gamma/(2 pi a)`. | +| S6 | proved mathematical result | The case `U=0`, `Gamma=2 pi a^2 Omega` exactly matches the rotating wall's tangential speed while remaining an Euler slip solution; therefore an absolute impossibility claim is false. | +| S7 | proved mathematical result | For the one-circle family with `U != 0`, no constant `Omega` can make tangential no-slip hold at every angle. | +| S8 | proved mathematical result | In general multi-body geometry, prescribed normal and tangential traces form overdetermined Cauchy data; the finite-dimensional circulation freedom can satisfy only tangential data lying in its compatible finite-dimensional trace space. | +| S9 | primary-literature-supported result | Inviscid circulation is transported under Kelvin's hypotheses, while viscous rotating-cylinder problems impose full wall velocity and generate/diffuse vorticity; Ueda et al. (2003), (2.4), (2.7)–(2.10), exhibits that viscous boundary-value structure. | +| S10 | modeling assumption | Any map `Gamma_eff(s)` from nondimensional wall speed to an outer circulation is a viscous-interface/empirical closure, not an Euler boundary condition. | +| S11 | numerical observation | Existing project aggregate CFD records report downstream profile errors; no surviving endpoint velocity fields support a fitted effective circulation, so historical fitted values are withdrawn from current evidence. | +| S12 | modeling assumption | Later stages may test rear-opposite circulations as a cloak mechanism, but stage 1 neither derives nor validates that mechanism. | + +## 1. Historical Stage-1 charter (superseded as current governance) + +**1.1 — Proposition [proved mathematical result].** For the domains and spaces stated below, fixing the three circulation periods removes the harmonic nonuniqueness of the irrotational Euler/Neumann problem; centered circular rotation does not enter impermeability; and imposing the complete rotating-wall tangential trace as well is in general incompatible, though the explicit `U=0`, `Gamma=2 pi a^2 Omega` one-circle case is compatible. + +**1.2 — Pass evidence [modeling assumption].** This stage passes only if the proposition is supported by numbered definitions and proofs, an explicit counterexample, primary-source links at the inviscid/viscous interface, an equation ledger, and an end-stage claim/file audit. + +**1.3 — Falsification or claim-limiting evidence [modeling assumption].** A missing flux condition, an unacknowledged strip/exterior function-space issue, a counterexample to fixed-period uniqueness under the stated hypotheses, or evidence that a claimed result holds only for one circle forces repair or narrowing; numerical agreement cannot repair a mathematical failure. + +## 2. Geometry, nondimensionalization, and signs + +**2.1 — Domain [modeling assumption; S1].** Use cylinder diameter `D`, inflow speed `U_inf>0`, and time `D/U_inf` as scales. Dimensionless coordinates and velocity are `x=x*/D` and `u=u*/U_inf`; pressure is scaled by `rho U_inf^2`. Three disjoint closed disks are + +`B_j={x in R^2: |x-c_j| <= a_j}`, `j=1,2,3`, + +with positive gaps. The unbounded fluid domain is `Omega_inf=R^2 \ union_j B_j`. The strip domain is + +`Omega_H={-infinityinfinity`, with derivatives sufficient for the integrations below. In `Omega_H`, require free slip `u dot n=0` at `y=+/-H` and approach to a specified through-flow as `x->+/-infinity`. The phrase “unbounded limit” means taking `H->infinity` only after the strip and exterior problems have each been defined; it is not an automatic uniform convergence claim. + +## 3. Euler, Hodge periods, compatibility, and uniqueness + +**3.1 — Governing equations [primary-literature-supported result; S4].** The steady incompressible Euler equations in the fluid are + +`(u dot grad)u = -grad p`, `div u=0`. + +For the irrotational outer subclass, `curl u=0`. Crowdy (2006), (16), imposes uniform behavior at infinity; its constant-streamfunction boundary conditions (18)–(19) encode impermeability, and (20), (25)–(26), (34) construct the multiply connected zero-circulation complex potential. These equations support the formulation, not viscous no-slip or circulation selection. + +**3.2 — Harmonic decomposition [proved mathematical result].** Assume a sufficiently smooth domain and a single-valued harmonic potential `phi` for the zero-period part. Choose harmonic vector fields `h_j` satisfying + +`div h_j=curl h_j=0`, `h_j dot n=0`, and `integral_(CCW around B_k) h_j dot dl=delta_jk`. + +Then every admissible irrotational field with the prescribed far field can be written + +`u = u_N + sum_(j=1)^3 Gamma_j h_j`, + +where `u_N` has zero periods and solves the required Neumann data. This is the planar Hodge/de Rham separation of an exact part from the three cohomological periods. Crowdy's single-valued uniform-flow potential is an exact representation of the zero-period member, consistent with (33)–(34). + +**3.3 — Flux compatibility [proved mathematical result; S2].** For a truncated domain `Omega_R`, the divergence theorem gives + +`0=integral_(Omega_R) div u dA=integral_(partial Omega_R) u dot n ds`. + +Therefore prescribed normal data must have zero total flux after including outer truncation/end sections. For fixed rigid bodies and impermeable strip walls, all solid-wall contributions vanish. In the exterior problem, uniform inflow has zero net flux through a large closed circle. In the strip, the upstream and downstream section fluxes must agree. A source-based representation must likewise have zero total source; imposing zero source per body is stronger than global compatibility and is a numerical representation choice, not a new Euler law. + +**3.4 — Fixed-circulation uniqueness theorem [proved mathematical result; S2].** Assume: (i) two `C^1` irrotational, divergence-free solutions have identical normal traces, far/end behavior, and all three geometric circulations; (ii) their difference `w` and a potential for it lie in a class permitting integration by parts; and (iii) the boundary term at infinity or the two strip ends tends to zero. Then the two velocity fields coincide. + +*Proof.* The difference satisfies `div w=curl w=0`, `w dot n=0`, zero far/end data, and zero periods around every hole. Zero periods make the closed one-form `w dot dx` exact, so `w=grad chi` for a single-valued harmonic `chi`. Green's identity on a truncation gives + +`integral |grad chi|^2 dA = integral_(boundary) chi partial_n chi ds`. + +Body and free-slip-wall terms vanish because `partial_n chi=0`; the outer/end term vanishes by assumption. Thus `grad chi=0`, so `w=0`. QED. + +**3.5 — Caveats [modeling assumption].** The theorem is conditional, not an existence theorem. Nonzero net circulation in the unbounded plane has a `1/r` velocity tail and logarithmically divergent total kinetic energy, so “finite energy” must not be imposed on the full field unless the circulation class is adjusted; the *difference* in the uniqueness proof has zero periods and can have finite energy. In an infinite strip, end modes and through-flow must be fixed, and sufficient decay must exclude additional harmonic end modes. Corners, touching bodies, non-smooth traces, or weak Euler solutions require separate functional analysis. Pressure is then recovered locally from Bernoulli for a steady irrotational field, up to constants compatible with the connected fluid domain. + +**3.6 — Literature scope [primary-literature-supported result; S4].** Glass, Lacave, Munnier & Sueur (2019) provides a modern perfect-fluid/rigid-body framework in which vorticity and body circulations are independent state data and circulation-induced harmonic fields enter the dynamics. The present fixed-body theorem is narrower and is proved above rather than attributed to an unstated theorem number. + +## 4. Rigid-body impermeability + +**4.1 — Euler wall condition [primary-literature-supported result].** For a rigid body with center velocity `V_j` and angular velocity `Omega_j e_z`, its boundary velocity is + +`U_B,j(x)=V_j + Omega_j e_z cross (x-c_j)`. + +The inviscid kinematic condition is `(u-U_B,j) dot n=0`. Modern rigid-body Euler formulations, including Glass et al. (2019), use this normal matching while retaining circulations as separate data. + +**4.2 — Centered-circle cancellation [proved mathematical result; S3].** On a circle, `x-c_j=a_j e_r`, so the rotational velocity is `Omega_j a_j e_theta`. Since `e_theta dot n=e_theta dot (-e_r)=0`, + +`(Omega_j e_z cross (x-c_j)) dot n=0`. + +Thus centered rotation drops out of normal data exactly. Translation does not: `U_B,j dot n=V_j dot n`. For the fixed circles here, impermeability is simply `u dot n=0`, independent of `Omega_j`. + +## 5. Exact one-cylinder audit and counterexample + +**5.1 — Exact potential [primary-literature-supported result; S5].** For a circle `r=a` centered at the origin, uniform flow `U e_x`, and geometric CCW circulation `Gamma`, classical Lamb/Milne-Thomson circle-theorem theory gives + +`W(z)=U(z+a^2/z) - i Gamma/(2 pi) log(z/a)`, + +with complex velocity `dW/dz=u_x-i u_y`. Crowdy (2006), (15) and the `M=0` reduction following (34), independently recover the zero-circulation term. Classical edition/page/equation details for Lamb and Milne-Thomson remain marked for bibliographic verification; none is guessed here. + +**5.2 — Velocity and wall trace [proved mathematical result; S5].** Direct differentiation or polar differentiation gives + +`u_r=U(1-a^2/r^2) cos(theta)`, + +`u_theta=-U(1+a^2/r^2) sin(theta)+Gamma/(2 pi r)`. + +Hence `u_r(a,theta)=0` and + +`u_theta(a,theta)=-2U sin(theta)+Gamma/(2 pi a)`. + +The entire one-parameter family satisfies the same Euler impermeability condition. Therefore wall rotation does not select `Gamma`. + +**5.3 — Explicit compatible special case [proved mathematical result; S6].** Set `U=0`. The outer field is the line-vortex field `u_theta=Gamma/(2 pi r)`, irrotational for `r>a`. A wall rotating CCW with angular velocity `Omega` has tangential speed `a Omega`. Choosing + +`Gamma=2 pi a^2 Omega` + +makes `u_theta(a,theta)=a Omega` for every `theta`, while `u_r=0`. This is an exact special counterexample to “potential flow can never match a rotating circular wall.” It does not show that Euler selects this circulation: every other `Gamma` still satisfies Euler impermeability. + +**5.4 — Nonzero-inflow obstruction [proved mathematical result; S7].** If constant rotating no-slip held for `U != 0`, then + +`-2U sin(theta)+Gamma/(2 pi a)=a Omega` + +for all `theta`. Evaluating at `theta=pi/2` and `3pi/2` gives respectively `-2U+C=a Omega` and `2U+C=a Omega`, which imply `U=0`, a contradiction. Thus within this exact one-cylinder family, no constants `Gamma,Omega` give full rotating no-slip when `U != 0`. + +## 6. Why multi-body no-slip is generally overdetermined + +**6.1 — Trace-space argument [proved mathematical result; S8].** Solve the Neumann problem first. With geometry, far field, and normal data fixed, its irrotational solutions form the affine family + +`u|_(boundary) = u_N|_(boundary) + sum_j Gamma_j h_j|_(boundary)`. + +The freely adjustable tangential traces therefore lie in a space of dimension at most three. Full rigid-wall no-slip would prescribe one function of arclength on every body, + +`u dot t = U_B,j dot t` on `partial B_j`, + +in addition to normal data. Such target traces belong to an infinite-dimensional function space. They are attainable only if their difference from `u_N dot t` lies exactly in the span of the three harmonic tangential traces. Consequently compatibility can occur in special symmetric cases, but in general—and generically under perturbation of geometry, inflow, or wall speeds—it does not. + +**6.2 — Cauchy-data formulation [proved mathematical result; S8].** Locally write the zero-period part as `grad phi` with `Delta phi=0`. Normal velocity prescribes `partial_n phi`; tangential velocity prescribes `partial_s phi` (after subtracting harmonic circulation fields). Together they determine the full boundary gradient and hence constitute Cauchy data for an elliptic equation. Arbitrary Cauchy data do not satisfy the nonlocal harmonic compatibility relation. This is an overdetermination argument, not a claim that compatibility is never possible; §5.3 is the required exception. + +**6.3 — Scope [modeling assumption].** The argument establishes “in general” or “generically,” not a measure-theoretic genericity theorem for every geometry class. A rigorous transversality statement is outside stage 1. Noncircular rotation can also contribute normal velocity if rotation is not about a symmetry center or the body motion changes the domain; those cases are not covered by §4.2. + +## 7. Kelvin, vorticity, and the viscous interface + +**7.1 — Kelvin transport [primary-literature-supported result; S9].** Under the classical hypotheses of inviscid barotropic flow, conservative body forces, sufficient smoothness, and a closed material contour `C(t)`, Kelvin's theorem states + +`d/dt integral_(C(t)) u dot dl = 0`. + +Glass et al. (2019) explicitly treats body circulations as conserved parameters for smooth two-dimensional perfect-fluid/rigid-body motion. Original Kelvin bibliographic details and any historical equation number require later verification; no quotation or number is supplied here. + +**7.2 — Vorticity consequence [proved mathematical result; S9].** In two-dimensional constant-density Euler, taking curl gives `partial_t omega+u dot grad omega=0`. Thus initially irrotational fluid remains irrotational along smooth trajectories; Euler slip supplies no viscous wall-vorticity flux capable of selecting a new `Gamma` from `Omega`. Multiply connected nonzero periods may nevertheless exist with `omega=0` in the fluid because loops around holes need not bound fluid-only surfaces. + +**7.3 — Viscous boundary [primary-literature-supported result; S9].** A viscous rotating-body problem instead uses Navier–Stokes and full no-slip/no-penetration `u=U_B` on the wall. Ueda et al. (2003), (2.4), prescribes uniform far velocity and rotating-cylinder wall velocity; (2.7) relates velocity, streamfunction, and vorticity; and (2.8)–(2.10) carry the boundary/vorticity coupling into their low-Re formulation. These equations supply no Euler rule `Gamma=2 pi a^2 Omega`. + +**7.4 — Outer/inner closure [primary-literature-supported result; S10].** Glauert (1957) treats rapidly rotating, nonseparating flow by taking an irrotational outer flow with unknown circulation and using a viscous boundary-layer solution/no-slip matching to determine it in that restricted regime. Moore's 1957 rotating-cylinder work is a related boundary-layer source. These are precedents for a viscous closure, not universal formulas for this three-cylinder, finite-Re, possibly separated flow. Exact Moore equation mapping and edition details require later bibliographic verification. + +**7.5 — Project closure [modeling assumption; S10].** Define nondimensional wall-speed ratio `s=Omega a/U_inf` (or record explicitly if code uses `Omega D/U_inf`). Any `Gamma_eff(s)` used by this project must be obtained from a stated viscous model or empirical outer-field procedure—e.g. contour plateaus or held-out outer-profile fits—with sign, contour/mask, uncertainty, Reynolds number, geometry, and confinement recorded. It must not be set to `2 pi a^2 Omega` merely because §5.3 makes that identity compatible at `U=0`. + +## 8. Project implications and prohibited claims + +**8.1 — Allowed implications [proved mathematical result; S2–S8].** The outer potential problem may legitimately treat body circulations as independent prescribed controls, and a fixed-circulation solution can serve as a mathematically unique reference under §3.4 assumptions. Circular wall rotation cannot be inserted through impermeability; it must enter through a separately justified circulation/viscous interface. + +**8.2 — Empirical boundary [numerical observation; S11].** Historical fitted `Gamma_eff/(UD)` values without source arrays remain withdrawn. The later v4 endpoint campaign supplies direct fields and geometric contour sign; its corrected WLS is explicitly a descriptive projection rather than a causal wall-speed law. + +**8.3 — Later mechanism status [modeling assumption; S12].** Opposite rear-cylinder circulations, multipole cancellation, and any “cloak” interpretation are hypotheses reserved for later stages. Nothing in Euler uniqueness implies disturbance reduction, an optimum, stability, or agreement with Navier–Stokes. + +**8.4 — Prohibited claims [modeling assumption].** Until later evidence exists, this project must not claim: (a) Euler wall rotation selects circulation; (b) potential flow can *never* match a rotating wall; (c) `Gamma_eff=2 pi a^2 Omega` for nonzero inflow or multiple bodies; (d) impermeability implies no-slip; (e) a small collocation residual proves physical accuracy; (f) potential flow predicts separation, drag, torque, wall vorticity, or viscous stability; (g) the strip result follows automatically from the plane result; or (h) rear-opposite circulation is the demonstrated cloak mechanism. + +## 9. Equation-to-source-to-implementation/test ledger + +| Derivation item | Source/proof | Current implementation/test touchpoint | Stage-1 status | +|---|---|---|---| +| Domain, signs, `Gamma_j` | §2 definition | `contract.py`; sign tests in `tests/test_core.py` | Documentation only; code not revalidated here | +| Euler far field and streamline boundaries | Crowdy (2006), (16), (18)–(20), (34) | `theory.py` outer MFS | Mathematical contract frozen; numerical validation deferred | +| Prime-function exact reference | Crowdy (2006), (25)–(26), (34) | No exact Crowdy implementation | Later independent-reference task | +| Hodge circulation basis | §3.2–§3.4 proof; Glass et al. (2019) context | circulation basis in `theory.py` | Contract only; dense/off-grid tests deferred | +| Flux compatibility | §3.3 proof | zero-source constraints in `theory.py` | Distinguishes PDE compatibility from representation choice | +| Rigid Euler impermeability | §4 proof; Glass et al. (2019) | body normal collocation | Contract frozen | +| One-cylinder exact solution | classical Lamb/Milne-Thomson; Crowdy (2006), (15), (34) reduction | intended exact test in `tests/test_core.py` | Equation frozen; test audit deferred to stage 2 | +| Special `U=0` counterexample | §5.3 proof | no implementation required | Passed analytically | +| `U!=0` sine obstruction | §5.4 proof | no implementation required | Passed analytically | +| General Cauchy overdetermination | §6 trace-space proof | no no-slip solver should be inferred from MFS | Passed with genericity limit | +| Viscous wall/vorticity system | Ueda et al. (2003), (2.4), (2.7)–(2.10) | CFD is external to outer MFS | Interface distinguished | +| Circulation transport | Kelvin theorem; Glass et al. (2019) | prescribed `Gamma` | Source details flagged where unverified | +| `Gamma_eff(s)` closure | Glauert (1957); Moore (1957) as restricted precedents | later contour/profile fitting | Explicitly modeling/empirical, deferred | + +## 10. Concentrated end-stage review + +**10.1 — Derivation and citation review: PASS [modeling assumption].** Sections 2–7 give numbered definitions, compatibility, conditional uniqueness, circle rotation, exact solution, overdetermination, and viscous interface. Crowdy and the relied-upon Ueda equation mappings were checked against accessible primary PDFs. Classical-book edition details, original Kelvin bibliographic details, and exact Moore equation mapping remain publication holds; Kharlamov–Filip is contextual only and no equation mapping is asserted. + +**10.2 — Counterexample review: PASS [proved mathematical result; S6].** Section 5.3 explicitly verifies both normal and tangential wall velocity for `U=0`, `Gamma=2 pi a^2 Omega`, and separately states that Euler does not select this value. + +**10.3 — Claim-limit review: PASS [modeling assumption].** The text uses “in general” and “generically” for multi-body incompatibility, preserves the special exception, separates strip from exterior function spaces, and prohibits circulation-selection, no-slip, stability, and later-mechanism claims. + +**10.4 — File-budget review: PASS [numerical observation].** At review time the package has 9 root source files including the sole new root file `DERIVATION.md`, and 10 total source files when `tests/test_core.py` is included. Transient `__pycache__` is excluded because it is generated bytecode, not source. No Python file was changed in stage 1. Both counts satisfy root `<=10` and total `<=30`. + +**10.5 — Stage-1 verdict [modeling assumption].** PASS, conditional on preserving the bibliographic-verification flags. This verdict freezes only the boundary contract and claim limits; it does not pass any stage-2-or-later solver, mechanism, DNS, or stability objective. + +## References (primary where used) + +- Crowdy, D. G. (2006), “Analytical solutions for uniform potential flow past multiple cylinders,” *European Journal of Mechanics B/Fluids* 25, 459–470. DOI `10.1016/j.euromechflu.2005.11.005`. +- Glass, O., Lacave, C., Munnier, A. & Sueur, F. (2019), “Dynamics of rigid bodies in a two dimensional incompressible perfect fluid,” *Journal of Differential Equations*. DOI `10.1016/j.jde.2019.04.017`. +- Glauert, M. B. (1957), “The flow past a rapidly rotating circular cylinder,” *Proceedings of the Royal Society A*. DOI `10.1098/rspa.1957.0157`. +- Kharlamov, A. A. & Filip, P. (2012), “Generalisation of the method of images for the calculation of inviscid potential flow past several arbitrarily moving parallel circular cylinders,” *Journal of Engineering Mathematics* 77. Context only; no equation mapping or project result relies on it. +- Moore, D. W. (1957), “The flow past a rapidly rotating circular cylinder in a uniform stream,” *Journal of Fluid Mechanics* 2, 541–550. DOI `10.1017/S002211205700035X`; exact equation mapping not used here. +- Ueda, Y., Sellier, A., Kida, T. & Nakanishi, M. (2003), “On the low-Reynolds-number flow about two rotating circular cylinders,” *Journal of Fluid Mechanics* 495, 255–281. DOI `10.1017/S002211200300627X` (PDF-verified; DOI hold lifted). +- Lamb, *Hydrodynamics*, and Milne-Thomson, *Theoretical Hydrodynamics*: classical circle-flow sources; edition/page/equation details require bibliographic verification. +- Kelvin circulation theorem: classical result; original historical citation details require bibliographic verification. Glass et al. (2019) is the modern application used here. + + +## 11. Stage 2: reference-validation formulation + +**11.1 — Core proposition [modeling assumption].** The prescribed-circulation MFS field is accepted as a high-order outer/strip reference only on geometrically valid inputs and only when independent, dense off-collocation diagnostics and parameter convergence bound its numerical error; collocation residual alone is not validation. + +**11.2 — MFS equations [proved mathematical result].** On each circle, interior logarithmic sources are constrained to have zero sum body by body. Their strengths solve the normal-velocity equations for uniform flow plus prescribed geometric-CCW point-vortex periods. Equal-sign source images and opposite-sign vortex images enforce the horizontal-wall streamline symmetry in the infinite-image limit. Finite image layers are a truncation and must converge numerically. + +**11.3 — Exact audit [proved mathematical result].** The one-circle velocity used as the analytic oracle is exactly §5.2: `u_r=U(1-a^2/r^2)cos(theta)` and `u_theta=-U(1+a^2/r^2)sin(theta)+Gamma/(2 pi r)`, with positive `Gamma` counterclockwise. Its wall normal trace is independent of `Gamma`, while its tangential trace changes by `Gamma/(2 pi a)`. + +**11.4 — Independent formulation [modeling assumption].** The unbounded, zero-circulation cross-check measures agreement between independently discretized MFS and Fourier/Laurent boundary collocation: a uniform complex potential plus finite, single-valued Laurent multipoles `sum_(j,n) C_(jn) a^n/(z-c_j)^n`. It shares geometry and boundary data with MFS but uses neither logarithmic source points nor the MFS source radius. It is independently discretized by oversampled angular collocation. It is not Crowdy exact, does not represent prescribed circulation, and does not validate strip images. + +**11.5 — Dense diagnostics [modeling assumption].** Validation samples use angular nodes distinct from all solve nodes; the Laurent check changes the angles rather than merely moving solve angles radially. Report per-body `L_inf` and RMS normal residuals; gap-facing and outer-facing angular-sector residuals; strip-wall normal residual on an explicitly declared finite `x` interval; circulation quadrature on exterior body contours; far-field recovery; singular values, numerical rank, condition number, coefficient norms, and per-body zero-source error. In-sample residuals are labeled `collocation_*` only. + +**11.6 — Common-exterior error [modeling assumption].** On a fixed rectangle, use a tensor grid with composite-trapezoid weights, discard points within a declared exclusion radius of every body, and compute the weighted RMS velocity difference. Normalize by the weighted RMS reference disturbance from the declared uniform velocity; also report normalization by `|U|` when nonzero. The rectangle, grid, mask, retained weight, and normalization are part of every result. This metric is distinct from the pointwise `x/D=10` `E_inf_vector` profile objective. + +**11.7 — Scientific acceptance rule [modeling assumption].** Stage 2 scientific status is judged from exact-circle identities; strict failure controls; dense off-grid body, circulation, and far-field diagnostics; order and source-radius sensitivity for both zero and rear-opposite circulation; independently discretized Laurent agreement; metric grid/mask sensitivity; and finite-image field differences. Thresholds chosen after observing outputs are regression guards only, not preregistered or frozen scientific evidence. Because the tested strip differences do not support a defensible asymptotic tail estimate, strip status is bounded finite-image consistency rather than a converged reference. + +**11.8 — Falsification or claim limit [modeling assumption].** Rank loss, nonfinite output, uncontrolled condition/coefficient growth, off-grid or sector residual drift, circulation error, image/source/order sensitivity, mask/quadrature sensitivity, or disagreement with the Laurent formulation forces repair or limits the MFS reference claim. This stage establishes no multipole cloak mechanism, viscous closure, or stability result. + +**11.9 — Stage-2 review [numerical observation].** Exact-circle and failure controls pass. Dense source-radius comparisons for both `Gamma=0` and `(0,2,-2)` agree on the weighted common exterior; the Fourier/Laurent solve uses distinct shifted check angles and agrees with MFS under the declared grid and exclusion-mask alternatives. The unbounded Stage-2 reference therefore **PASSes for bounded agreement between independently discretized MFS and Fourier/Laurent boundary collocation**, not as exact independent truth. Strip wall residuals decrease and 20/40/80-layer exterior field differences shrink, but no defensible asymptotic tail estimate is inferred; the strip verdict is **BOUNDED finite-image consistency**. Numerical cutoffs in tests are post-hoc regression guards with stated safety margins, not frozen scientific evidence. + + +## 12. Stage 3: frozen circulation--multipole derivation and charter + +**12.1 — Frozen core proposition [modeling assumption].** In the unbounded outer problem, geometric-CCW rear circulations `(0,+Gamma,-Gamma)` have zero net circulation and therefore no logarithmic potential term. They generate a real potential-dipole coefficient `-Gamma b/pi` before body-induced source readjustment. Stage 3 passes only if the complete MFS coefficient is affine in real `Gamma`, its least-squares cancellation lowers both frozen reduced-field errors, and source truncations converge on declared common-exterior/profile regions and at held-out `Gamma`. It is falsified or claim-limited if the coefficient/sign is absent or wrong, the dipole is non-dominant, cancellation is not attainable on the real affine line, or reduced fields fail those held-out tests. Topology, stagnation, DNS, stability, and new metrics are excluded. + +**12.2 — Complex convention [proved mathematical result].** Let `z=x+i y`, `W=phi+i psi`, and + +`q(z)=dW/dz=u_x-i u_y`. + +A real source strength `Q` and geometric-CCW vortex circulation `Gamma` at `zeta` have + +`W_Q=Q/(2 pi) log(z-zeta)`, `q_Q=Q/[2 pi(z-zeta)]`, + +`W_Gamma=-i Gamma/(2 pi) log(z-zeta)`, `q_Gamma=-i Gamma/[2 pi(z-zeta)]`. + +Indeed `q_Q` gives `(u_x,u_y)=Q(dx,dy)/(2 pi r^2)`, while `q_Gamma` gives `Gamma(-dy,dx)/(2 pi r^2)`. These are exactly the signs in `singular_velocity`; adding `U(z+a^2/z)` gives the sign in `cylinder_velocity`. + +**12.3 — Exact rear-pair expansion and hypothesis challenge [proved mathematical result].** Put `z_+=x_r+i b`, `z_-=x_r-i b`, with assignments `(Gamma_+,Gamma_-)=(Gamma,-Gamma)`. For `|z|>max(|z_+|,|z_-|)`, on one consistent logarithm branch, + +`W_pair=-i Gamma/(2 pi)[log(z-z_+)-log(z-z_-)]` + +`= i Gamma/(2 pi) sum_(n>=1) (z_+^n-z_-^n)/(n z^n)`. + +The two `log z` terms cancel exactly because `Gamma_++Gamma_-=0`. The exact `1/z` potential coefficient is + +`C_pair=i Gamma(z_+-z_-)/(2 pi)=-Gamma b/pi`. + +Thus positive geometric-CCW circulation on the upper rear cylinder produces a **negative real** dipole coefficient; the prior narrative is accepted only with this sign. A positive real zero-circulation blockage coefficient can therefore be opposed by `Gamma>0`. This verifies the algebraic core hypothesis for the prescribed vortices, but does not yet prove that the body-readjusted coefficient has the same slope or that the dipole dominates finite-distance error. + +**12.4 — Reflection and parity [proved mathematical result].** Let `R(x,y)=(x,-y)` and `R_v=diag(1,-1)`. A physical velocity is a polar vector, so reflection acts as + +`(T u)(x,y)=R_v u(x,-y)`. + +A reflection-symmetric field satisfies `T u=u`, equivalently `u_x(x,-y)=u_x(x,y)` and `u_y(x,-y)=-u_y(x,y)`. The zero-circulation geometry, uniform inflow, and unique fixed-period solution are reflection invariant, hence have this parity. For a vortex field, direct substitution gives `T v_Gamma(.;x_0,y_0)=v_-Gamma(.;x_0,-y_0)`: geometric circulation changes sign under orientation reversal. Therefore the geometric assignment upper `+Gamma`, lower `-Gamma` is invariant as a whole and its velocity has the same `(even,odd)` parity. This statement concerns a geometric CCW assignment. Calling `Gamma` a scalar without its orientation convention is misleading; circulation/vorticity is pseudoscalar under reflection. The common-sign rear assignment instead maps to its negative and has perturbation parity `(u_x odd in y, u_y even in y)` when isolated from the symmetric base. + +**12.5 — Bodywise source multipoles [proved mathematical result].** For MFS sources `Q_jk` at `s_jk=c_j+delta_jk`, + +`W_s,j=sum_k Q_jk/(2 pi) log(z-s_jk)`. + +When `sum_k Q_jk=0`, and `|z-c_j|>rho_j=max_k|delta_jk|`, + +`W_s,j=sum_(n>=1) A_jn/(z-c_j)^n`, + +`A_jn=-[1/(2 pi n)] sum_k Q_jk delta_jk^n`, + +`q_s,j=sum_(n>=1) -n A_jn/(z-c_j)^(n+1)`. + +Truncation through `N` retains `1<=n<=N`; circulations remain separate exact vortex terms. Convergence is absolute outside every source ring. The implemented reconstruction therefore excludes all points with `|z-c_j|<=rho_j`; it is not a boundary-interior continuation and says nothing about viscous layers. + +**12.6 — Global unbounded far field [proved mathematical result].** Expanding all singularities about the fixed global origin gives + +`W(z)=U z + L log z + C/z+O(z^-2)`, + +`L=[sum Q_k-i sum Gamma_j]/(2 pi)`, + +`C=-(1/(2 pi)) sum_k Q_k s_k + (i/(2 pi)) sum_j Gamma_j z_j`. + +Bodywise zero source makes `sum Q_k=0`; rear-opposite circulation makes `sum Gamma_j=0`, so `L=0`. The source moment includes the circulation-dependent MFS readjustment, while the second term is the prescribed vortex-position moment. Because the boundary equations are linear, solves at `Gamma=0` and unit rear-opposite basis give exactly + +`C(Gamma)=C_0+Gamma dC`. + +For real `Gamma`, minimizing `|C_0+Gamma dC|^2` gives + +`Gamma_*=-Re(conj(dC) C_0)/|dC|^2`, + +provided `dC != 0`. Exact cancellation occurs iff the residual `C_*` vanishes (within a declared numerical tolerance); otherwise `|C_*|` is the distance from the origin to the real affine coefficient line. This is a closest complex cancellation, not permission to use complex circulation. + +**12.7 — Frozen reduced diagnostics [modeling assumption].** For term counts `N=1,2,...`, compare the source-multipole reconstruction plus exact circulation terms against the full unbounded MFS field using only: (i) the Stage-2 weighted common-exterior velocity error on `[-3,6] x [-3,3]`, `181 x 121`, exclusion `1.1a`; (ii) the complete `x/D=10` profile over `y/D in [-3,3]` with 1201 points and `profile_errors`; and (iii) reflection parity defect, the maximum absolute mismatch in `u_x(x,y)-u_x(x,-y)` and `u_y(x,y)+u_y(x,-y)`, normalized by `U`. No topology or stagnation diagnostic enters Stage 3. + +**12.8 — Strip asymptotic result [proved mathematical result].** The horizontal strip does not have the unbounded-plane Laurent basis as its downstream asymptotic basis. Wall-compatible harmonic disturbances separate into transverse Neumann/Dirichlet modes with exponential streamwise factors, while the uniform through-flow is the zero mode. Finite image sums therefore do not justify an algebraic `1/z` far-field claim. + +**12.9 — Strip scope [modeling assumption].** No strip modal diagnostic is added in Stage 3: cancellation and `Gamma_*` are scoped strictly to the unbounded outer solution, and any strip mechanism claim remains bounded pending a separately derived converged wall-compatible modal analysis. + + +**12.10 — Concentrated Stage-3 review [numerical observation].** Derivation review: PASS; §§12.2–12.6 derive every implemented sign and coefficient directly. Reproducibility/counterexample review: PASS; direct source velocities, pair sign, zero log coefficient, source-series convergence, polar reflection, affine prediction, real cancellation, and held-out `Gamma=1.37`/region convergence are tested. Claim review: PASS with limitation; the unbounded canonical dipole cancels essentially exactly and the downstream profile improves, but finite common-exterior disturbance does not vanish and strip/DNS/topology claims remain excluded. File review: PASS; 9 package-root source files and 10 source files including `tests/test_core.py`; no file was added. Stage-3 verdict: **PASS for an unbounded outer dipole-cancellation mechanism, bounded to its far-field and tested finite-distance consequences.** + + +## 13. Historical Stage-4 mechanism-test charter and preregistration + +**13.1 — Sole question [modeling assumption].** Does the geometric-CCW rear-opposite basis `(0,+Gamma,-Gamma)` explain the observed downstream disturbance reduction? Passing requires the frozen outer-model counterfactuals and genuinely held-out viscous evidence to agree in sign, relative strength, profile shape, and optimum-side degradation. Comparable counterfactual performance, a wrong sign/parity, failed held-out prediction, or absent field provenance limits or falsifies the claim. No stability question enters Stage 4. + +**13.2 — Frozen bases and norm [modeling assumption].** In body order `(front,rear_y_plus,rear_y_minus)`, define unit Euclidean-circulation-norm controls `b_ro=(0,1,-1)/sqrt(2)`, `b_cr=(0,1,1)/sqrt(2)`, and `b_f=(1,0,0)`. A scalar amplitude `g` means `Gamma_vector=g b`, so all ablations use identical `||Gamma_vector||_2=|g|`, geometry, discretization, and profile; no basis-specific rescaling is allowed after results are seen. + +**13.3 — Affine basis response [proved mathematical result].** The MFS Neumann system is linear at fixed geometry and discretization; therefore `u_b(g)=u_0+g v_b` and every global Laurent coefficient is affine in real `g`. + +**13.4 — Frozen analytic tests [modeling assumption].** For each basis, report: net geometric circulation/log coefficient; `dC/dg` for the complex dipole coefficient; reflection parity; the smooth complete-profile disturbance norm `J_2(g)=[mean_y |u_b(g)-U e_x|^2]^(1/2)` and its analytic directional derivative at `g=0`, `J_2'(0)=mean[(u_0-Ue_x) dot v_b]/J_2(0)` when `J_2(0)>0`; and `E_inf_vector` one-sided derivatives at `g=0` for `h={0.2,0.1,0.05,0.025}` with convergence reported, not relabeled as an analytic derivative. Also minimize `J_2` on each real affine basis at fixed norm convention, report the resulting dipole and full `x/D=10`, `y/D in [-3,3]`, 1201-point profile errors, and evaluate equal-amplitude ablations. Rear-opposite passes the theoretical-basis gate only if it alone has zero net circulation, correct symmetric `(u_x even,u_y odd)` parity, a dipole direction opposing blockage, and materially larger smooth-profile reduction than both counterfactuals. `E_inf` is acknowledged as nonsmooth; only declared finite-difference directional slopes are admissible. + +**13.5 — Frozen gap-flux diagnostic [modeling assumption].** Gap flux is the oriented line integral `integral u dot n ds` across each shortest center-to-center gap segment after removing the two radii; the line normal is the left rotation of the segment tangent. Report signed upper-front and lower-front values and their sum. It is descriptive and cannot replace the dipole/profile gates. + +**13.6 — DNS preregistration and evidence contract [modeling assumption].** A DNS circulation mapping may be fit only from endpoint `ux,uy` arrays with coordinates, body mask, `D,U`, action/body IDs, and q-in provenance. Positive fitted circulation is geometric CCW and must be inferred from an explicitly sampled CCW contour or from outer velocity WLS using the same `u_x-i u_y` convention as §12.2. The training mask is frozen as `s={3.45,3.65}` and held-out mask as `s={3.55}` for a linear `Gamma_eff(s)` closure; complete `x/D=10` profiles and the Stage-2 common-exterior norm are predicted without retuning. D20 aggregate scan points `s={3.4,3.5,3.6,3.8}` and D30 points `s={3.45,3.55,3.65}` are frozen only for the independent optimum-side performance test: the held-out center must be no worse than the neighboring values, and at least one point on each sufficiently separated side must degrade. Aggregate errors cannot determine `Gamma_eff`, profile shape, contour circulation, full-exterior error, or the action-to-geometric-circulation sign. + +**13.7 — Scope omissions frozen before implementation [modeling assumption].** Robust stagnation/separatrix/virtual-body diagnostics are omitted because the existing files have no continuation, root-completeness, or separatrix-closure machinery; isolated grid/root guesses would be fragile. Potential pressure and individual/total force are omitted because Bernoulli/Blasius force is not needed to answer the sole dipole/profile hypothesis and DNS pressure/force fields are absent. These omissions bound topology and force claims to “not tested.” The minimum implemented metrics are therefore dominant log/dipole coefficients, analytic smooth-profile sensitivity, converged one-sided `E_inf` slopes, parity, gap flux, complete profile errors, common-exterior capability, and held-out DNS/performance evidence when its contract is met. + +**13.8 — Frozen execution rule [modeling assumption].** Search narrowly for existing endpoint arrays first. If absent, aggregate summaries receive only their limited performance role; historical fitted `Gamma_eff=-4.293...` values are non-evidence until source arrays are recovered. No CFD is launched unless field-level evidence remains essential after the analytic/counterfactual result, and any run must be the smallest serial D20 train/held-out design with printed body/action/wall oracle and external `/tmp` output. Completion may be PASS, FAIL, or BOUNDED. + + +**13.9 — Historical Stage-4 review [numerical observation].** This pre-campaign review was BOUNDED because endpoint fields were then absent. It is superseded by §§16–18 and retained only as execution history: v4 now supplies direct fields and contour sign, while corrected descriptive WLS and the strip sign comparison reject the actual-actuation cancellation hypothesis. + + +## 14. Stage 5: frozen physical-value and stability hierarchy + +**14.1 — Sole question [modeling assumption].** For the fixed prescribed-circulation steady harmonic outer solution used by the sole rear-opposite mechanism, which precisely defined notions of well-posedness, numerical stability, structural persistence, and dynamical stability are supported? Passing requires the Stage-1 fixed-period uniqueness result, Stage-2 convergence/conditioning evidence, and a reproducible sampled audit showing nondegenerate interior stagnation roots persist under the frozen small parameter perturbations. A missed/failed root, count change, small Jacobian singular value, uncontrolled discretization drift, or absent evolution law limits the claim. No Euler or Navier–Stokes eigenanalysis is introduced. + +**14.2 — Four noninterchangeable levels [modeling assumption].** (i) *Mathematical BVP well-posedness* means existence, uniqueness, and continuous dependence in stated spaces; Stage 1 supplies only conditional fixed-circulation uniqueness. (ii) *Numerical stability* means conditioning plus convergence under representation parameters; Stage 2's convergence and independently discretized agreement are scientific evidence, while measured singular values and conditions are reported diagnostics with broad fail-fast regression guards. (iii) *Structural stability* here means only local persistence of sampled interior stagnation roots. (iv) *Dynamical stability* requires a state, evolution operator, equilibrium, and perturbation class. The present model prescribes no such dynamics, so decay, spectral, Hamiltonian, Euler-vorticity, and Navier–Stokes stability are undefined rather than positive. + +**14.3 — Discrete continuous dependence [proved mathematical result].** For a fixed nondegenerate discrete MFS matrix `A(mu)`, source coefficients satisfy `A(mu)q(mu)=b(mu)`. Continuity of `A,b` and `sigma_min(A(mu_0))>0` imply locally continuous `q(mu)=A(mu)^+b(mu)`, and affine dependence on prescribed circulation is exact at fixed geometry. This is discrete continuous dependence, not a complete PDE existence or shape-differentiability theorem. + +**14.4 — Interior stagnation definition and Jacobian [proved mathematical result].** For parameters `mu` (circulation, geometry, or a separately valid confinement representation), an interior stagnation point is `x_*` in the open fluid domain with + +`F(x_*,mu)=u(x_*;mu)=0`, `r=||F(x_*,mu)||_2`. + +The velocity Jacobian is `J=D_x F`, approximated by centered differences + +`J[:,k]=[F(x+h e_k,mu)-F(x-h e_k,mu)]/(2h)`. + +Record `det J` and singular values `sigma_max>=sigma_min>=0`. If `F` is continuously differentiable and `det J(x_*,mu_*) != 0` (equivalently `sigma_min>0`), the implicit-function theorem gives a unique local root branch `x(mu)` and + +`dx/dmu = -J^(-1) partial_mu F`. + +This proves local root persistence only. It does not prove global root completeness, separatrix equivalence, or absence of bifurcations elsewhere. Near `det J=0`, Brøns & Hartnack (1999) is the primary topology precedent for local streamline bifurcations near degenerate interior critical points; no equation number is imported. + +**14.5 — Frozen sampled-root audit [modeling assumption].** The canonical unbounded geometry is centers `(0,0),(1.3,+0.75),(1.3,-0.75)`, radius `a=0.5`, `U=1`, `n_boundary=64`, source ratio `0.65`, and Stage-3 `Gamma_*=4.818148415799425` in `(0,+Gamma,-Gamma)`. Search only the compact rectangle `[-2,5] x [-2.5,2.5]` from a `29 x 25` seed grid. Accept roots only at least `0.08D` outside every body (`distance >= a+0.08`), with residual `<=1e-9`; use centered-Jacobian step `h=2e-5`, deduplicate within `2e-5D`, and classify as nondegenerate only when `sigma_min>=1e-4`. Because a finite seed grid cannot establish completeness, every result is called a **sampled root audit**, never a proof of global topology. Boundary stagnation points are excluded: they require boundary coordinates and a separate boundary-critical-point theory. + +**14.6 — Frozen perturbations and continuation [modeling assumption].** Track baseline sampled roots by one-to-one nearest continuation, flagging unmatched roots, count changes, displacement above `0.20D`, residual failure, or `sigma_min<1e-4`. The preregistered unbounded perturbations are `Gamma/Gamma_* in {0.98,1.02}` and rear-center changes `(delta x_r,delta b) in {(-0.02,0),(+0.02,0),(0,-0.02),(0,+0.02)}`, applied symmetrically as rear centers `(1.3+delta x_r,+/-(0.75+delta b))`. Strip `H` and image-layer perturbations are excluded: Stage 3 established that the plane Laurent mechanism does not transfer to strip asymptotics, and no converged strip `Gamma_*` or structural charter is defined. This is an explicit scope limit, not evidence of confinement persistence. + +**14.7 — Analytic failure controls [proved mathematical result].** For the exact one-cylinder field with `Gamma=0`, the two stagnation points lie on the body boundary. The affine field `F(x,y)=(x,0)` has a singular Jacobian and a continuum of roots, while `F(x,y)=(x,y)` has one nondegenerate root. + +**14.8 — Required control behavior [modeling assumption].** The audit excludes the exact-circle boundary roots by its interior margin, classifies `F=(x,0)` as degenerate and `F=(x,y)` as nondegenerate, and returns no roots for a deliberately root-free constant field. These controls prevent an audit that always passes. + +**14.9 — Dynamical precedents and non-transfer [primary-literature-supported result].** Crowdy & Marshall (2005) derive Hamiltonian point-vortex motion around multiple circular islands; that problem evolves vortex position and is different from evaluating a prescribed harmonic velocity field. Classical Föppl and Protas's higher-order Föppl models evolve free point vortices or finite-area vortex moments and discuss stability of those equilibria; they do not establish stability of this fixed prescribed-circulation BVP. Passive-particle dynamics `dot x=u(x)` could define trajectory stability of a stagnation point, and Euler-vorticity or Navier–Stokes perturbations could define other stability problems, but none is introduced in Stage 5. + +**14.10 — Concentrated-review rule [modeling assumption].** Exactly one end-stage review must jointly check derivation/citations, sampled-root reproducibility and failure controls, claim limits, tests, no-CFD compliance, and file budget. The final verdict may be PASS, BOUNDED, or FAIL. Uniqueness, numerical convergence, and structural persistence must never be relabeled as perturbation decay or global hydrodynamic stability. + + +**14.11 — Concentrated Stage-5 review [numerical observation].** Derivation/citation review: PASS; §§14.1–14.7 separate the four levels, derive the root/Jacobian/implicit-function definitions, and scope Brøns–Hartnack, Crowdy–Marshall, and Föppl/Protas without invented equation numbers. Reproducibility/failure-control review: PASS; exact affine roots verify residual and centered Jacobians, a shifted affine root verifies nearest continuation, and singular, constant, and exact-circle boundary cases do not pass as nondegenerate interior persistence. Canonical sampled-root review: BOUNDED; the frozen `29 x 25` audit finds no admissible interior root at `Gamma_*`, `0.98/1.02 Gamma_*`, or the four rear-geometry perturbations. Thus there is no interior root branch to qualify; unchanged sampled count zero is evidence only on the frozen seeds/rectangle, not a global topology theorem. Numerical review: PASS for the tested convergence evidence; as a regression snapshot, at `n=64` the canonical matrix has `sigma_min=2.11372e-5`, condition `6.98404e5` independent of `Gamma`, and the `+/-2%` fields obey affine midpoint continuity to the test tolerance. Claim review: PASS with limitation; conditional uniqueness, numerical convergence, and the absence of sampled interior degeneracy are physically useful outer-reference properties, but dynamic stability is undefined and confinement persistence is untested. No-CFD/file review: PASS; no CFD was run and no file was added. Stage-5 verdict: **BOUNDED**—the hierarchy is rigorous and the sampled audit is numerically controlled, but it supplies no positive interior-root persistence branch and no dynamical-stability result. + + +## 15. Historical Stage-6 evidence-freeze charter + +**15.1 — Sole question [modeling assumption].** Does the accumulated evidence support one bounded mechanism claim: prescribed rear-opposite circulation is the unique tested direction that cancels the leading unbounded potential-flow dipole and reduces the declared downstream disturbance, while its causal mapping to the finite-Re rotating-cylinder flow remains unvalidated? Stage 6 introduces no science, metric, simulation, or fit. + +**15.2 — Pass evidence [modeling assumption].** The evidence package passes only if the numbered derivation and four-category statement audit are internally consistent; the source-to-equation ledger retains every bibliographic hold; Stage 2 and Stage 3 theoretical assertions are regenerated by `pinball_math`; Stage 4 is resolved as a split result: endpoint fields and contour sign now exist; geometric sign is PASS, affine WLS closure is BOUNDED, and the actual-actuation favorable-cancellation hypothesis FAILS; Stage 5 remains BOUNDED and dynamical stability remains undefined; aggregate CFD performance is retained only with provenance and explicit scalar-only limitations; the authority/reproduction order is unambiguous; and root/total file counts remain within `10/30` excluding generated bytecode. + +**15.3 — Claim-limiting evidence [modeling assumption].** Any mixed statement label, unsupported citation or equation mapping, missing reproduction command, claim based on absent arrays, inferred equality between wall action and geometric circulation, promotion of aggregate errors to field evidence, stability claim without an evolution law, unresolved cross-stage contradiction, failed test/compile/lint check, or file-budget breach prevents a Stage-6 package PASS until repaired or explicitly bounded. + +**15.4 — Concentrated-review rule [modeling assumption].** Exactly one final review jointly audits derivation, citations, reproducibility, counterexamples and held-out limits, claim matrix, environment guidance, public API, scoped diff, and file budget. Scientific stages may remain BOUNDED even if the evidence package passes, provided every boundary is explicit and no missing evidence is silently promoted. + + +**15.5 — Concentrated Stage-6 review record [numerical observation].** The evidence-package governance verdict is **PASS** after the v4 reconciliation: endpoint contour sign is PASS, corrected WLS and strip representation are BOUNDED, the actual-actuation favorable-cancellation hypothesis is FAIL, and Stage 5 remains BOUNDED with dynamical stability undefined. The package makes no causal WLS, full-PPO, or no-slip-channel claim. + + +## 16. Finite-Re endpoint bridge and strip charter + +**16.1 — Endpoint evidence contract [modeling assumption].** The only production endpoint set is canonical D20 `q_in` plus accepted numeric wall branch `[0,+Omega,-Omega]` at `s={3.45,3.55,3.65}` under one frozen configuration; `s=3.45,3.65` are training endpoints and `s=3.55` is held out. `q_blk` is nonranking, and diagnostics are separate artifacts. Schema v3 preserves raw uint16 solver flags and defines fluid cells exactly by Celeris `FLUID=0x0001`; `body_id=-1` means solver fluid, `-2` means static solver-nonfluid wall/inlet/outlet, and controlled circle interiors receive registry IDs `0,1,2` in semantic order `(front,rear_y_plus,rear_y_minus)`. The body-config loader ignores a JSON `id` key and allocates those IDs by insertion order. Geometry may label a body only where the solver says nonfluid, and every controlled ID must be nonempty. Every artifact also preserves coordinates, `(y,x)` axes, masks, centers, signed action and wall oracle, complete configurations, source/environment identity and hashes, final lattice and advective times, settling windows, finite/shape validation, and no-clobber hashes. Publication is from a validated temporary sibling by an atomic no-replace rename where supported, so a failed write is not an endpoint artifact. Production endpoints are prospectively frozen at final `tU/D=250`, sampling interval `2 D/U`, and two adjacent 10-sample windows. For each window, average `[E_inf_vector,E_L2_vector]`; define settling change as the Euclidean RMS across the two componentwise mean differences and require a finite value `<=1e-4`. Equality passes. A short diagnostic with fewer than 20 samples records JSON `null`, `computed=false`, `qualified=false`, and `reason=insufficient_samples`. The `1e-4` threshold is below 0.5% of the historical low-error magnitude near `0.023` and above historical scalar tail ranges up to approximately `4.6e-5`; those preexisting values informed prospective resolution design but do not prove that any new endpoint qualifies. This is an evidence schema, not physical evidence. + +**16.2 — Geometric contour sign [proved mathematical result].** Parameterize every contour explicitly counterclockwise by `r(theta)=c+R(cos theta,sin theta)`, `0<=theta<2pi`, with tangent `t=(-sin theta,cos theta)`. Then `Gamma_CCW=integral u(r(theta)) dot t R dtheta`; a positive point vortex gives positive `Gamma_CCW`. Bilinear interpolation is admissible only when all four stencil cells are finite fluid cells. Multiple radii must agree in sign before the numeric wall branch is named by geometric circulation. + +**16.3 — Preregistered outer WLS [modeling assumption].** On one frozen common-fluid mask separated from bodies and strip walls, fit the endpoint difference `d=u_ctl-u_in` to the strip rear-opposite unit field `v` with fixed nonnegative quadrature weights: `Gamma_eff=sum w d dot v/sum w |v|^2`. Report mask, weights, denominator and weighted vector residual. The fit has no intercept because `d=0` at zero model amplitude by construction; contour and WLS signs must agree. + +**16.4 — Two-point closure [proved mathematical result].** Two distinct training pairs `(s_-,Gamma_-)`, `(s_+,Gamma_+)` determine exactly `Gamma_eff(s)=a+b s`, with `b=(Gamma_+-Gamma_-)/(s_+-s_-)` and `a=Gamma_--b s_-`. The value at `s=3.55`, its complete `x/D=10` two-component profile, and frozen common-exterior field are predictions with no retuning. No odd symmetry is imposed. + +**16.5 — Exact free-slip strip modes [proved mathematical result].** Downstream of all bodies, an irrotational disturbance has potential `phi`; `Delta phi=0`, wall impermeability gives `partial_y phi=0` at `y=+-H`, and fixed through-flow removes any varying zero mode. The normalized Neumann potential basis is `cos(k_n(y+H))`, `k_n=n pi/(2H)`, whose squared integral is `H` for `n>=1`. A downstream-decaying potential `phi_n=-(A_n/k_n) exp[-k_n(x-x0)] cos[k_n(y+H)]` gives `u'_x=A_n exp[-k_n dx] cos[k_n(y+H)]` and `u'_y=A_n exp[-k_n dx] sin[k_n(y+H)]`. Thus longitudinal cosine and transverse sine coefficients are equal at a station and both propagate by `exp(-k_n dx)`. Under midline reflection, odd `n` potential modes are antisymmetric and even `n` modes symmetric; velocity parity follows by differentiating. + +**16.6 — Strip numerical representation [modeling assumption].** `strip_basis_affine` constructs `rear_opposite`, `common_rear`, and `front_only` equal-norm affine fields with finite MFS image layers. Modal station projection and exponential propagation, image-layer differences, station stability, and ablation determine the bounded strip claim. Unbounded `far_field_coefficients` are prohibited for strip asymptotics; decreasing wall residual alone is insufficient. + +**16.7 — No-slip-channel PDE contract [modeling assumption].** The independent future problem is steady incompressible Navier–Stokes at `Re_D=50`, with fully developed no-body `q_in`, stationary no-slip walls, rotating-cylinder full no-slip, and direct profiles against that same `q_in`. Its optimum `s` is not inherited from uniform/free-slip flow. Method priority is direct steady/mean continuation and convergence, then viscous gap momentum/boundary-layer/separation/base-bleeding analysis, then mean-linearized or resolvent modes after a qualified base. A future PASS requires settled profile improvement plus held-out or perturbation mechanism support; FAIL is nonimprovement/nonconvergence or wrong mechanism sign/shape; BOUNDED is performance without mechanism/robustness. No no-slip run/eigenanalysis is performed here. + +**16.8 — Asymptotic limit [primary-literature-supported result].** Watson's Stokes–Oseen rotating-cylinder construction concerns `Re<<1`; it does not asymptotically control `Re_D=50`. Attached boundary-layer closures likewise lack a controlled parameter in a separated moderate-Re three-body channel. These methods are limiting references, not the current no-slip model. + +**16.9 — Stage-3 field-analysis preregistration [modeling assumption].** Before reading endpoint field values, freeze normalized coordinates about the front center, velocity by `U`, and differences `delta q=q_ctl-q_in`. Primary `E_inf_vector` is the maximum pointwise norm over the complete common solver-fluid `x/D=10` cross-section after excluding the two outermost lattice rows; `x/D={2,4,6}` are diagnostics. Rear-body CCW contours use radii `r/D={0.60,0.65,0.70}` for both bodies: each exceeds `R/D=0.5` by at least two D20 lattice cells, paired `0.70D` contours do not intersect because rear centers are `1.5D` apart, and they remain separated from the front body. Every bilinear stencil must be fluid in both endpoint and q-in. Radius variation is reported as viscous enclosed-vorticity evidence, not required to form a mathematical plateau or identified with a topological potential period. + +**16.10 — Stage-3 strip-WLS preregistration [modeling assumption].** Fit dimensionless `delta q` with uniform weights on the common solver-fluid tensor subset `x/D in [-2,10]`, `|y/D|<=6`, sampled every second D20 lattice cell (`Delta x/D=Delta y/D=0.1`), excluding distance `<0.75D=1.5R` from every body. This domain is already at least `9D` from the free-slip walls, so no additional active wall clipping occurs; record the `1D` wall-margin rule. The model is `strip_basis_affine` at normalized centers `[(0,0),(1.3,0.75),(1.3,-0.75)]`, `R=0.5`, `H=15`, `U=1`, rear-opposite unit-L2 basis `(0,+1/sqrt(2),-1/sqrt(2))`, `n_boundary=32`, source ratio `0.65`, and 40 image layers. The fitted scalar `g` converts to each rear geometric circulation as `Gamma_upper/(UD)=g/sqrt(2)` and `Gamma_lower/(UD)=-g/sqrt(2)`. Only `s={3.45,3.65}` train `g(s)=a+bs`; `s=3.55` is held out. Report held-out scalar error, full-profile vector residual, common-domain weighted RMS/relative RMS, and residual reflection-parity defect. No material-usefulness threshold was preregistered, so predictive usefulness receives no numerical PASS threshold after observing data. The sign gate passes only if upper/lower contours are respectively positive/negative at every valid frozen radius and the WLS per-rear sign agrees; opposite signs fail, while missing/strongly inconsistent magnitudes bound the claim. + +**16.11 — Scientific status [numerical observation].** The v4 immutable endpoint analysis validates contour sampling, corrected blockage-subtracted WLS, two-point held-out arithmetic, and direct profiles. The geometric contour sign is a PASS field observation; WLS interpolation and full-field prediction remain BOUNDED. WLS is descriptive projection, not a causal action-to-circulation map. + +**16.12 — Stage-3 endpoint verdict [numerical observation].** The immutable v4 analysis passes the contour geometric sign gate: accepted numeric `[0,+Omega,-Omega]` produces upper negative/lower positive geometric circulation. Corrected WLS gives `g={-12.02563,-12.20055,-12.37465}`; scalar held-out error is `4.17e-4`, while common-field relative residual is `0.117943` and profile residual remains nonzero, so affine closure is BOUNDED. The projected WLS amplitude is descriptive and cannot be called causal effective circulation. + +## 17. Stage-4 free-slip strip modal qualification charter + +**17.1 — Modal sign convention [proved mathematical result].** For `phi_n=B_n exp[-k_n(x-x0)] cos[k_n(y+H)]`, direct differentiation gives `u_x=-k_n B_n exp[-k_n dx] cos[k_n(y+H)]` and `u_y=-k_n B_n exp[-k_n dx] sin[k_n(y+H)]`. Defining velocity amplitude `A_n=-k_n B_n` therefore gives equal signed cosine/sine coefficients. `strip_mode_field` accepts `A_n`; `strip_modal_projection` independently recovers the `u_x` cosine and `u_y` sine coefficients. No sign is inserted to improve agreement. + +**17.2 — Frozen modal audit [modeling assumption].** Use canonical normalized geometry, `H/D=15`, `U=1`, `R/D=0.5`, `n_boundary=32`, source ratio `0.65`, image layers `{20,40,80}`, stations `x/D={4,6,8,10}`, a 3001-point full-wall-to-wall `y` grid, and modes `n=1,...,12`. All bodies lie upstream because the rears end at `x/D=1.8`. Since `k_1=pi/30`, the slowest mode decays only by `exp(-pi Delta x/30)`. For base disturbance `u_0-Ue_x` and each unit-L2 affine direction, report zero mode, independently projected `u_x/u_y` coefficient disagreement, and station-collapse values obtained by multiplying station coefficients by `exp[k_n(x-4)]`. Modes whose reference vector amplitude exceeds `1e-8` times the largest reference mode are significant; no post-observation coefficient threshold is introduced. + +**17.3 — Frozen objective and ablation [modeling assumption].** Before computing Stage 4, freeze the complete smooth full-height profile objective at `x/D=10`, `J(g)=[mean_y |u_0+g v_b-Ue_x|^2]^(1/2)`, on the same 3001-point grid. For each unchanged equal-L2 basis `rear_opposite`, `common_rear`, and `front_only`, use the analytic real optimum from the affine quadratic and report `J(0)`, `g_opt`, `J_opt`, complete-profile `E_inf_vector`, and leading modal coefficients. Rear-opposite is uniquely favorable only if its `J_opt` is strictly below both counterfactual values at every image layer. A held amplitude `g=0.5 g_opt` must equal direct affine reconstruction to roundoff; this checks exact discrete linearity, not independent PDE validity. + +**17.4 — Convergence and verdict [modeling assumption].** Compare projected coefficients and `g_opt` at 20/40/80 image layers; decreasing differences are evidence of bounded finite-image consistency, while the previously observed approximate `0.5` image-tail ratio prohibits claiming a certified infinite-image error bound. The confinement cancellation mechanism PASSes only if rear-opposite is uniquely favorable, modal relations and station propagation are qualitatively consistent, and theoretical `g_opt` has the same sign as the actual finite-Re WLS `g<0`. Opposite theoretical/actual signs FAIL the proposed cancellation link without redefining the basis. Otherwise unresolved image/modal behavior yields BOUNDED. No-slip remains outside this stage. + +**17.5 — Stage-4 observed audit [numerical observation].** The modal sign audit confirms the `A_n=-k_nB_n` convention: synthetic projected mode tests recover equal signed components. At `H/D=15`, `k_1=0.1047198`. For the canonical zero-circulation base, the through-flow mode is approximately `-2.09e-5` at stations `4,6,8,10`; rear-opposite/common-rear/front-only direction zero modes are approximately `+3.07e-6/-9.26e-5/-6.55e-5`. At layer 40, significant symmetry-allowed even rear-opposite modes satisfy the independent ux/uy projection and station-collapse audit; the prior order-one comparison came from negligible forbidden odd `n=1` coefficients and is withdrawn. + +**17.6 — Stage-4 qualification verdict [numerical observation].** Rear-opposite is uniquely favorable under the frozen full-profile smooth RMS objective at layers 20/40/80: `J_opt` is approximately `1.47136e-4/1.47095e-4/1.47085e-4`, versus about `5.26245e-3/5.26244e-3/5.26247e-3` for both counterfactuals. Its optimal theoretical amplitude is `g_opt=+6.14794` at layer 40. The omitted-base v1 value `g=-14.63058` is withdrawn; corrected v4 WLS gives `g=-12.20055`, still opposite in sign. Exact held-amplitude affine reconstruction errors are below `9e-15`, which validates discrete linearity only. Image-layer changes in `g_opt` shrink from `1.20e-5` to `2.28e-7`, but the prior approximate image-tail ratio still prevents an infinite-image certification. Because the favorable theoretical sign opposes the measured finite-Re sign, the actual-actuation-as-favorable-strip-cancellation hypothesis is **FAIL** under the frozen Stage-4 charter; the bounded finite-image numerical observations and finite-Re WLS sign result remain separately reported. + +## 18. Critical Stage-3/4 correction + +**18.1 — Correct finite-Re comparison [proved mathematical result].** If `u_0` is the zero-circulation three-body strip field and `v=u_1-u_0` is the unchanged unit-L2 circulation direction, then the theoretical controlled disturbance relative to uniform no-body inflow is `(u_0-Ue_x)+g v`. Because the CFD reference `q_in` has no bodies, fitting `q_ctl-q_in` directly to `g v` omits blockage and biases `g`. The corrected WLS fits `[q_ctl-q_in-(u_0-Ue_x)]` to `v`, and held-out prediction is `(u_0-Ue_x)+g_pred v`. Contour circulation is unaffected. + +**18.2 — Symmetry correction [proved mathematical result].** Reflection-symmetric polar velocity has `u_x` even and `u_y` odd. In the shifted strip basis, even `n` gives `cos[n pi(y+H)/(2H)]` even about `y=0` and `sin[...]` odd; odd `n` occupies the opposite parity sector. Therefore rear-opposite and the symmetric base must be audited on significant even modes, beginning with `n=2`; the prior order-one relative error of negligible forbidden `n=1` is methodologically invalid and withdrawn. Common-rear/front-only are not required to share that sector. + +**18.3 — Corrected modal audit [modeling assumption].** Use stations `x/D={4,6,8,10,12,14,16}`; all are downstream of physical singularities at `x<=1.3`, while transverse images share those x coordinates. For each station and mode report raw coefficients and absolute disagreement. A coefficient is significant only when its vector amplitude exceeds `max(1e-8` times the dominant station coefficient, `1e-12)`; relative diagnostics below that floor are forbidden. For rear-opposite/base conclusions use significant even modes. Exact propagation is an infinite-strip property; finite image truncation and trapezoidal endpoint quadrature can leave absolute residuals, which must decrease or remain resolution-bounded with image layers. + +**18.4 — Corrected results [numerical observation].** At layer 40, rear-opposite `n=2` coefficients are `(-2.84940170e-3,-2.84940177e-3)` at `x/D=4`, `(-8.10966882e-4,-8.10967014e-4)` at 10, and `(-2.30808880e-4,-2.30809072e-4)` at 16. Absolute ux/uy disagreements are `7.28e-11`, `1.32e-10`, and `1.92e-10`; collapsed n=2 relative spreads are below `3.1e-7`. Thus the prior modal-propagation failure is withdrawn: significant symmetry-allowed rear-opposite modes pass the finite-image modal audit to the reported numerical resolution. + +**18.5 — Corrected qualification [numerical observation].** Corrected Stage-3 WLS gives `g={-12.02563,-12.20055,-12.37465}` with cosine similarities `{-0.99078,-0.98924,-0.98755}` after subtracting theoretical blockage. Held-out common-field relative residual improves from `0.292` to `0.11794`, while scalar interpolation error remains `4.17e-4`. The negative coefficient is a descriptive projection and is strongly anti-correlated with the unchanged positive unit direction. The favorable theoretical total-field optimum remains `g_opt=+6.14794`; conventions and strip implementation are identical. The earlier modal reason for FAIL is withdrawn; the sign contradiction alone rejects the proposed actual-actuation cancellation mechanism. The confinement mechanism remains **FAIL** specifically because measured finite-Re control drives the opposite potential direction; finite-image modal representation is BOUNDED and numerically consistent, and Stage-3 closure remains BOUNDED. + +## 19. Finite free-vortex feasibility model + +**19.1 — Scope and state [modeling assumption].** In the unbounded plane only, let the fixed three-cylinder base solution `u_base` be the existing MFS field with its prescribed geometric-CCW body circulations `Gamma_j`. Add a finite set of free point vortices at exterior positions `X_i` with fixed geometric-CCW strengths `kappa_i`. This first feasibility model excludes free-slip walls, vortex shedding or production, viscosity and diffusion, finite vortex cores, and Mow's global dispersion relation; it is an instantaneous inviscid transport model, not a Karman-street generation or stability theory. + +**19.2 — Instantaneous impermeability response [proved mathematical result].** The physical incident velocity of the free vortices is + +`u_free(x;X,kappa)=sum_i kappa_i K(x-X_i)`, `K(dx,dy)=(-dy,dx)/(2 pi (dx^2+dy^2))`, + +with the same positive-CCW sign as `singular_velocity(..., vortex=True)`. Because `u_free dot n` is generally nonzero on a cylinder, static superposition with `u_base` violates impermeability. At every vortex configuration solve a zero-period MFS Neumann response `u_resp`: its source strengths have zero sum on each body, its far field decays, it contains no body-vortex terms, and its boundary data satisfy `u_resp dot n=-u_free dot n`. Therefore `(u_base+u_free+u_resp) dot n=0` up to MFS discretization error, while the prescribed base body circulations remain unchanged. + +**19.3 — Finite-vortex ODE [proved mathematical result].** Omitting only the singular physical self term, each vortex is transported by the regular velocity + +`dX_i/dt = u_base(X_i) + sum_(m != i) kappa_m K(X_i-X_m) + u_resp(X_i;X,kappa)`. + +The response is generated by the complete incident set and is retained at `X_i`; in particular, a vortex moves under its own body-induced regular image/response field. Mutual induction retains the geometric-CCW signs above. Exterior, distinct positions are required so neither body collision nor vortex-vortex collision reaches a singular state. + +**19.4 — Hamiltonian status [modeling assumption].** Exact point-vortex motion around fixed bodies can be written using the domain Green function/Kirchhoff--Routh Hamiltonian, including its regular Robin part. The present collocated, zero-period MFS response is only a noncanonical numerical Hamiltonian approximation: it is not asserted to be an exact discrete Hamiltonian system, and MFS truncation and least-squares error may cause Hamiltonian drift. This model therefore tests instantaneous kinematic feasibility, not long-time conservative fidelity. + +**19.5 — Transmission observables [modeling assumption].** For a prescribed incoming finite staggered train, transparent passage can be assessed by matching vortices upstream and downstream and reporting nondimensional position/phase displacement, transverse displacement, spacing distortion, and velocity/strength preservation, together with minimum body clearance and accumulated impermeability error. These are conceptual diagnostics for later trajectory integrations; no acceptance threshold, campaign, or claim that the train passes unchanged is introduced here. + +**19.6 — Numerical qualification [numerical observation].** Qualification is limited to dense shifted-angle impermeability, zero bodywise source monopoles/no added body circulation, far-field decay of the response, correct no-body mutual induction, singular-self exclusion, finite RHS values, and fail-fast invalid/collision controls. Passing those checks establishes a narrow CPU feasibility prototype only. + + + +## 20. Stage 0: primary-paper equation maps and exact CPU oracles + +**20.1 — Vasconcelos--Moura--Schakel map [primary-literature-supported result].** Vasconcelos et al. (2012), DOI `10.1063/1.3667269`, nondimensionalize lengths by cylinder radius `a`, velocities by `U`, time by `a/U`, and define the upper wake vortex strength by `kappa=-Gamma/(2 pi U a)>0`; the upper vortex is therefore clockwise in this paper's convention and the lower one is its opposite-sign reflection. On the symmetric invariant subspace, their (7)--(8) give `H=y(1-1/r^2)-(kappa/2)log[y(r^2-1)/sqrt((r^2-1)^2+4y^2)]`, `xdot=H_y`, `ydot=-H_x`. Their Föppl equations (9)--(10) give `r0^2-1=2r0 y0` and `kappa=(r0^2+1)(r0^2-1)^2/r0^5`. At `r0=2`, the exact downstream point is `(sqrt(55)/4,3/4)` and `kappa=45/32`. Their critical level (26), `Hc=(kappa/2)[1-log(kappa/2)]`, belongs to the nilpotent saddle at infinity `(x,y)=(+/-infinity,kappa/2)`; it is **not** the finite Föppl equilibrium's Hamiltonian value. + +**20.2 — Kármán-street map [primary-literature-supported result].** Mowlavi, Arratia & Gallaire (2016), DOI `10.1017/jfm.2016.195`, use streamwise spacing `a`, row separation `h`, circulation magnitude `Gamma`, lengths scaled by `a`, and time `2 pi a^2/Gamma`. For the physical unconfined street (`n=0` in their confined array), lower vortices are `(ma,-h/2)` with `+Gamma` in the paper and upper vortices are `(ma+a/2,+h/2)` with `-Gamma`. With this project's geometric-CCW kernel, that paper assignment translates in negative x (consistent with the paper's negative unconfined values of `v0`). To expose the requested positive-advection baseline without hiding a sign change, `staggered_karman_train` reverses both rows: lower `-Gamma`, upper `+Gamma`. For this explicitly reversed convention the common positive x self-advection is `U_self=Gamma/(2a)tanh(pi h/a)`. The exact unconfined temporal-neutral aspect is `p0=h/a=asinh(1)/pi`. The finite constructor is only a symmetric truncation oracle; it converges algebraically to the infinite sum. The confined dispersion coefficients (2.7), dispersion relation (2.11), unconfined coefficients (4.4), and Briggs--Bers continuation are not implemented: no temporal growth curve or convective threshold is claimed. + +**20.3 — Green/Robin/Routh map [primary-literature-supported result].** Crowdy & Marshall (2005), DOI `10.1063/1.1900583`, formulate one-vortex motion around multiple circular islands through the domain Green function, its regular Robin self-part, and the Kirchhoff--Routh Hamiltonian, in the special case of zero circulation around every island. Any imposed irrotational background contributes its streamfunction term `H_B`; the vortex moves with the regular velocity after its singular self field is removed (Routh rule). `exact_circle_vortex_response` is the independently derivable one-circle reduction: a physical vortex is accompanied by its opposite image and a same-sign central vortex so the island circulation is zero, and both image terms contribute to regular self velocity. `MFSBodyResponse.response` is compared to this exact reduction; it is not promoted to Crowdy--Marshall's exact multiply connected prime-function formula. + +**20.4 — Routh/body coupling scope [primary-literature-supported result].** Streitlien's 1994 thesis record, DOI `10.1575/1912/5563`, treats incoming vortex streets interacting with a Joukowski foil using two-dimensional potential flow, complex-variable force/moment formulas, and nonlinear foil--vortex coupling. It supports retaining each incoming vortex's regular body-induced response and coupling the street to the body boundary; it does not make a prescribed finite train an equilibrium, prove transparent passage, or transfer foil force formulas to three fixed circles. + +**20.5 — Steady evidence map and sign non-equivalence [primary-literature-supported result].** Cornejo Maceda et al. (2021), DOI `10.1017/jfm.2021.301`, order controls `(front,bottom,top)` as `(b1,b2,b3)`, define positive command as counter-clockwise wall rotation, and call `b2=-b3<0` base bleed while `b2=-b3>0` is boat tailing/Coanda forcing. Chan et al. (2011), DOI `10.1017/jfm.2011.134`, define their side-by-side pair by figure 2's **doublet-like** and **reverse doublet-like** rotation drawings and associate the former at high speed with a virtual elliptical body; those names encode that paper's pair geometry and arrows, not this project's rear-pair labels. Rodrigues et al. (2026), DOI `10.1016/j.expthermflusci.2026.111798`, now has a **partially lifted** figure/sign map in `LITERATURE.md`: Eqs. (1)–(2) and Fig. 3 authorize wall-sense comparison, with project accepted `[0,+Omega,-Omega]` mapping to the literature **base-bleeding / gap-jet** family and literature **boat-tailing** mapping to project reverse. Quantitative Rod26 thresholds, forces, and `Re=9100` coordinates remain held. None of `base bleed`, `boat tailing`, `doublet-like`, `reverse doublet-like`, or this project's `rear_opposite` may be equated as identical mechanisms across different body orderings, Reynolds numbers, wall laws, or metrics; wall-sense family labels are comparative only. + +**20.6 — Stage-0 implementation boundary [modeling assumption].** Public CPU helpers are limited to the Vas Hamiltonian/RHS/equilibrium/critical level, one-circle exact zero-period response and Routh velocity, and finite/infinite Kármán baselines. Tests cover the exact Vas residual and critical-level distinction, finite-difference Hamiltonian gradient, short high-accuracy Hamiltonian conservation, exact-circle MFS response convergence, finite-window Kármán convergence, and the `sinh(pi p0)=1` identity. No CFD, wall images for the Kármán street, finite-train equilibrium, temporal growth oracle, convective threshold, multi-island prime function, or viscous branch transfer is implemented. + +## 21. Steady-contract mechanism comparison derivation + +1. **Frozen question and failure rule [modeling assumption].** Under one D20, uniform-inlet/free-slip, `Re_D=50` CFD setting, compare four preregistered branch outcomes: qualified no-body `q_in`, intentionally unsteady stationary pinball, qualified accepted `plus-minus` at `s=3.55`, and the historical reverse `minus-plus` stability candidate at `s=5.2`. The analyzer must fail if reverse `s=5.2` is absent or unqualified; in that event the stable-reverse claim is rejected. The settling threshold remains `1e-4`. + +2. **Role lock [modeling assumption].** Reverse production permits only `s={3.55,5.2}`. Reverse `s=3.55` is the same-amplitude negative control and is reported separately when present; it is not required to qualify and cannot support the stable-reverse claim. Reverse `s=5.2` is preregistered as the historical stability candidate because the earlier stable, high-deficit wrong-direction observation came from old `s=5.2` runs. Accepted production support remains `s={3.45,3.55,3.65}` and the frozen mechanism role is accepted `s=3.55`. + +3. **Comparison boundary [modeling assumption].** All roles retain exact shared grid, physics, boundary, runtime, sampling, settling, coordinate, and topology conventions; only the role parameter `s` may differ. Accepted `s=3.55` and reverse `s=5.2` are therefore not exact action reversals at equal amplitude. This comparison separates branch outcomes and is **not an equal-amplitude causal effect**. Source provenance is reported per role because the follow-up artifact is acquired after this preregistration, while exact CFD settings remain mandatory. + +4. **Output contract [modeling assumption].** The analyzer computes direct profile differences against `q_in` at `x/D={2,4,6,10}`, pairwise two-component field L2 on common-fluid masks, and controlled-case force-tail mean/std. If reverse `s=3.55` exists, the same descriptive outputs and its qualification/settling record are included under a separate negative-control report. No threshold relaxation, stability inference from an unqualified endpoint, or circulation/separation/causal mechanism metric is permitted. + + +## 22. Steady residual S2 charter + +**22.1 — Sole S2 question [modeling assumption].** Under the frozen D20, uniform-inlet/free-slip, `Re_D=50` geometry, can a common rear-opposite affine outer-potential description account for both the qualified accepted low-deficit endpoint at `s=3.55` and the qualified stable reverse high-deficit endpoint at `s=5.2`; and, after subtracting each endpoint's corrected total potential model (including zero-circulation blockage), which endpoint-feasible viscous residual observable distinguishes those outcomes? Fits are descriptive per endpoint because `s` differs; fitted amplitudes are not equal-intervention effects. A final endpoint cannot establish temporal causality. + +**22.2 — Frozen fields, signs, and outer fit [modeling assumption].** Normalize coordinates about the front center by `D` and velocity by `U_inf`. For accepted and stable reverse separately, fit `q_case-q_in=(q_0-U_inf e_x)+g(q_1-q_0)` by uniform-weight vector WLS on the Stage-3 strip mask `x/D in [-2,10]`, `|y/D|<=6`, every second D20 cell, common solver-fluid cells, distance `>=0.75D` from each cylinder, and at least `1D` from strip walls. The basis is the unchanged canonical strip rear-opposite unit-L2 circulation field with `H/D=15`, `R/D=0.5`, 32 boundary points, source ratio `0.65`, and 40 image layers. Report `g`, per-rear geometric circulation, cosine sign, weighted residual, and geometric-CCW contour circulation at `r/D={0.60,0.65,0.70}`. The residual total field is `q_nu=q_case-[q_in+(q_0-U_inf e_x)+g(q_1-q_0)]`. Opposite measured and favorable theoretical signs remain a contradiction; no canceled-circulation mechanism may be revived. + +**22.3 — Frozen residual regions and quadrature [modeling assumption].** Every area metric uses the common q-in/case solver-fluid mask and physical composite-trapezoid cell weights, with cylinder/nonfluid cells excluded exactly by that mask. Regions in front-centered coordinates are: `near_gap: -0.5<=x/D<1.8, |y/D|<=1.5`; `immediate_wake: 1.8<=x/D<4, |y/D|<=3`; `recovery: 4<=x/D<=10, |y/D|<=3`; and the observer line at the nearest `x/D=10` column with the two outermost rows excluded. Report explicit quadrature `L2=[integral |q_nu|^2 dA]^(1/2)` (never RMS), normalized `L2/[integral |q_case-q_in|^2 dA]^(1/2)`, retained area/line length, and observer-line `L2=[integral |q_nu|^2dy]^(1/2)` with the analogous normalization. Empty masks, nonfinite fields, or zero normalizers fail fast. + +**22.4 — Frozen viscous observables [modeling assumption].** Compute `omega_z=partial_x u_y-partial_y u_x` only where conservative centered differences have fluid neighbors on both sides; all other cells are invalid. Report endpoint-field gap fluxes across the shortest rear--rear, front--upper-rear, and front--lower-rear open segments, requiring every bilinear stencil to be common fluid. In `near_gap` and `immediate_wake`, report absolute-vorticity-weighted transverse centroid and width using physical area weights. Define recirculation by `u_x/U_inf<0` in the frozen symmetric window `1.8<=x/D<=10`, `|y/D|<=1.5`: report weighted area and streamwise extent from occupied columns (zero if absent). At nearest stations `x/D={2,4,6,10}`, report momentum-deficit proxy `integral max(0,1-u_x/U_inf)dy`, positive-deficit line measure, and signed deficit integral over common fluid rows after excluding the two outermost rows. Force observables are bodywise and total `Fx,Fy` means and population tail standard deviations over the final 10 samples; they are not pressure drag. + +**22.5 — Spatial-sequence and classification rule [modeling assumption].** Endpoint fields can support only ordered spatial coexistence/association. A mechanism-association PASS requires at least one preregistered observable to distinguish accepted from stable reverse in one direction at two or more of `x/D={2,4,6,10}`, with a nonzero strict difference at each station and no direction reversal across those stations; the reported candidate and all station values must be named. If no observable meets that criterion but all required data and metrics are valid, S2 is BOUNDED. A required-mask/model/qualification contradiction or an observable direction reversal falsely presented as consistent is FAIL. Reverse `s=3.55` is unsteady negative context only and cannot serve as a mechanism endpoint. + +**22.6 — Claim and literature limits [modeling assumption].** Rod26 (partial sign lift), Cornejo Maceda et al. (2021), and Chan et al. (2011) are qualitative literature frameworks for rotating-cylinder branches, gap transport, and wake organization. Wall-sense comparison may use the Stage-1 master map (accepted ↔ base-bleed family; boat-tail ↔ reverse), but Reynolds numbers, geometry, confinement, force thresholds, and drag optima do not transfer quantitatively to this D20 three-cylinder endpoint comparison. S2 may conclude spatial association, not temporal causality, pressure-drag decomposition, equal-amplitude intervention response, a literature proof that “boat-tailing explains the cloak,” or a universal circulation law. + +**22.7 — Immutable output and verdict contract [modeling assumption].** The analyzer writes a no-clobber external directory containing strict `analysis.json` and only essential NPZ arrays, records SHA-256 hashes of every endpoint payload and the analyzed source files, and records the exact reproduction command. Required controls are synthetic quadrature/regions, conservative masked vorticity, gap flux, recirculation, wake moments, sign/parity, empty/invalid mask failure, and runner no-clobber/role contract. The final verdict is exactly PASS, BOUNDED, or FAIL under §22.5. + + +## 23. K1 finite unbounded Kármán baseline qualification + +1. **Sole K1 question [modeling assumption].** Does the existing positive-advection, unbounded point-vortex Kármán street convention reproduce the infinite-street translation at the center and a short finite-horizon central propagation oracle under independent train-window and RK4-step refinement? This is a mathematical qualification baseline only. It is not CFD parameter identification: no trustworthy phase-resolved `q_in` extraction is available, so `a`, `h`, and `Gamma` are dimensionless Mowlavi-literature baseline quantities rather than fitted pinball values. + +2. **Signs, rows, stagger, and scaling [proved mathematical result].** Coordinates are x-right/y-up and positive circulation is geometric CCW, with kernel `K(dx,dy)=(-dy,dx)/(2 pi r^2)`. The implemented positive-x street reverses Mowlavi et al.'s physical signs explicitly: lower row `(m a,-h/2)` has `-Gamma`; upper row `((m+1/2)a,+h/2)` has `+Gamma`. Set `a=Gamma=1`, `p=h/a`, velocity scale `Gamma/(2 pi a)`, and time scale `2 pi a^2/Gamma`; the code uses the equivalent dimensional kernel and reports physical code time. The exact common speed is `U_self=Gamma/(2a)tanh(pi h/a)`, and the nominal aspect is `p0=asinh(1)/pi`. + +3. **Finite train and frozen observer [modeling assumption].** For half-window `M`, retain lower indices `m=-M,...,M` and upper indices `m=-M-1,...,M`, exactly as `staggered_karman_train`. Use `M={12,24,48}`. Freeze the observer by initial labels, not moving coordinates: both rows with initial `|x|<=2.5a`. End vortices remain in the ODE but never enter central acceptance metrics. The finite open train is not an equilibrium; only convergence of this fixed central observer as its separation from the ends grows may be claimed. + +4. **Evolution and collision scope [modeling assumption].** Integrate `dX_i/dt=sum_(j!=i) Gamma_j K(X_i-X_j)` by deterministic classical RK4 over `0<=t<=0.25 a^2/Gamma`, with fixed steps `dt={0.01,0.005,0.0025}` (the final step is shortened only to land exactly on the horizon). Reject nonfinite states or pair distance `<=1e-6 a`. No cylinders, pinball, walls, images, viscosity, shedding, CFD, GPU, or confinement are present. + +5. **Exact finite-plane Hamiltonian convention [proved mathematical result].** With fixed reference length exactly `a`, use +`H=-sum_(i24` to `24->48`, with the finest `<1e-2 a`; (iv) at `M=48`, successive time-step aligned differences decrease or both reach a `8 eps a` roundoff plateau, and the `0.005->0.0025` value is `<1e-7 a`; (v) finest normalized Hamiltonian drift is `<1e-8`, minimum pair distance remains `>0.2h`, and every metric is finite; and (vi) rerunning the complete analysis yields byte-identical canonical config/result payloads. Failure of any item makes K1 **FAIL** and stops the K lane. + +8. **Classification and K2 gate [modeling assumption].** Even when the mathematical core passes, overall K1 is **BOUNDED**, not PASS, because the attached plan requires at least a growth/impulse oracle while Mowlavi confined dispersion/growth and trustworthy phase-resolved extraction remain publication-held. The implemented perturbation observable is explicitly a finite-open-train sensitivity and cannot substitute for Mowlavi's periodic dispersion relation. Therefore K2 is **NO-GO** unless a later, separately frozen source-verified Mowlavi growth/impulse oracle is reproduced. No Mowlavi dispersion coefficient, temporal/convective stability, or confinement conclusion may be invented or inferred here. + +9. **Immutable output [modeling assumption].** The CPU runner publishes `/tmp/karman-baseline-20260806` atomically without replacement, containing strict canonical `config.json`, `result.json`, and `manifest.json` with SHA-256 hashes of both payloads and the four allowed edited source files. Arrays are omitted because all acceptance data are scalar or short metric records. Existing output is an error, never overwritten. + + +## 24. Inviscid→viscous theory boundary (Stage-1 continuous closure) + +This section continuously closes the Stage-1 inviscid contract against the finite-Re accepted branch. It does not reopen §§3–6 proofs, does not revive the canceled-blockage identification, and does not import Kármán/Föppl into the steady manuscript claim path. + +**24.1 — Impermeability and independent circulations [proved mathematical result; S2–S8].** Subject to §§3–6: the irrotational outer problem is a Neumann impermeability BVP whose body circulations are independent periods; centered circular rotation drops out of normal data (§4.2); the one-cylinder family shows wall rotation does not select `Gamma` under Euler slip (§5); and full rotating no-slip is generically overdetermined once periods are free only finitely (§6). Crowdy/Glass literature support for impermeable boundaries and independent perfect-fluid circulations remains as in §7 and S4/S9. Consequently any map from wall speed to outer circulation is a viscous-interface/empirical closure (S10), not an Euler boundary condition. + +**24.2 — Natural cancellation direction of prescribed `(0,+Gamma,-Gamma)` [proved mathematical result + numerical observation].** With body order `(front,rear_y_plus,rear_y_minus)`, the geometric-CCW rear-opposite assignment has zero net circulation, reflection-symmetric `(u_x` even, `u_y` odd) parity, and pair dipole coefficient `-Gamma b/pi` before body-source readjustment (§§12.3–12.6). Among the three equal-norm bases of §13.2, the strip smooth full-height profile objective uniquely favors that direction with theoretical optimum `g_opt=+6.147944` at 40 image layers (§§17.6, 18.5). That sign is therefore the natural *prescribed-circulation* cancellation direction for the outer potential problem; it is not a prediction that Navier–Stokes wall rotation must produce the same geometric periods. + +**24.3 — Accepted CFD effective sign contradiction [numerical observation; failed identification].** Accepted numeric wall action `[0,+Omega,-Omega]` at held-out `s=3.55` produces geometric contour circulation `(0,-,+)` and corrected descriptive WLS amplitude `g=-12.200554` on the same unit-L2 rear-opposite basis (§§16.12, 18.5). The theoretical favorable sign `g_opt=+6.147944` and the measured descriptive sign `g=-12.200554` therefore contradict under identical geometry, basis, and convention. The rear-opposite dipole algebra remains true; what fails is identifying prescribed potential-circulation cancellation as the accepted CFD mechanism. + +**24.4 — Mathematical entry of viscous wall vorticity, separation, and gap transport [primary-literature-supported result + modeling assumption].** Euler slip and Kelvin transport supply no wall-vorticity flux that can select `Gamma` from `Omega` (§§7.1–7.2). The viscous rotating-body problem instead imposes full no-slip and couples wall velocity to vorticity generation/diffusion (Ueda et al. 2003; §7.3). Restricted attached-layer closures (Glauert/Moore) do not control this moderate-Re, possibly separated three-body flow (§§7.4, 16.8). Therefore the continuum location where the Stage-1 outer contract ends—and where wall vorticity, separation/reattachment, and gap momentum transport must enter—is exactly the viscous no-slip interface and its near-wall/gap vorticity field, not the Neumann period problem. Downstream deficit then responds to that viscous near-field organization rather than to an a-priori prescribed outer `Gamma`. + +**24.5 — Sole surviving mechanism chain [modeling assumption / hypothesis].** After the sign contradiction, the sole modeling chain retained for the steady accepted/reverse comparison is the ordered spatial association already gated in §22: + +`wall rotation direction → gap / outer shear → recirculation / integrated force → downstream momentum deficit`. + +This is an endpoint coexistence hypothesis, not a proved evolution law. It does not assert equal-amplitude causality across different `s`, pressure-drag decomposition, or a universal `Gamma(Omega)` formula. + +**24.6 — Claim labels and falsification [modeling assumption].** Labels for this boundary: + +| Claim | Label | +|---|---| +| §§3–6 impermeability, independent periods, no-slip overdetermination | proved mathematical result | +| Crowdy/Glass/Ueda/Glauert interface distinction | primary-literature-supported result | +| `g_opt=+6.147944` vs accepted `g=-12.200554` and geometric `(0,-,+)` | numerical observation | +| Identification of prescribed `(0,+Gamma,-Gamma)` as the accepted CFD cancellation mechanism | failed/withdrawn | +| Chain wall → gap/shear → recirculation/force → downstream deficit | modeling assumption / hypothesis | +| Any `Gamma_eff(s)` as Euler wall law | modeling assumption (forbidden as proved) | + +Falsification or claim-limiting conditions: (i) a derived Euler rule selecting `Gamma` from centered `Omega` under the Stage-1 hypotheses; (ii) accepted geometric/WLS sign agreeing with `g_opt>0` under the frozen basis without redefinition; (iii) an equal-amplitude controlled intervention showing the residual chain reverses while the outer potential identification holds; (iv) promoting aggregate scalars or absent endpoint arrays to field mechanism evidence; (v) treating dynamical stability as proved for the static prescribed-circulation BVP (§14). + +**24.7 — Kármán/Föppl quarantine [modeling assumption].** Vasconcelos–Föppl oracles (§20.1), Kármán-street constructors/baselines (§§20.2, 23), and related free-vortex feasibility code (§19) remain available as mathematical CPU oracles only. They are **frozen quarantine** relative to the steady manuscript claim path: no Kármán phase, street transmission, Föppl equilibrium stability, or PPO-feedback conclusion is part of the Stage-1→S2 steady cloak identification. K1 FAIL / K2 NO-GO (§23) reinforces the pause; those results do not amend §§24.1–24.5. + + +## 25. Historical mechanism-completion charter (steady only) + +**25.1 — Sole scientific proposition [modeling assumption].** In the canonical uniform-inlet/free-slip `Re_D=50` pinball, accepted numeric rear-symmetric action `[0,+Omega,-Omega]` produces a qualified steady low-deficit state relative to uniform no-body `q_in` at `x/D=10`, whereas the potential-flow-favored opposite circulation direction corresponds to a stable high-deficit reverse branch rather than a cloak. The surviving explanatory hypothesis is viscous wall actuation that reorganizes gap transport and outer shear layers, then recirculation/force, then downstream deficit. Prescribed-circulation dipole cancellation is a proved outer-field property and a falsified CFD mechanism. + +**25.2 — Evidence governance [modeling assumption].** Physical payloads reside only under `/home/frank14f/optane/DynamisLab/steady_pinball_theory/` with top-level directories `authoritative/` and `archive/`. The package exposes exactly one entry, the symlink `evidence/`. `/tmp` is the sole scratch/discovery area. Promotion is atomic, no-clobber, one canonical result per scientific question, with `PROMOTION.json` hashes. Failed diagnostics are deleted unless uniquely valuable negative evidence. Kármán/Föppl implementations (§§19,23 and related APIs) are quarantine: they may remain for historical CPU tests but do not enter the steady manuscript claim path. CCD is excluded. + +**25.3 — Metric hierarchy [modeling assumption].** Primary cloak metric: full two-component `E_inf_vector(q_ctl,q_in)` at front-centered `x/D=10`. Secondary: explicit integral profile `L2`. Diagnostic only: stations `2,4,6`, field residuals, force tails, gap fluxes, vorticity widths, recirculation. `q_blk` never ranks. + +**25.4 — Inviscid→viscous entry point [proved mathematical result + numerical observation].** Impermeability and independent circulations are Euler data (§§3–6). The rear-opposite basis `(0,+Gamma,-Gamma)` has zero net circulation and an affine dipole (§12). Strip cancellation selects favorable `g_opt=+6.147944` [numerical observation]. Accepted CFD instead yields geometric `(0,-,+)` and descriptive `g=-12.200554` [numerical observation]. Therefore wall-speed → outer-circulation cancellation cannot be the measured cloak mechanism. Viscous no-slip generates wall vorticity, modifies separation and gap jets, and must enter before any finite-Re cloak claim (§§5–7,22,24). + +**25.5 — Surviving mechanism chain [modeling assumption].** Pre-registered ordered association only: +`wall direction → gap/outer shear → recirculation/force → downstream deficit`. +PASS requires at least one local, one near-wake, and one downstream discriminator coherent across stations without direction reversal. Temporal causality requires a separately frozen transient intervention. Incomplete control-volume ledgers must list unavailable pressure/viscous/torque terms and must not be called closed balances. + +**25.6 — Falsification [modeling assumption].** The viscous association fails if accepted and reverse are not distinguished by the pre-registered chain, if discriminators reverse across stations, if D20/D30 disagree beyond claim-tolerable uncertainty on the primary profile, or if a new equal-setting intervention shows local response after, not before, the observer-plane change. Cross-project SR/DRL salience remains contextual and cannot rescue a failed local mechanism. + +**25.7 — Mechanism-completion gate status [numerical observation; superseded].** Stage-2 credibility remains a numerical-observation **PASS** and Stage-3 remains a spatial-association **PASS** only; causality is **NOT_ESTABLISHED** and prescribed-circulation cancellation remains **FAIL**. The promoted semi-analytic artifact subsequently failed audit (§26.0), so no composite, validation, or manuscript-completion PASS survives. Section 27 supersedes the mechanism-completion path with an NS-first preregistration. + + +## 26. Withdrawn composite semi-analytic charter + +**26.0 — Audit disposition [failed/withdrawn].** This charter records a historical preregistration, not an active mechanism route. The promoted artifact double-subtracted the reference in its profile metric; its valid internal comparison is approximately `70.29%` improvement for `MFS0+Gamma` versus `70.51%` for the full fit. `q_VI` is independent of `omega`/branch, `q_wake` is inactive, and the speed/direction gates refit or read held-out CFD rather than independently predicting it. Every composite held-out PASS is withdrawn. The immutable artifact is bounded descriptive historical evidence at most and is non-authoritative for active claims. + +**26.1 — Historical target [modeling assumption; withdrawn].** Explain accepted numeric `[0,+Omega,-Omega]` (project base-bleed / gap-jet wall sense) with a low-dimensional composite model + +\[ +q_{SA}=q_{MFS,0}+q_{VI}+q_{gap}+q_{wake}, + +\] + +optionally compared against descriptive `q_{Gamma}` only. Pure prescribed `(0,+Gamma,-Gamma)` cancellation remains a **failed** outer counterexample (§§17–18, 24.3), not the measured mechanism or a stopping condition. + +**26.2 — Component contracts [modeling assumption].** +- `q_MFS,0`: zero-period `solve_mfs` strip field; impermeable geometric backbone only. +- `q_VI`: zero-net-per-body Neumann transpiration from moving-wall displacement proxy `v_n=d(U_e delta^*)/ds`; accepted/reverse signs enter through the wall oracle and branch, never through empirical circulation sign flips. +- `q_gap`: finite-gap Couette–Poiseuille / localized jet ansatz at `h/D=0.5`; reports `Q_g`, `J_g`, power scale; **not** a lubrication claim. +- `q_wake`: convected Gaussian deficit with parameters fit only from `x/D<=2`, wall, or gap regions; predicts `x/D={4,6,10}`. +- `q_Gamma`: descriptive `strip_basis_affine` rear-opposite circulation; optional baseline only. + +**26.3 — Historical fitting and held-out gates [modeling assumption; withdrawn].** These preregistered gates were not validly met and cannot support PASS. Three baselines: `MFS0`, `MFS0+Gamma`, full composite. Spatial held-out: fit near field only, score `x/D={4,6,10}` profiles and `E_inf_vector`. Speed held-out: train `s={3.45,3.65}`, predict `s=3.55`. Direction held-out: same equations on stable reverse `s=5.2` must yield higher deficit ranking and opposite gap-flux sign. **PASS** requires downstream ranking, gap sign, and significant held-out improvement over both potential baselines; else **BOUNDED** or **FAIL** by component. CFD fit alone is insufficient for mechanism claims. + +**26.4 — Historical literature method map [primary-literature-supported result + modeling assumption; withdrawn implementation].** Viscous–inviscid transpiration and displacement-thickness closures follow Fansler–Danberg / Celik–Patel / Yiu–Giles / Soares families; gap transport follows Dormy–Moffatt / Ueda / Watson / Umemura low-Re and finite-gap ansätze; wake replenishment follows Leal–Acrivos / Steiros / Freund–Mungal base-bleed motifs; branch topology follows Chan / Maceda / Rod26 qualitative maps (`LITERATURE.md` Stage-2 ledger). All asymptotic formulas are sign/scale templates at `Re_D=50`, `h/D=0.5`. + +**26.5 — Historical causality and minimal numerics [modeling assumption; withdrawn].** Reuse existing D20/D30 endpoints unless a missing quantity would change model selection. Equal-amplitude transients and V5 sanity run only if composite PASS still leaves direction causality ambiguous. Legacy steady-field ratios do not substitute for V5 sanity. + +**26.6 — Historical claim boundary [modeling assumption; withdrawn].** The never-achieved **PASS** would have meant: potential flow supplies the outer geometry; accepted wall actuation is represented by locatable viscous corrections that improve held-out profiles and preserve accepted/reverse ordering. It does **not** mean potential flow equals Navier–Stokes, nor that `Gamma_eff(s)` is causal. + +## 27. Historical NS-first execution charter + +**27.1 — Sole proposition [modeling assumption].** Determine whether accepted rear action `[0,+Omega,-Omega]` establishes a qualified stable low-deficit Navier–Stokes base flow through measurable actuator power, boundary-vorticity production, gap momentum, separation/base-pressure/recirculation reorganization, force and wake momentum-energy recovery, and stability. Potential flow remains an impermeability reference and failed mechanism counterexample; velocity-field fitting alone cannot pass. + +**27.2 — Four noninterchangeable roles [modeling assumption].** Freeze: (i) stationary; (ii) accepted `s=3.55`; (iii) equal-amplitude reverse `s=3.55`, which is an unsteady intervention/causal control; and (iv) stable reverse `s=5.2`, which is a different-amplitude steady topology control. No result from role (iv) may be represented as an equal-amplitude causal effect, and role (iii) need not qualify as a steady endpoint. + +**27.3 — Conservation and stability chain [modeling assumption].** The preregistered order is +`wall torque / actuator power → boundary vorticity + gap mass/momentum → separation, base pressure, recirculation → body force + wake momentum/mechanical-energy deficit → stability → x/D=10 E_inf_vector`. +Resolved station mass, momentum, kinetic/mechanical-energy fluxes, volume viscous dissipation, wall work, and control-volume residuals must retain physical quadrature and signs. Missing pressure, viscous, boundary, or torque terms force an explicit partial-ledger/BOUNDED status; no residual may be called closed without grid/control-volume convergence. Stability is separate: settling is not global stability; perturbation return is empirical evidence, while spectral claims require a qualified base state, perturbation class, and converged linear operator. + +**27.4 — Stage reflection and memory contract [modeling assumption].** Before each stage: read current Working Memory, perform targeted durable/thread recall when prior decisions matter, reread the governing plan, code contracts, and relevant Undermind source ledger, then preregister equations, dimensions, controls, PASS/BOUNDED/FAIL, and stopping rules here. After each stage: state what was answered, what remains absent, whether the result became a fit rather than a conservation/mechanism test, update `RESULTS.md`, `LITERATURE.md`, and `README.md`, and revise rather than duplicate durable memory. Code, reproducible CFD, immutable artifacts, and primary literature outrank memory summaries. + +**27.5 — Stage gates and chronology [modeling assumption + audited numerical status].** Stage 0 froze these gates before later acquisition. Torque endpoints, an NS diagnostic ledger, a same-parent switch, and pulse returns were subsequently run; therefore it is stale to call all NS work unimplemented. The 2026-08-08 audit nevertheless finds the gates unmet: fluxes and dissipation do not share a control volume, pressure was unavailable and represented as zero, the single deterministic switch uses heuristic gates, and the dimensionful return norm cannot identify a basin transition. Thus energy closure, causal mechanism, branch switching, nonlinear stability, held-out reduction, and global stability remain unestablished. + + +## 28. 2026-08-08 NS-first evidence boundary + +The Stage-1 source-only cut-link inference was falsified by the runtime manufactured oracle. Fluid-to-solid link traversal and the positive-drag force convention do not determine ownership of the public torque readback. Fresh `+omega`, `-omega`, and zero runs show same-sign `tau_read` and `omega`, odd parity defect `1.14e-5`, and zero/driven ratio `9.5e-6`; the project torque telemetry work convention is therefore `celeris_torque_channel_work_sign=actuator_on_fluid`. This does not establish Newton-pair ownership of the force channel: force and moving-wall torque readback semantics may differ, so force ownership remains unestablished. The runtime oracle overrides the earlier torque-work inference: +\[P_{act\to fluid}=\sum_{i=1}^3\Omega_i\tau_{i,read}^{act\to fluid},\qquad C_P=P_{act\to fluid}/(\tfrac12\rho_{ref} U_\infty^3D).\] +`read_force/read_torque(..., normalize=True)` means the cut-link lattice sum averaged once per accumulated LBM step. It performs no body, force/torque-coefficient, density, dynamic-pressure, or span normalization. All force, torque, and power quantities here are two-dimensional per-unit-span. The frozen project conversion is `x*=x/D`, `t*=t U_inf/D`, `nu*=nu/(U_inf D)`, `omega*=omega D/U_inf`, `Q*=Q/(U_inf D)`, `J*=J/(rho_ref U_inf^2 D)`, `C_F=F/(0.5 rho_ref U_inf^2 D)`, `C_tau=tau/(0.5 rho_ref U_inf^2 D^2)`, and `C_P=P/(0.5 rho_ref U_inf^3 D)`. +The accepted/reverse endpoints provide bounded power, signed rear-gap, kinetic-flux, and wake diagnostics. They do not form a mechanical-energy ledger: station fluxes cover x/D=2-to-10 while dissipation covers the full domain, pressure is absent despite zero-valued placeholders, and lateral/storage terms are missing. The switch is one deterministic same-parent response screened by heuristic polarity/dose/onset gates, so causal language is not licensed. Pulse norms describe finite-time field-distance histories only; their dimensionful threshold cannot determine branch switching. The promoted switch/return analyses also lack strong authenticated loader, telemetry-hash, and payload provenance. Matrix-free Arnoldi/global stability remains unavailable. + + +## 29. Publication-v3 formula freeze + +Exactly four main formula groups govern the article: (1) Celeris wall law `(Uw,Vw)=(-omega ry,omega rx)` and the x-right/y-up sign map; (2) lattice-to-dimensionless conversion, including `C_P=sum(omega tau_read)/(0.5 rho_ref U_inf^3 D)`, `normalize=True` step averaging only, and two-dimensional per-unit-span scope; (3) same-body-enclosing-CV momentum/mechanical-energy spatial terms, with storage/time-consistent and body-adjacent gradients explicitly unavailable and no residual; (4) `E_inf_vector(q_ctl,q_in)=max_y ||q_ctl-q_in||/U_inf` on the complete common-fluid `x/D=10` profile after excluding two outer rows. Potential amplitude `g` and finite-horizon return `r,m` are secondary explanations, not additional main formula groups. diff --git a/src/steady_pinball_theory/HISTORY_AND_LESSONS.md b/src/steady_pinball_theory/HISTORY_AND_LESSONS.md new file mode 100644 index 0000000..f9158ef --- /dev/null +++ b/src/steady_pinball_theory/HISTORY_AND_LESSONS.md @@ -0,0 +1,53 @@ +# Steady pinball history and lessons + +## Purpose + +Navigation and methodological history, not scientific evidence. Claims resolve through [evidence/INDEX.json](evidence/INDEX.json) and immutable artifacts. Plans, memory, and Undermind are **navigation not evidence**. + +## Chronology + +### Minimal reset +The package was reduced to verified mathematics, contracts, and a small evidence surface after prior finite-Re claims proved untrustworthy. Plan: [separated roadmap](/home/frank14f/.cursor/plans/steady-karman_separated_roadmap_6c64c1c0.plan.md). Lesson: remove unsupported authority while preserving unique negative evidence and provenance. + +### Finite-Re bridge +Four D20 endpoints connected action to measured outer fields and corrected total-field WLS. Plan: [finite-Re bridge](/home/frank14f/.cursor/plans/steady-cloak_finite-re_bridge_9074c427.plan.md). The result falsified potential cancellation by sign. + +### Mechanism completion +Credibility, endpoint residual diagnostics, and bounded DRL sanity were organized under one evidence root. Plan: [mechanism completion](/home/frank14f/.cursor/plans/steady-cloak_mechanism_completion_492ea630.plan.md). Endpoint association survived; causality did not. + +### Semi-analytic failure +A composite model was promoted too early. Audit found metric double subtraction, nearly identical baseline/full improvement, inactive wake contribution, and non-independent gates. Plan: [semi-analytic closure](/home/frank14f/.cursor/plans/accepted-direction_semi-analytic_closure_67ca3c02.plan.md). Its immutable payload remains failed descriptive history. + +### NS-first report +The project shifted from fitting to torque, momentum, vorticity, energy, intervention, and return diagnostics. Plan: [NS mechanism report](/home/frank14f/.cursor/plans/ns_cloak_mechanism_report_d2305159.plan.md). Runtime manufacture corrected torque-work interpretation; audit bounded ledger, switch, and return claims. + +### Article closeout +Exact formulas, hashes, figures, and the direct v5 metric were frozen while retaining publication supersession. Plan: [article closeout](/home/frank14f/.cursor/plans/steady理论收尾_7e4c9476.plan.md). + +### Current display +Authenticated endpoints and diagnostics were rendered into figures/CSVs without CFD. Plan: [display closeout](/home/frank14f/.cursor/plans/steady结果整理收尾_bd8df5c5.plan.md). Display v2 supersedes v1 as a reader view, not new evidence. + +## Key mistakes + +1. **Sign/body mapping:** array position or link traversal cannot replace semantic body IDs and wall-point oracles. +2. **Potential fit vs mechanism:** projection quality is descriptive; opposite `g` sign falsifies cancellation. +3. **Metric double subtraction:** never feed an already-subtracted disturbance to an absolute-profile metric. +4. **Lattice nondimensionalization:** `normalize=True` is one step average, not coefficient/density/dynamic-pressure/body/span normalization. +5. **Torque ownership/source inference:** cut-link direction did not establish API ownership. Runtime evidence establishes torque work sign only; force ownership remains open. +6. **Control-volume mismatch:** station fluxes and full-domain dissipation are not a common-CV balance. +7. **Mixed-unit transient:** dimensionful norms and arbitrary thresholds cannot identify a branch/basin. +8. **Immutable disposition:** archiving and supersession are index states, not permission to move or rewrite payloads. + +## Durable rules + +- Freeze order, signs, coordinates, units, metric, comparator, and claim boundary before analysis. +- Separate endpoint observation, association, intervention, conservation closure, and stability. +- Authenticate derived outputs to exact source paths/hashes; displays create no authority. +- Use no-clobber outputs and replacement links; preserve failures and superseded artifacts. +- A residual requires one control volume and all storage, boundary, pressure, viscous, and work terms. +- State realization count, horizon, amplitude matching, and uncertainty beside transient claims. +- Keep SR and CCD separate: SR supplies rear-constant context; CCD is pending for the steady total claim. + +## Memory and literature navigation + +Useful Nowledge topics: “Steady pinball minimal verified reset,” “finite-Re bridge,” and “mechanism-completion closure.” Useful Undermind topics: rotating-wall viscous interfaces, base-bleed/boat-tail context, and qualified-base stability. These are **navigation not evidence**; repository proofs/tests, primary-source mappings, and immutable artifacts remain authority. diff --git a/src/steady_pinball_theory/LITERATURE.md b/src/steady_pinball_theory/LITERATURE.md index 7a0ffc4..54827fd 100644 --- a/src/steady_pinball_theory/LITERATURE.md +++ b/src/steady_pinball_theory/LITERATURE.md @@ -1,18 +1,208 @@ -# Source-to-equation ledger +# Frozen source-to-claim ledger -This ledger separates inviscid geometry, finite-Re closure, and viscous stability. +`DERIVATION.md` is authoritative for project proofs. `RESULTS.md` freezes numeric observations. This ledger attributes only external equations/results actually used, with explicit transferable conclusions and prohibited transfers to the canonical D20 `Re_D=50` free-slip-channel pinball (cylinder walls rotate under Celeris no-slip; channel walls free-slip). A verification hold means the detail is deliberately not asserted; no DOI or equation mapping is inferred from secondary metadata alone. -- Crowdy (2006), *Analytical solutions for uniform potential flow past multiple cylinders*: exact multiply connected circular-domain uniform-flow construction. Reuse: independent reference for impermeability, circulation periods and far field; it does not impose no slip or predict separation. -- Crowdy & Marshall (2007), *Green's functions for Laplace's equation in multiply connected domains*: Schottky–Klein Green-function machinery. Reuse: exact/reference formulation for circular multiply connected domains. -- Kharlamov & Filip (2012), generalized method of images for several moving parallel cylinders. Reuse: iterative image cross-check and convergence logic. -- Chan, Jameson & Smits (2011), *Vortex suppression and drag reduction in the wake of counter-rotating cylinders*: viscous doublet-like/reverse-doublet topologies and virtual-body mechanism. Reuse: mechanism observables, not a sign oracle for this code. -- Mittal (2001), *Control of flow past bluff bodies using rotating control cylinders*: steady-wake suppression near tip-speed ratio five in a different geometry. Reuse: prior for search scale only, never a fixed optimum. -- Watson (1996), *Slow viscous flow past two rotating cylinders*: matched/Oseen rotating-cylinder precedent. Reuse: conceptual finite-Re interface; regime and geometry differ. -- Deng et al. (2018), fluidic-pinball bifurcations; Sierra et al. (2020), rotating-cylinder bifurcations. Reuse: require continuation/perturbation and do not assume unique symmetric steady state. -- Marquet, Sipp & Jacquin (2008): global sensitivity of cylinder flow. Reuse: independent viscous base-flow/eigenvalue workflow after empirical stability. +## Stage-1 literature charter -## Equations and claim limits +**Scope.** Deepen the viscous-mechanism half of the steady-cloak plan: why accepted rear-symmetric rotation can be both steady and low-deficit while potential-favored cancellation fails by sign. Corrected CCD is admitted only as contextual triangulation; Kármán transmission claims and CCD mechanism claims are not imported into the steady chain. -The outer field is `u = U_inf e_x + sum_j grad[Q_j log|z-z_j|/(2pi)] + sum_k Gamma_k e_theta/(2pi r)` with source strengths chosen to satisfy cylinder no penetration and zero net source per body. In a strip, scalar sources use equal-sign reflections and vortices opposite-sign reflections at free-slip walls. Truncation, source radius, collocation order, precision, boundary residual, wall residual and an independent exact/image formulation must be reported. +**Frozen project frame (not literature-derived).** +- Body order: `(front, rear_y_plus, rear_y_minus)`. +- Accepted numeric action: `[0,+Omega,-Omega]` with `Omega>0`, `s=Omega a/U_inf`. +- Celeris wall law: `(Uw,Vw)=(-omega*ry, omega*rx)` in x-right/y-up; positive `omega` matches geometric-CCW wall sense (outer cardinal of the upper rear driven upstream; gap-facing cardinals downstream). +- Primary metric: full two-component `E_inf_vector` of `q_ctl` versus uniform no-body `q_in` at `x/D=10`. +- Project telemetry contract (source-audited, not literature-derived): Celeris cut-link loads are lattice sums; `normalize=True` averages once per accumulated LBM step and applies no coefficient/density/dynamic-pressure/span normalization. The runtime manufactured oracle establishes raw torque as boundary/actuator-on-fluid for project use; actuator-to-fluid power is `sum(omega*tau_read)`. This runtime result overrides the falsified source-only cut-link ownership inference. +- Potential favorable cancellation `(0,+Gamma,-Gamma)` / `g_opt=+6.147944` **FAILS** against accepted geometric circulation `(0,-,+)` and descriptive `g=-12.200554` (`RESULTS.md`). +- Surviving modeling hypothesis: viscous gap momentum, shear/separation modification, and wake replenishment (literature boat-tail / base-bleed families as qualitative templates only). -`Gamma_k` is prescribed in the inviscid problem. Mapping wall rotation to an effective circulation is a finite-Re empirical interface requiring contour plateaus and held-out outer profiles; it is not `Gamma=2pi R^2 omega` by assumption. Potential flow cannot predict viscous separation, drag, base pressure, or global stability. +**Claim IDs used below.** Cross-link to `RESULTS.md` classes: `L-PF` potential/interface; `L-VIS` viscous rotating-wall; `L-BR` branch/topology context; `L-ST` stability-window context; `L-CLO` cloaking analogy; `H-ROD` Rod26 hold status; `X-KAR` Kármán quarantine; `X-CCD` CCD exclusion. + +## Sign-convention master map + +| Source | Body order | Positive rotation | Boat-tail / outer-shear family | Base-bleed / gap-jet family | Map to project accepted `[0,+Omega,-Omega]` | +|---|---|---|---|---|---| +| Project (Celeris) | `(front, rear_y_plus, rear_y_minus)` | geometric-CCW / Celeris `+omega` | `[0,-Omega,+Omega]` (outer downstream) | `[0,+Omega,-Omega]` (gap downstream) | **is** the gap-downstream family | +| Mac20 / Mac21 [= Cornejo Maceda et al. 2021] | `(front,bottom,top)=(b1,b2,b3)` | CCW | `b2=-b3>0` (bottom CCW, top CW) | `b2=-b3<0` | accepted ↔ Mac20 **base bleed** wall sense, not boat-tail | +| Rod26 | `(1 front, 2 upper, 3 lower)` | CCW-positive lab frame for mapping | `p>0`: upper CW, lower CCW (Fig. 3b,c) | `p<0`: upper CCW, lower CW (Fig. 3e,f) | accepted ↔ Rod26 **base-bleeding** wall sense (`p<0` family) | +| Cha11b | side-by-side pair | Fig. 2 arrows | doublet-like: upper CW, lower CCW (gap with freestream) | reverse doublet-like: upper CCW, lower CW (gap opposing) | names are pair-only; do not rename project branches | + +Do not call project accepted “boat-tailing” by Mac20/Rod26 labels. Literature boat-tail drag optima are not project-accepted optima. + +## Primary-source ledger + +- **Crowdy (2006), “Analytical solutions for uniform potential flow past multiple cylinders,” *European Journal of Mechanics B/Fluids* 25, 459–470, DOI `10.1016/j.euromechflu.2005.11.005` [Cro06].** Equations (16), (18)–(20), (25)–(26), and (34) support uniform far behavior, constant-streamfunction impermeable boundaries, the prime-function construction, and a zero-period (zero round-obstacle circulation) uniform-flow potential. **Transfer:** outer impermeability reference (`L-PF`). **Prohibit:** no-slip, `Gamma(Omega)`, separation, drag, or cloak metric (`X-CCD` unused). +- **Glass, Lacave, Munnier & Sueur (2019), “Dynamics of rigid bodies in a two dimensional incompressible perfect fluid,” *Journal of Differential Equations*, DOI `10.1016/j.jde.2019.04.017`.** Supports rigid-body normal matching and treatment of vorticity/body circulations as independent perfect-fluid state data. No theorem number is imported; the narrower fixed-body uniqueness result is proved in `DERIVATION.md` (`L-PF`). +- **Ueda, Sellier, Kida & Nakanishi (2003), “On the low-Reynolds-number flow about two rotating circular cylinders,” *Journal of Fluid Mechanics* 495, 255–281, DOI `10.1017/S002211200300627X` [Ued03].** PDF-verified. Equations (2.4) and (2.7)–(2.10) prescribe far velocity plus rotating no-slip walls, relate `(u,v,w)` to streamfunction, and carry modified vorticity into the unsteady Oseen form. **Transfer:** viscous wall/vorticity distinction vs Euler impermeability (`L-VIS`). **Prohibit:** quantitative forces or closures at `Re_D=50` (analysis is `Re≪1`). **DOI hold lifted.** +- **Glauert (1957), “The flow past a rapidly rotating circular cylinder,” *Proceedings of the Royal Society A*, DOI `10.1098/rspa.1957.0157` [Gla57].** Supports a restricted irrotational-outer/viscous-boundary-layer circulation closure precedent, not a universal `Gamma(Omega)` law (`L-VIS`). **Hold:** Undermind PDF unavailable; no new equation mapping. +- **Moore (1957), “The flow past a rapidly rotating circular cylinder in a uniform stream,” *Journal of Fluid Mechanics* 2, 541–550, DOI `10.1017/S002211205700035X` [Moo57].** Related rotating-cylinder boundary-layer precedent (`L-VIS`). **Hold:** PDF unavailable; no equation mapping. +- **Brøns & Hartnack (1999), “Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries,” *Physics of Fluids* 11, 314–324, DOI `10.1063/1.869881`.** Primary precedent for local bifurcation near degenerate interior critical points. No equation number or global-topology theorem is imported. +- **Crowdy & Marshall (2005), “The motion of a point vortex around multiple circular islands,” *Physics of Fluids* 17, DOI `10.1063/1.1900583`.** Establishes a Hamiltonian problem with evolving vortex position; it does not establish stability of a fixed prescribed-circulation harmonic field (`X-KAR` if reused for street motion). +- **Protas (2006), “Higher-order Föppl models of steady wake flows,” *Physics of Fluids* 18, DOI `10.1063/1.2389033`.** Provides free-vortex/finite-area-vortex equilibrium and stability context; it does not transfer to this static BVP. + +## Stage-1 viscous-mechanism paper ledger + +Each entry records geometry, Re, body order, rotation convention, control parameter, key equations/figures, stability criterion, gap/shear/separation/force evidence, transferable conclusions, and prohibited transfers to D20 `Re_D=50` free-slip-channel pinball. + +### Rod26 — Rodrigues-Asensio et al. (2026) [claim `H-ROD` partially lifted] + +- **Citation.** “On the turbulent wake of the actuated fluidic pinball: Dynamics, bifurcations and control authority,” *Experimental Thermal and Fluid Science* 177, 111798, DOI `10.1016/j.expthermflusci.2026.111798`. PDF available in Undermind DynamisLab. +- **Geometry / Re.** Three equal cylinders, `D=30 mm`, equilateral centres `1.5D`, upstream-pointing triangle; water tunnel, blockage ~14%; `Re=U_∞D/ν=9100`. +- **Body order.** Cylinder 1 front (fixed); 2 upper rear; 3 lower rear (Fig. 1). +- **Rotation / control.** `b_i=Ω_i D/(2U_∞)` (Eq. 1); boat-tailing parameter `p=(b_3-b_2)/2` (Eq. 2). Verbatim physical labels (§2.2): base-bleeding `p<0` “opposes the freestream and generates a jet between the two downstream cylinders”; boat-tailing `p>0` “weakens the gap flow and accelerates the outer shear layer.” Fig. 3: `p>0` upper CW / lower CCW; `p<0` upper CCW / lower CW. In CCW-positive lab frame, boat-tail ↔ `(0,-,+)`, base-bleed ↔ `(0,+,-)` on `(front,upper,lower)`. +- **Key figures.** Fig. 3 mean wakes; Fig. 7 separation motion under boat-tailing; Fig. 8 `C_D(p)` with optimum near `p≈1.8` and loss of authority beyond; Fig. 9 three-dimensional actuation manifold with two inverse-pitchfork symmetrizations (`p≥0.8` boat-tail; `p≤-2.6` base-bleed). +- **Stability / forces.** Symmetrization thresholds above; drag non-monotonic on boat-tail branch; strong base-bleed can change shedding symmetry (mode-S) without changing mean-wake character. +- **Transfer (`L-BR`).** Qualitative: distinct boat-tail vs base-bleed topologies; gap vs outer-shear organization; actuation magnitude, mean symmetry, and drag are different coordinates; excessive actuation can lose authority. Exact Fig. 3 / Eq. 2 sign map now authorized for literature comparison. +- **Prohibit.** Do not transfer `Re=9100`, turbulent thresholds `p=0.8/-2.6`, `p≈1.8` drag optimum, force magnitudes, or URANS details to D20 `Re_D=50`. Do not equate project accepted `[0,+Omega,-Omega]` with Rod26 boat-tailing: accepted maps to the **base-bleeding wall-sense family**. Do not import Kármán-street transmission claims (`X-KAR`). +- **Hold status.** Full-text/figure-sign publication hold **partially lifted** (sign/branch map above). Remaining hold: no quantitative equivalence of thresholds, forces, or manifold coordinates to the project CFD. + +### Mac20 / Mac21 — Cornejo Maceda et al. (2021) [claim `L-BR`] + +- **Citation.** “Stabilization of the fluidic pinball with gradient-enriched machine learning control,” *J. Fluid Mech.* 917, A42, DOI `10.1017/jfm.2021.301`. Undermind cite key `Mac20`; published 2021 (Mac20/Mac21 denote the same JFM paper / thesis lineage, not two mechanisms). +- **Geometry / Re.** Equilateral centres `1.5D`, upstream apex; domain `[-6,20]×[-6,6]`; `Re_D=100`. +- **Body order / sign.** `(b1,b2,b3)=(front,bottom,top)`; positive command = CCW (§2.1). Symmetric scan `b2=-b3`: boat-tail `b2>0` accelerates outer layers and sucks near-wake fluid upstream; base-bleed `b2<0` ejects a gap jet (§4.1, Fig. 6). +- **Control / cost.** Commands `b`; cost `Ja` is space-time `L²` distance to unstable symmetric steady NS target `u_s` (Eqs. 2.3–2.4)—**not** project `E_inf(q_ctl,q_in)` at `x/D=10`. +- **Key regimes.** Six mechanisms (§2.2): boat-tailing, base bleeding, phasor, Magnus/unified rotation, high- and low-frequency forcing. Symmetric regimes include steady branches for `b2<-4` and `b2>2.375` (strong Coanda boat-tail), with global symmetric `Ja` minimum at weak base-bleed `b2=-0.375` still unsteady/chaotic (§4.1). +- **Transfer.** Two high-amplitude symmetric steady branches can exist with different physics; steady ≠ close to `u_s`; gap jet / outer shear are the organizing viscous motifs for rear-opposite rotation. +- **Prohibit.** Do not transfer `Ja` optima, `b` thresholds, `Re=100`, asymmetric EGM/gMLC laws, or sensor-feedback structure to the rear-only D20 cloak metric. Do not relabel project accepted as Mac20 boat-tailing (see master map). + +### Cha11b — Chan et al. (2011) [claim `L-BR`] + +- **Citation.** “Vortex suppression and drag reduction in the wake of counter-rotating cylinders,” *J. Fluid Mech.* 679, 343–382, DOI `10.1017/jfm.2011.134`. +- **Geometry / Re.** Side-by-side equal cylinders; gaps `g*=1,3,5`; `Re=100,150,200`; no front cylinder. +- **Sign.** Fig. 2: doublet-like = upper CW / lower CCW (gap with freestream); reverse doublet-like = opposite. `Ω=ωd/(2U)`. +- **Stability.** Unsteadiness suppressed when force fluctuations vanish (`σ(C_L)`, `σ(C_D)` → 0); `Ω_crit` in Table 1. Doublet-like high-`Ω` forms virtual elliptic body (Figs. 8–9) with gap flow reversal and total drag ≈ 0 (Fig. 11); reverse doublet-like also steadies by separating wakes, generally without the elliptic body. +- **Transfer.** Both opposite counter-rotation directions can suppress shedding via **different** topologies; “steady” ≠ “cloak-like / zero-deficit.” +- **Prohibit.** No quantitative `Ω_crit`, drag-zero claim, or pair-gap thresholds for the three-cylinder D20 case; figure names are not project branch names. + +### Mit01 — Mittal (2001) [claim `L-VIS` / `L-BR`] + +- **Citation.** “Control of flow past bluff bodies using rotating control cylinders,” *J. Fluids Struct.* 15, 291–326, DOI `10.1006/jfls.2000.0337`. +- **Geometry / Re.** Main cylinder + two small controls, `D/D2=20`, centres on a line normal to the stream; gaps `0.01D`, `0.075D`; `Re=100` and `10^4`. +- **Sign / control.** Upper CW, lower anti-clockwise (Fig. 4); tip-speed ratio `Uc/U=5` yields steady narrow wake at `Re=100` (Fig. 6) and organized narrower wake at `Re=10^4`. +- **Transfer.** Order-of-magnitude tip-speed ~O(1–5) and rotating-surface momentum injection as a viscous wake-narrowing motif. +- **Prohibit.** Not equilateral three-equal-cylinder geometry; MSBC relies on cylinder no-slip (project cylinders rotate no-slip, but size ratio and alignment differ); no free-slip-channel transfer; power/drag numbers do not carry to D20. + +### Ued03 — Ueda et al. (2003) [claim `L-VIS`] + +- See primary-source ledger. Two cylinders, arbitrary radii/Ω, `Re≪1` matched Stokes–Oseen. **Transfer:** rotating no-slip selects vorticity; Euler does not. **Prohibit:** `Re_D=50` forces/closures. + +### Wat96 — Watson (1996) [claim `L-VIS`] + +- **Citation.** “Slow viscous flow past two rotating cylinders,” *Q. J. Mech. Appl. Math.* 49, 195–216, DOI `10.1093/qjmam/49.2.195`. +- **Geometry / regime.** Bipolar Stokes inner + Oseen outer; `Re=Uc/ν≪1`; equal contra-rotating cases with stream normal or parallel to the line of centres; lift can be O(drag). +- **Transfer.** Low-Re rotating-pair force coupling precedent only. +- **Prohibit.** Does not control `Re_D=50` free-slip or no-slip channel pinball; no cloak metric. + +### Gla57 / Moo57 — Glauert & Moore (1957) [claim `L-VIS`, PDF hold] + +- Single rapidly rotating cylinder boundary-layer / outer irrotational closure precedents. **Transfer:** restricted `Gamma`–rotation coupling idea. **Prohibit:** universal `Gamma(Omega)` for multi-body `Re_D=50`. PDFs unavailable in Undermind → equation-level hold retained. + +### Kim92 — Kimura, Tsutahara & Wang (1992) [claim `L-ST`] + +- **Citation.** “Wake of a rotating circular cylinder,” *AIAA J.* 30, 555–556, DOI `10.2514/3.10953`. +- **Geometry / Re.** Single cylinder; experiments `Re~2e2–7e4`; spin `α=` peripheral/freestream up to ~2.5. +- **Findings.** Wake meandering amplitude falls and St rises with spin; critical spin decreases as Re increases (Fig. 3). +- **Transfer.** Qualitative: higher spin can suppress meandering; lower Re may need larger spin. +- **Prohibit:** single-body thresholds; no three-cylinder or free-slip-channel map; lowest Re still above project `50` shedding neighborhood. + +### Sie20 — Sierra et al. (2020) [claim `L-ST`] + +- **Citation.** “Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder,” *J. Fluid Mech.* 905, A2, DOI `10.1017/jfm.2020.692`. +- **Geometry / Re.** Single rotating cylinder to `Re=200`; `α=ΩD/(2U_∞)` with positive = CW. +- **Findings.** Codimension-two points (cusp, Takens–Bogdanov, generalized Hopf); multiple steady states; bistability windows (Fig. 5, Table 1). +- **Transfer.** Finite actuation windows and coexisting steady/unsteady states are generic for rotating cylinders—motivates treating reverse high-deficit steady as a distinct branch, not a sign error. +- **Prohibit.** No transfer of `(Re,α)` coordinates to the three-cylinder pinball. + +### Den18b — Deng et al. (2018/2019) [claim `L-ST`] + +- **Citation.** “Low-order model for successive bifurcations of the fluidic pinball,” *J. Fluid Mech.*, DOI `10.1017/jfm.2019.959` (Undermind `Den18b`). +- **Geometry / Re.** Equilateral three equal cylinders, side `3R`, upstream apex; unforced Hopf `Re1≈18` and pitchfork `Re2≈68` (D-based). +- **Model.** Five-mode mean-field Galerkin system (Eqs. 3.30–3.31, 5.5) for shedding + shift + jet-deflection modes. +- **Transfer.** Unforced context: at `Re_D=50` (between Hopf and pitchfork) the natural mean is symmetric with unstable steady `u_s`; controlled steady cloak must suppress the Hopf. +- **Prohibit.** Coefficients/ROM not recalibrated for rotating control; no cloak or CCD claim (`X-CCD`). + +### Cro06 — Crowdy (2006) [claim `L-PF`] + +- See primary-source ledger. Zero-circulation multi-cylinder potential only. + +### Urz12 — Urzhumov & Smith (2012) [claim `L-CLO`, workspace gap] + +- **Citation (mem-backed).** “Flow stabilization with active hydrodynamic cloaks,” *Phys. Rev. E* 86, 056313 (2012). Active Brinkman porous shell raises critical Re ~5× for a single cylinder. +- **Transfer.** Analogy only: active momentum injection can stabilize a low-signature steady wake. +- **Prohibit.** Not rotating pinball; Brinkman `κ(r)` ≠ cylinder `Ω`; no PDF in the Undermind folder for this Stage-1 pass → no equation import. **Bibliographic gap:** add PDF to workspace before any equation-level use. + +## Publication holds and unused context + +- **Kharlamov & Filip (2012), generalized images for several parallel cylinders:** only a broad independent image-method precedent. No equation-number mapping is asserted; pages and DOI remain unverified and are not needed for the implemented MFS or Laurent cross-check. This publication hold does not block the present evidence-package verdict. +- **Lamb, *Hydrodynamics*; Milne-Thomson, *Theoretical Hydrodynamics*:** classical circle-flow sources. Edition/page/equation details remain unverified; the velocity formulas and counterexample are directly derived and tested. +- **Kelvin circulation theorem:** used under its classical inviscid/barotropic/conservative-force/smooth-material-loop hypotheses; original historical citation details remain unverified. Glass et al. supplies the modern application context. +- Crowdy & Marshall (2007) [Cro07b] remains multiply-connected Green context only unless a prime-function backend is implemented. +- **Gla57 / Moo57:** PDF unavailable → equation hold retained (above). +- **Urz12:** not in Undermind folder PDF set for this pass → equation hold (above). + +## Project-derived equations and implementation boundary + +The following are derived in `DERIVATION.md` and validated by project tests, not attributed to external equation numbers: + +- Hodge-period form `u=u_N+sum_j Gamma_j h_j`, fixed-period uniqueness under stated hypotheses, flux compatibility, centered-circle rotational impermeability, and the one-circle trace `u_theta(a,theta)=-2U sin(theta)+Gamma/(2 pi a)`. +- MFS zero-source constraints, image truncation, diagnostics, independent finite Laurent collocation, and the common-exterior metric. +- Rear-pair log cancellation, `C_pair=-Gamma b/pi`, body-source multipoles, the affine coefficient `C(Gamma)=C0+Gamma dC`, real least-squares cancellation, symmetry parity, equal-norm ablation, gap flux, and sampled-root/Jacobian controls. + +`Gamma_j` is prescribed in the inviscid problem. Any `Gamma_eff(s)` is an empirical or viscous closure requiring endpoint fields, coordinates, masks, sign convention, uncertainty, Reynolds number, geometry, confinement, and held-out validation. Historical fitted values without source arrays remain withdrawn. The v4 endpoint fields now support contour geometric sign and a corrected descriptive WLS projection, but not a causal `Gamma_eff(s)` law. Potential flow alone does not predict no-slip vorticity generation, separation, drag, torque, base pressure, or viscous/global/dynamical stability. + +## Finite-Re/no-slip scope addition + +- **Watson (1996)** supports only a low-Reynolds-number Stokes–Oseen reference. It does not control the present `Re_D=50` free-slip or no-slip channel. +- **Mao, Blackburn & Sherwin (2015), JFM, DOI `10.1017/jfm.2015.304`; Kharlamov & Filip (2012), DOI `10.1007/S10665-012-9532-6`.** Retained as channel/global-mode and image-method context respectively; neither supplies the finite-Re circulation closure or licenses transfer from free-slip potential flow to no-slip flow. + +The exact free-slip strip modal relations in `DERIVATION.md` are project derivations from Laplace separation with Neumann walls. Watson is scoped only to low-Re Stokes–Oseen flow; Mao, Blackburn & Sherwin supplies channel/global-mode method context; Kharlamov–Filip supplies image-method context. None transfers the free-slip optimum or rescues the failed potential-circulation mechanism in a no-slip `Re_D=50` channel. New direct Navier–Stokes evidence is required because no-slip changes wall-vorticity production, base flow, separation, and modal operators. + +## Stage-0 paper-oracle ledger + +- **Vasconcelos, Moura & Schakel (2012), “Vortex motion around a circular cylinder,” DOI `10.1063/1.3667269`.** Equations (7)--(10), (13), and (26) map respectively to the symmetric Hamiltonian/canonical equations, Föppl locus/strength, infinity saddle, and its critical Hamiltonian level. The exact `kappa=45/32` finite equilibrium and the distinct infinity level are tested. +- **Mowlavi, Arratia & Gallaire (2016), “Spatio-temporal stability of the Kármán vortex street and the effect of confinement,” DOI `10.1017/jfm.2016.195`.** Physical-row coordinates/signs and scales are mapped from §2; the unconfined self-advection and `p0=asinh(1)/pi` are exact baselines. Equations (2.7), (2.11), and (4.3)--(4.9) are documented but intentionally not reproduced; temporal growth and convective thresholds remain publication holds (`X-KAR`). +- **Crowdy & Marshall (2005), “The motion of a point vortex around multiple circular islands,” DOI `10.1063/1.1900583`.** Supports Green/Robin/Kirchhoff--Routh motion for zero island circulations, background-flow Hamiltonian contribution, and regular self-response. Only the independently derived exact one-circle image reduction is implemented. +- **Streitlien (1994), “Extracting energy from unsteady flows through vortex control,” DOI `10.1575/1912/5563`.** Supports incoming-street/body coupling and Routh-regular vortex transport in a Joukowski-foil setting; no three-circle force or transparency claim is imported. +- **Cornejo Maceda et al. (2021)** — see Stage-1 Mac20 entry; Stage-0 retains paper-specific `(front,bottom,top)` labels only. +- **Chan et al. (2011)** — see Stage-1 Cha11b entry; Stage-0 retains figure-2 arrow specificity only. +- **Rodrigues et al. (2026)** — see Stage-1 Rod26 entry. Stage-0 metadata-only hold is superseded by the partial lift above; quantitative equivalence remains held (`H-ROD`). + +## Same-setting contract claim boundary + +The four-role steady contract is an internal CFD comparability and residual-readiness design, not a literature-derived mechanism test. Branch labels remain project-specific wall-action labels; accepted/reverse symmetry does not imply circulation, base-bleed, boat-tail, doublet, separation, force, or stability equivalence without the Stage-1 sign map. Fresh fields and forces must be regenerated before any new physical statement is made. + +## S2 residual interpretation boundary + +Rod26 (partially lifted), Cornejo Maceda et al. (2021), and Chan et al. (2011) are used only as qualitative frameworks for distinct steady rotating-cylinder branches, gap transport, and wake organization. The S2 endpoint result does not import their Reynolds numbers, geometry, confinement, body order, branch names, or force thresholds. Under the Stage-1 master map, project accepted wall sense aligns with literature **base-bleed / gap-jet** families, while literature **boat-tail** aligns with project reverse wall sense—yet project reverse is the high-deficit branch. Therefore S2 association (gap flux, shear width, recirculation, `Fx`, downstream deficit) is an internal D20 observation; it is not a literature proof that “boat-tailing explains the cloak,” nor a transfer of Rod26’s boat-tail drag optimum. + +## Frozen cross-project source/evidence map + +- **SR:** `src/SR_analysis/results/README.md`, `src/SR_analysis/PIPELINE.md`, `src/SR_analysis/results/runs/article2-steady-analysis-20260720/interpretation.md`, and the canonical term-deletion table support the ranking `rear constant > rear lift feedback > tested front feedback` only among the tested terms, plus order-of-magnitude steady correspondence. They do not establish necessity, global dominance, PPO mechanism, uniqueness, circulation, or a momentum-balance law. +- **CCD (`X-CCD`):** pending/not frozen for the steady total claim. No quantitative CCD value is imported here. Any later interface remains a separate estimand and cannot alone establish steady mechanism, actuator isolation, or causality. +- **Rod26 (`H-ROD`):** figure/sign map partially lifted in Stage-1; quantitative thresholds and force equivalence remain held. +- **Kármán (`X-KAR`):** vortex-street, phase, feedback, and control conclusions form a separate evidence chain and are not imported into the canonical uniform-inlet steady result. + +## K1 qualification boundary + +The 2026-08-06 K1 run uses only Mowlavi et al.'s documented unconfined row/stagger/scaling baseline and the exact neutral-aspect identity. A finite open train is integrated as a project numerical sensitivity problem; its end effects, central propagation, and perturbation amplification are not equations (2.7), (2.11), or (4.3)--(4.9), and are not temporal or convective growth. Mowlavi confined dispersion/growth and the plan-required growth/impulse oracle remain publication-held. Consequently K2 is NO-GO. + + +## Mechanism-completion literature boundary + +Stage-1 theory closure and later numerical work remain governed by the ledgers above. Ueda/Glauert/Moore support only the viscous-interface distinction; Maceda/Chan/Rod26 remain qualitative branch/gap context. SR supports rear-constant ranking only among tested terms. CCD remains pending/not frozen for the steady total claim and supplies no quantitative term here. None transfers Legacy layouts, PPO feedback, causality, or steady-mechanism proof into the canonical free-slip direct-`q_in` claim. + + +## Historical composite discussion + +The failed composite semi-analytic route, its source-family mapping, and its audit are recorded in [HISTORY_AND_LESSONS.md](HISTORY_AND_LESSONS.md#semi-analytic-failure) and the immutable `steady-semi-analytic-analysis-20260807` disposition in [evidence/INDEX.json](evidence/INDEX.json). Those sources remain useful historical context but are not active source-to-claim support. + +## NS-first literature governance + +The intended chain uses Drela for actuator/wake energy-accounting method, Steiros and related base-bleed work for conservation-reduction context, Mittal for rotating-control wake modification, Liu/Terrington for wall-motion and boundary-vorticity accounting, Mao–Blackburn–Sherwin for qualified-base global-stability methods, and Urzhumov–Smith for a limited active-cloak analogy. These anchors do not repair the audited project artifacts: the NS ledger is bounded diagnostics, and the causal/nonlinear promotions lack strong provenance. + +These are method anchors, not transferred results. No paper supplies the project torque sign, `C_P`, gap flux, energy closure, `Re_D=50` coefficients, accepted/reverse ranking, causal timing, or eigenvalues. Equation-level use requires the exact primary-source mapping already verified in the ledger or a publication hold; memory or synthesis text alone cannot authorize a number. The literature chain must follow `power → momentum/vorticity → wake energy → stability`, with each transfer and prohibited transfer recorded before analysis. + + +## Publication-v3 claim mapping + +The v3 report maps the wall/interface distinction to Crowdy, Glass, Ueda, and Glauert; qualitative gap/base-bleed branch context to Cornejo Maceda, Chan, and Rodrigues-Asensio; and stability-method context to Mao–Blackburn–Sherwin. None supplies the project torque sign, `C_P`, same-CV closure, direct `q_ctl-q_in` metric, causal timing, or return labels. Those are authenticated project results and remain BOUNDED. SR is contextual cross-project evidence only; CCD is pending/not frozen for this steady claim. diff --git a/src/steady_pinball_theory/README.md b/src/steady_pinball_theory/README.md index f679ad0..5bbcb85 100644 --- a/src/steady_pinball_theory/README.md +++ b/src/steady_pinball_theory/README.md @@ -1,19 +1,61 @@ -# Steady pinball theory (reset) +# Steady pinball theory -Minimal, from-scratch implementation for the uniform-inflow/free-slip steady-cloak study. -Nothing from the deleted implementation is promoted as evidence. +A bounded `Re_D=50` steady-flow evidence package. The strongest result is a settling-qualified low-deficit endpoint; prescribed-circulation cancellation fails by sign, and available NS diagnostics do not close a mechanism, causal effect, or stability proof. -## Frozen scientific scope +## Start here -- Canonical geometry: three equal cylinders, rear centers at `(1.3D, +/-0.75D)` from the front; `Re_D=50`; channel half-height `15D`; uniform inlet and free-slip horizontal walls. -- Primary observer: full cross-section at `x/D=10` from the front-cylinder center. -- Primary score: `max_y sqrt((u_ctl-u_in)^2+(v_ctl-v_in)^2)/U_inf`; passive `q_blk` is non-ranking. -- Celeris source uses x-right/y-up lattice coordinates and `(Uw,Vw)=(-omega*ry,omega*rx)`. Both signed rear actions are retained until the paired CFD oracle is reviewed. Names such as clockwise or cloak never override numeric body IDs and actions. +1. [RESULTS.md](RESULTS.md) — current results and limits. +2. [evidence/README.md](evidence/README.md) — conclusion-to-artifact and family index. +3. [DERIVATION.md](DERIVATION.md) — mathematics and historical charters. +4. [LITERATURE.md](LITERATURE.md) — active source boundaries. +5. [HISTORY_AND_LESSONS.md](HISTORY_AND_LESSONS.md) — chronology and durable rules. -## Files and evidence policy +Machine authority is [evidence/INDEX.json](evidence/INDEX.json). The sole `evidence/` symlink reaches the external physical root; path/hash-bound directories are never moved for semantic cleanup. -The package remains below 30 files. Runtime results are written outside this tree. `contract.py` and its tests define source-level facts; `runner.py` produces paired action-reversal diagnostics; `theory.py` is the MFS outer/strip representation; `metrics.py` owns the direct-q_in objective. Literature assumptions and equation provenance are in `LITERATURE.md`. +## Unified reader plotting deliverable -## Environments +[`plot_results.py`](plot_results.py) regenerates the unified lattice-exact raw field canvases, family-specific error colorbars, analytical-zero potential vorticity, titled PNG/PDF metric plates, CSVs, and summary curves/bars in [`figures/`](figures/): -CPU theory/tests: `conda run -n pinball_math ...`. CFD: `PYTHONPATH=CelerisLab/src:src conda run -n pycuda_3_10 python -m steady_pinball_theory.runner ...`. GPU cases execute serially. +```bash +PYTHONPATH="$PWD/src" conda run -n pinball_math python src/steady_pinball_theory/plot_results.py +``` + +Raw canvases preserve one pixel per lattice cell; companion plates are explicitly presentation assets rather than pixel-exact arrays. This is a CPU-only, regenerable reader-facing visualization of existing authenticated sources, not new evidence. It refuses to clobber an existing output unless `--overwrite` is explicit. + +## Display and CSV command + +```bash +xdg-open "$PWD/src/steady_pinball_theory/evidence/authoritative/steady-results-display-v2-20260809/01_total_velocity_streamlines.pdf" +xdg-open "$PWD/src/steady_pinball_theory/evidence/authoritative/steady-results-display-v2-20260809/02_cfd_disturbance_vorticity_streamlines.pdf" +xdg-open "$PWD/src/steady_pinball_theory/evidence/authoritative/steady-results-display-v2-20260809/03_ns_diagnostics_partial_no_residual.pdf" +python3 -c 'import pandas as pd; print(pd.read_csv("src/steady_pinball_theory/evidence/authoritative/steady-results-display-v2-20260809/summary.csv").to_string(index=False))' +``` + +Exact CPU-only display reproduction (change only `--out` to another fresh path): + +```bash +PYTHONPATH="$PWD/src" TZ=UTC LC_ALL=C.UTF-8 conda run -n pinball_math python -m steady_pinball_theory.runner publish-results-display --steady "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808" --strip "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-strip-modal-analysis-20260804-v4/analysis.json" --ledger "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/ns-ledger-v2-oracle-bound-d20-20260809/analysis.json" --out "/tmp/steady-results-display-v2-REPRO" +``` + +Verification: reproducing to a fresh `--out` path yields byte-identical figures, CSVs, and display README. `manifest.json` intentionally records the requested output path, so its `exact_reproduction_command` and derived `payload_sha256` differ when `--out` differs; this is provenance-path dependence, not a scientific/data difference. + +The [display manifest](evidence/authoritative/steady-results-display-v2-20260809/manifest.json) authenticates its sources. This derived view ran no CFD. + +## Frozen boundaries + +- Body order `(front, rear_y_plus, rear_y_minus)`; accepted action `[0,+Omega,-Omega]`. +- Primary metric: common-fluid `E_inf_vector(q_ctl,q_in)` at `x/D=10`; `q_blk` is nonranking. +- Celeris wall law `(Uw,Vw)=(-omega*ry,omega*rx)` in x-right/y-up. +- Runtime evidence establishes torque telemetry work sign, not force ownership. +- Potential flow is an impermeability/circulation reference, not rotating-wall no-slip closure. +- SR supplies only current rear-constant context. CCD is pending/not frozen here and contributes no quantitative term to the steady frozen claim. + +## Verification + +```bash +PYTHONPATH="$PWD/src" conda run -n pinball_math python -m pytest -q src/steady_pinball_theory/tests/test_core.py +conda run -n pinball_math python -m compileall -q src/steady_pinball_theory +git diff --check -- src/steady_pinball_theory +``` + +No CFD belongs in documentation or display verification. diff --git a/src/steady_pinball_theory/RESULTS.md b/src/steady_pinball_theory/RESULTS.md index 887bf21..412ee98 100644 --- a/src/steady_pinball_theory/RESULTS.md +++ b/src/steady_pinball_theory/RESULTS.md @@ -1,46 +1,41 @@ -# Reset campaign results and claim matrix +# Current steady results -All values below were generated from scratch after deletion of the previous project. Runtime arrays remain outside this source tree under `/tmp/steady-*`; these are diagnostic/production candidates, not a clean tagged archival release. +Only current valuable results are indexed here. Exact statuses, replacements, and entry files are in [evidence/README.md](evidence/README.md) and [evidence/INDEX.json](evidence/INDEX.json). -## Sign oracle +## Potential mathematics and failure -Celeris source defines Cartesian lattice coordinates and `(Uw,Vw)=(-omega*ry,omega*rx)`. With body order `front, rear_y_plus, rear_y_minus`, paired D20 runs at `s=5`, `tU/D=250` give: +The inviscid problem supports independent prescribed circulations and a rear-opposite dipole basis. The tested cancellation explanation fails: strip analysis requires `g_opt=+6.147944`, while accepted finite-Re flow has descriptive `g=-12.200554`. Potential flow remains a bounded outer reference, not a no-slip closure or viscous mechanism. -- `[0,+Omega,-Omega]`: direct `q_ctl-q_in` `E_inf_vector(x/D=10)=0.13764`; compact steady wake. -- `[0,-Omega,+Omega]`: `E_inf_vector=0.64593`; broad deficit/wake. +Evidence: [strip analysis](evidence/authoritative/steady-strip-modal-analysis-20260804-v4/analysis.json), [finite-Re analysis](evidence/authoritative/steady-finite-re-bridge-analysis-20260804-v4/analysis.json), [derivation](DERIVATION.md). -The accepted numerical cloak branch is therefore `[0,+Omega,-Omega]`. Its outer cardinal surfaces move upstream and its gap-facing cardinal surfaces downstream under the solver law; “outer-surface downstream boat-tail” is not an accurate description of this branch. +## Steady endpoint -## Rotation search +In the canonical uniform-inlet/free-slip `Re_D=50` setup, accepted `[0,+Omega,-Omega]`, `s=3.55`, is settling-qualified. Direct current-v5 recomputation gives exactly `E_inf_vector(q_ctl,q_in)=0.0231672176752314` at `x/D=10`; nearby `s={3.45,3.55,3.65}` values are approximately `{0.0232525,0.0231671,0.0312490}`. -At D20, `Re_D=50`, `H/D=15`, uniform inlet and free-slip horizontal walls, the accepted branch was scanned from `s=0` to `7` for `tU/D=250`. The direct profile objective falls from `1.046` at passive `s=0` to `0.0232` near `s=3.45-3.55`, then rises to `0.0604` at `s=4`, `0.1376` at `s=5`, and `0.2972` at `s=7`. The current candidate interval is `s=3.45-3.55`; resolution of the flat pointwise maximum does not justify a unique optimum more precise than this interval. +This is an endpoint observation, not uniqueness, global attraction, no-slip transfer, or causal mechanism. -## Numerical sensitivity +Evidence: [v5 contract](evidence/authoritative/steady-contract-v5-torque-d20-20260808/), [publication v3b](evidence/authoritative/steady-article-publication-v3b-20260809/REPORT.md), [display v2](evidence/authoritative/steady-results-display-v2-20260809/README.md). -At `s=3.55`, matched q-in references give `E_inf={0.04549,0.02317,0.02348}` for `D={10,20,30}`. D20 and D30 agree within `3.1e-4`; D10 is not converged. Lateral half-height sensitivity at D20 gives `E_inf=0.02382` for `H/D=12`, `0.02317` for `15`, and `0.02478` for `18`. Fine-grid D30 local values are `0.02353,0.02348,0.02921` at `s=3.45,3.55,3.65`. +## NS diagnostics -Late-window changes in the scanned steady candidates are `O(1e-5-1e-4)` in the profile diagnostic. Neighboring cold-start cases at D30 (`s=3.4,3.5,3.6,3.7`) likewise settle over `tU/D=250`. This is empirical cold-start steadiness only; no checkpoint perturbation decay or global eigenanalysis has been completed. +The oracle-bound ledger provides actuator power, signed gap fluxes, wake-profile errors, recirculation, force readbacks, and vorticity diagnostics. It is an endpoint spatial partial ledger: storage/time-consistent and some body-adjacent terms are unavailable, force ownership is not established, and no residual exists. Accepted `s=3.55` and stable reverse `s=5.2` are not amplitude matched. -## Analytical representation and finite-Re interface +Evidence: [ledger](evidence/authoritative/ns-ledger-v2-oracle-bound-d20-20260809/analysis.json), CSVs [cases](evidence/authoritative/steady-results-display-v2-20260809/ns_case_summary.csv), [gaps](evidence/authoritative/steady-results-display-v2-20260809/ns_gap_fluxes.csv), [stations](evidence/authoritative/steady-results-display-v2-20260809/ns_station_diagnostics.csv). -The MFS solver enforces cylinder no penetration and zero source per body for unbounded and image-strip formulations. Tests cover collocation order, source radius and image-layer sensitivity. A strip circulation scan predicts near cancellation at `|Gamma|/(U D) about 4.25` (sign depends on body/circulation convention), with boundary residual below `1e-14` in that solve. Outer-mask fits to D30 CFD at `s=3.45,3.55,3.65` yield signed `Gamma_eff/(UD)=-4.293,-4.339,-4.384`, close in magnitude to the inviscid cancellation value; residual component RMS is about `1.9-2.1% U`. This supports a circulation-dominated outer mechanism but does not close boundary layers, pressure, force or separation. +## Limits of transient evidence -## Claim matrix +Migrated switch and return products are bounded diagnostics. The switch is one deterministic same-parent realization with heuristic gates; return labels are finite-horizon field-distance descriptions. They establish neither replicated causality, branch switching/basins, nonlinear stability, eigenvalues, nor global stability. Earlier pre-migration artifacts have explicit replacements in [INDEX.json](evidence/INDEX.json). -Supported now: -- exact numeric action/body mapping and action-reversal ordering; -- direct q-in profile metric at the historical `x/D=10` plane; -- a D20/D30-converged low-error candidate interval near `s=3.45-3.55` in the tested Celeris setup; -- numerical MFS no-penetration/image-strip representation and effective-circulation magnitude agreement. +Evidence: [causal v3c](evidence/authoritative/steady-causal-analysis-v3c-d20-s3.55-20260808T2245/analysis.json), [return v2c](evidence/authoritative/steady-return-analysis-v2c-d20-s3.55-20260808T2250/analysis.json). -Bounded/descriptive: -- empirical cold-start steadiness through `tU/D=250`; -- circulation-dominated outer-flow interpretation; -- lateral-domain sensitivity over `H/D=12-18`. +## SR interface -Not supported: -- global stability, unique attractor, perturbation decay, or exact optimum; -- independent Navier-Stokes reproduction (no independent NS package is installed); -- pressure/drag/base-bleed/separation closure; -- JFM-ready exact Schottky-Klein derivation or clean immutable production release; -- three-dimensional, experimental, energetic or other-Re generality. +The only current SR link is contextual: persistent rear constant is the dominant tested term; rear-lift feedback is secondary and the tested front term weak over the declared deletion window. Use [SR claim K2](../SR_analysis/CLAIMS.md#k2--persistent-rear-counter-rotation-is-the-dominant-tested-element--current) and its exact evidence paths. This transfers neither Legacy metrics nor mechanism, necessity, uniqueness, or PPO explanation. + +## CCD pending + +CCD is **pending/not frozen for the steady total claim**. No quantitative CCD value contributes to this package's frozen conclusion. Any later interface must remain a separately identified estimand and cannot alone prove the steady mechanism. + +## Bottom line + +Evidence supports a qualified low-deficit steady endpoint and bounded NS diagnostics, and rejects potential-circulation cancellation. Mechanical-energy closure, same-amplitude steady comparison, replicated causality, branch/global stability, and no-slip transfer remain unestablished. diff --git a/src/steady_pinball_theory/contract.py b/src/steady_pinball_theory/contract.py index 5409b17..0b31d21 100644 --- a/src/steady_pinball_theory/contract.py +++ b/src/steady_pinball_theory/contract.py @@ -7,6 +7,59 @@ from __future__ import annotations from dataclasses import dataclass import numpy as np +REVERSE_PRODUCTION_S = (3.55, 5.2) +REVERSE_ROLE_BY_S = {3.55: "same_amplitude_negative_control", 5.2: "historical_stability_candidate"} + + +@dataclass(frozen=True) +class NondimensionalContract: + """2-D per-unit-span lattice-to-project reference contract.""" + + diameter: float + u_inf: float + rho_ref: float + + def __post_init__(self) -> None: + refs = np.asarray([self.diameter, self.u_inf, self.rho_ref], dtype=float) + if not np.isfinite(refs).all() or np.any(refs <= 0): + raise ValueError("diameter, u_inf, and rho_ref must be finite positive references") + + def convert(self, *, x=None, t=None, nu=None, omega=None, Q=None, J=None, + force=None, torque=None, power=None, mass_flux=None, + momentum_flux=None, energy_flux=None, pressure=None) -> dict: + """Convert supplied lattice quantities to project nondimensional values.""" + D, U, rho = float(self.diameter), float(self.u_inf), float(self.rho_ref) + scales = { + "x_star": D, "t_star": D / U, "nu_star": U * D, + "omega_star": U / D, "Q_star": U * D, "J_star": rho * U**2 * D, + "C_F": .5 * rho * U**2 * D, "C_tau": .5 * rho * U**2 * D**2, + "C_P": .5 * rho * U**3 * D, + "mass_flux_star": rho * U * D, + "momentum_flux_star": rho * U**2 * D, + "energy_flux_star": rho * U**3 * D, + "pressure_star": rho * U**2, + } + supplied = {"x_star": x, "t_star": t, "nu_star": nu, + "omega_star": omega, "Q_star": Q, "J_star": J, + "C_F": force, "C_tau": torque, "C_P": power, + "mass_flux_star": mass_flux, "momentum_flux_star": momentum_flux, + "energy_flux_star": energy_flux, "pressure_star": pressure} + out = {} + for name, value in supplied.items(): + if value is None: + continue + array = np.asarray(value, dtype=float) + if not np.isfinite(array).all(): + raise ValueError(f"{name} input must be finite") + converted = array / scales[name] + out[name] = float(converted) if converted.ndim == 0 else converted + out["metadata"] = { + "reference": {"D": D, "U_inf": U, "rho_ref": rho}, + "scope": "two-dimensional per-unit-span", + "definitions": "x/D; tU_inf/D; nu/(U_inf D); omega D/U_inf; Q/(U_inf D); J/(rho_ref U_inf^2 D); mass/(rho_ref U_inf D); momentum/(rho_ref U_inf^2 D); energy/(rho_ref U_inf^3 D); p/(rho_ref U_inf^2); force, torque, power coefficients use one-half dynamic-pressure scales", + } + return out + def wall_velocity(omega: float, rx: float, ry: float) -> tuple[float, float]: """Celeris curved-wall law: (Uw,Vw)=(-omega*ry, omega*rx).""" diff --git a/src/steady_pinball_theory/evidence b/src/steady_pinball_theory/evidence new file mode 120000 index 0000000..5d1333d --- /dev/null +++ b/src/steady_pinball_theory/evidence @@ -0,0 +1 @@ +/home/frank14f/optane/DynamisLab/steady_pinball_theory \ No newline at end of file diff --git a/src/steady_pinball_theory/figures/README.md b/src/steady_pinball_theory/figures/README.md new file mode 100644 index 0000000..f9b4773 --- /dev/null +++ b/src/steady_pinball_theory/figures/README.md @@ -0,0 +1,84 @@ +# Unified steady-pinball figures + +Regenerable reader-facing visualization, not new evidence. CPU-only; no CFD/CUDA ran. + +## Redraw +```bash +PYTHONPATH="$PWD/src" conda run -n pinball_math python src/steady_pinball_theory/plot_results.py --steady "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808" --strip "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-strip-modal-analysis-20260804-v4/analysis.json" --ledger "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/ns-ledger-v2-oracle-bound-d20-20260809/analysis.json" --output "/home/frank14f/DynamisLab/src/steady_pinball_theory/figures" +``` +Defaults permit omitting all flags. Existing output fails unless `--overwrite` is supplied; replacement uses atomic staging and affects only this generated root. + +## Contents and definitions +- `fields/error`: six raw `|q_case-q_in|/U_inf` canvases (dimensionless, not percent). +- `fields/vorticity`: six raw `omega D/U_inf` canvases. Potential exterior values are the analytical irrotational value zero; CFD retains conservative masked numerical curl. +- `fields/streamlines`: total-velocity streamlines, arrows enabled. +- `colorbars` and `annotations`: family-named standalone legends and separate metric assets. +- `plates/{error,vorticity,streamlines}`: publication-friendly PNG/PDF companions with titles and framed metrics. Plates are presentation assets, not pixel-exact arrays. +- `field_metrics.csv`, `profiles_long.csv`, and `summary`: direct redraw data; every summary PNG/PDF has a same-basename CSV. + +Crop indices x=960..1200, y=239..359; exact x/D=[-2,10], y/D=[-3.025,2.975], canvas=241x121 pixels. Arrays are yx, x is horizontal, y is up, origin is the front center. Potential uses these exact CFD lattice coordinates and analytic cylinders; CFD uses solver fluid masks. Scalar images use nearest mapping, one pixel/cell, no axes/titles/padding. Bodies are white with thin black outlines. Streamline paths are vector-rendered, but their PNG canvas has the same exact dimensions and lattice-edge extent. + +Potential and CFD errors use separate pooled-family 97.5-percentile limits: potential `1.131928670277732`, CFD `1.440698623657227`. Both use the same discrete Greys style, but grayscale darkness is only comparable within its named family colorbar. Shared CFD-only symmetric vorticity limit is `+/-2.374693971069057`. Potential displayed/exported vorticity is analytical zero. Values beyond limits map to end bins and raw maxima remain in CSV. Vorticity uses discrete RdBu_r with a forced-white center and no zero contour. + +Crop L2 is `sqrt(integral_common |q_case-q_in|^2 dA / integral_common dA)/U_inf` with tensor trapezoid weights. Profiles are direct differences, not deltas misused with a uniform-reference helper. Accepted x/D=10 direct vector E_inf is `0.0231672176752314`. + +Potential `g_opt=6.1479442395622` and fitted `g=-12.200554143243473` have opposite signs: do not infer a potential mechanism. Body order is front, rear_y_plus, rear_y_minus; accepted is `[0,+Omega,-Omega]`. Stationary is an unsteady reference. Accepted s=3.55 and reverse s=5.2 have mismatched amplitudes. The NS ledger is partial. No mechanism, causality, stability, or closure is established; no CCD numbers are used. + +## Sources +```json +{ + "ledger": { + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/ns-ledger-v2-oracle-bound-d20-20260809/analysis.json", + "sha256": "c5d1395dd438e0f9c1f98489fd94fe309349ee554d0a21752ddfa571fe4d66cb" + }, + "steady_root": { + "files": { + "accepted-s3.55/endpoint.npz": { + "bytes": 7493746, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/accepted-s3.55/endpoint.npz", + "sha256": "b6c70b76c7cf2a2e4330b27fb0d4e82a914b40fde8171076704e825a79ac72db" + }, + "accepted-s3.55/manifest.json": { + "bytes": 7701, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/accepted-s3.55/manifest.json", + "sha256": "0fef464f8acc445a772db9792d8bb751f5f7a1502b4bf4f545833c29b861eeb1" + }, + "qin/endpoint.npz": { + "bytes": 4783748, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/qin/endpoint.npz", + "sha256": "88cbeac1069336716c30d18fd5afd4fc9d6ae87617c7f390b1366fe7098e419b" + }, + "qin/manifest.json": { + "bytes": 6203, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/qin/manifest.json", + "sha256": "e68dc9c2ac5f64f3db024c1c1b0ff729d3403781c2ca6a2cae6740f060ce14ff" + }, + "reverse-s5.2/endpoint.npz": { + "bytes": 8376367, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/reverse-s5.2/endpoint.npz", + "sha256": "760c1e84dd9b7784151ed180d3f16d17619465a08ddb767ce23a87517cc28ec3" + }, + "reverse-s5.2/manifest.json": { + "bytes": 7750, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/reverse-s5.2/manifest.json", + "sha256": "99313ced195070fdeb2daefde792ea50d48ccb59ae211eb2493af021713dea69" + }, + "stationary/endpoint.npz": { + "bytes": 8795812, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/stationary/endpoint.npz", + "sha256": "c2edc9e4173fb6bbde7937314e4984c1c501de75f0dd4916b67aa68388dde8f3" + }, + "stationary/manifest.json": { + "bytes": 7197, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808/stationary/manifest.json", + "sha256": "d9c4d4b8760116011bfe4c077fde8ffda69935c5eb79240aaca5ec9fc2654346" + } + }, + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808" + }, + "strip_analysis": { + "path": "/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-strip-modal-analysis-20260804-v4/analysis.json", + "sha256": "10aba0798dea28b7803318c912e310aae385b0e7e8886e2f1bf533dc37f0a74c" + } 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z{);1x3eR%e9gg_g4J{QOqwJ`f1d0aOIa)j>n+oX`*=#wT<7Z$U3AXMWYGI;av(lHd z19L&fu_X;_CgxZ6E6z{o-1{+C-aIr9()+AE3ZtyrttB;}%)L!v)1^vEcWI#!dxWMh zh!3Azq@Yrmw}upJ6L+APa1wpu=Lm%&b6op{3_&ee%r z_J{nd&3XUt++ml dict[str, float]: ux=np.asarray(ux,dtype=float); uy=np.asarray(uy,dtype=float) if ux.shape != uy.shape or ux.ndim != 1: raise ValueError("profiles must be aligned 1-D arrays") @@ -19,3 +26,870 @@ def two_window_change(samples: np.ndarray) -> float: n=a.shape[0]//2 x=np.mean(a[:n],axis=0); y=np.mean(a[-n:],axis=0) return float(np.sqrt(np.mean((y-x)**2))) + + +def common_exterior_error(reference_velocity, candidate_velocity, centers, radius, *, + bounds=(-3.0, 6.0, -3.0, 3.0), shape=(181, 121), + exclusion_factor=1.1, u_inf=1.0): + """Fixed rectangular tensor quadrature over the declared common exterior.""" + c = np.asarray(centers, dtype=float) + if c.ndim != 2 or c.shape[1] != 2 or not np.isfinite(c).all(): + raise ValueError("centers must be a finite (B,2) array") + vals = np.asarray([radius, exclusion_factor, u_inf, *bounds], dtype=float) + if not np.isfinite(vals).all() or radius <= 0 or exclusion_factor <= 1: + raise ValueError("invalid exterior-error geometry") + if len(bounds) != 4 or bounds[0] >= bounds[1] or bounds[2] >= bounds[3]: + raise ValueError("bounds must be (xmin,xmax,ymin,ymax)") + if (len(shape) != 2 or any(isinstance(x, (bool, np.bool_)) or + not isinstance(x, (int, np.integer)) or x < 3 for x in shape)): + raise ValueError("shape must contain two integers >= 3") + x = np.linspace(bounds[0], bounds[1], shape[0]) + y = np.linspace(bounds[2], bounds[3], shape[1]) + xx, yy = np.meshgrid(x, y, indexing="xy") + points = np.column_stack((xx.ravel(), yy.ravel())) + mask = np.ones(len(points), dtype=bool) + for center in c: + mask &= np.linalg.norm(points - center, axis=1) >= exclusion_factor * radius + points = points[mask] + if not len(points): + raise ValueError("exterior mask retains no points") + wx = np.ones(shape[0]); wx[[0, -1]] = 0.5 + wy = np.ones(shape[1]); wy[[0, -1]] = 0.5 + weights = np.outer(wy, wx).ravel()[mask] + ref = np.asarray(reference_velocity(points), dtype=float) + cand = np.asarray(candidate_velocity(points), dtype=float) + if ref.shape != cand.shape or ref.shape != points.shape or not np.isfinite(ref).all() or not np.isfinite(cand).all(): + raise ValueError("velocity functions must return finite aligned (N,2) arrays") + def wrms(a): + return float(np.sqrt(np.sum(weights * np.sum(a * a, axis=1)) / np.sum(weights))) + absolute = wrms(cand - ref) + disturbance = wrms(ref - np.array([u_inf, 0.0])) + return { + "weighted_RMS": absolute, + "relative_to_reference_disturbance": absolute / disturbance if disturbance > 0 else float("nan"), + "relative_to_uniform_speed": absolute / abs(u_inf) if u_inf != 0 else float("nan"), + "bounds": [float(v) for v in bounds], "shape": [int(v) for v in shape], + "exclusion_factor": float(exclusion_factor), "retained_points": int(len(points)), + "retained_weight": float(np.sum(weights)), "reference_disturbance_RMS": disturbance, + } + + +def reflection_parity_defect(velocity, points, *, u_inf=1.0): + """Polar-vector reflection defect: ux even and uy odd across y=0.""" + p = np.asarray(points, dtype=float) + if p.ndim != 2 or p.shape[1] != 2 or not np.isfinite(p).all() or u_inf <= 0: + raise ValueError("points must be finite (N,2) and u_inf positive") + reflected = p.copy(); reflected[:, 1] *= -1 + v = np.asarray(velocity(p), dtype=float) + vr = np.asarray(velocity(reflected), dtype=float) + if v.shape != p.shape or vr.shape != p.shape or not np.isfinite(v).all() or not np.isfinite(vr).all(): + raise ValueError("velocity must return finite aligned (N,2) arrays") + component = np.column_stack((v[:, 0] - vr[:, 0], v[:, 1] + vr[:, 1])) / u_inf + return {"Linf": float(np.max(np.abs(component))), + "RMS": float(np.sqrt(np.mean(component**2)))} + + + +def affine_profile_sensitivity(base_velocity, direction_velocity, *, u_inf=1.0): + """Analytic derivative and optimum of smooth RMS profile disturbance.""" + u0 = np.asarray(base_velocity, dtype=float) + v = np.asarray(direction_velocity, dtype=float) + if u0.ndim != 2 or u0.shape[1] != 2 or v.shape != u0.shape: + raise ValueError("profile velocities must be aligned (N,2) arrays") + if not np.isfinite(u0).all() or not np.isfinite(v).all() or u_inf <= 0: + raise ValueError("invalid affine profile") + disturbance = u0 - np.array([u_inf, 0.0]) + a = float(np.mean(np.sum(v*v, axis=1))) + b = float(np.mean(np.sum(disturbance*v, axis=1))) + c = float(np.mean(np.sum(disturbance*disturbance, axis=1))) + if a <= 0 or c <= 0: + raise ValueError("nonzero base disturbance and direction are required") + optimum = -b/a + minimum2 = max(0.0, c - b*b/a) + return {"J0": float(np.sqrt(c)), "dJ_dg_at_zero": b/np.sqrt(c), + "g_opt": optimum, "J_opt": float(np.sqrt(minimum2)), + "quadratic": [a, 2*b, c]} + + +def one_sided_profile_error_slopes(base_velocity, direction_velocity, steps, *, u_inf=1.0): + """Declared forward quotients for nonsmooth E_inf_vector; not derivatives.""" + u0 = np.asarray(base_velocity, dtype=float) + v = np.asarray(direction_velocity, dtype=float) + hs = np.asarray(steps, dtype=float) + if u0.ndim != 2 or u0.shape[1] != 2 or v.shape != u0.shape: + raise ValueError("profile velocities must be aligned (N,2) arrays") + if hs.ndim != 1 or len(hs) < 2 or not np.isfinite(hs).all() or np.any(hs <= 0): + raise ValueError("steps must be at least two finite positive values") + e0 = profile_errors(u0[:, 0], u0[:, 1], u_inf=u_inf)["E_inf_vector"] + values = [] + for h in hs: + uh = u0 + h*v + eh = profile_errors(uh[:, 0], uh[:, 1], u_inf=u_inf)["E_inf_vector"] + values.append((eh-e0)/h) + return {"definition": "forward quotient [E(g=h)-E(g=0)]/h", + "steps": hs.tolist(), "slopes": [float(x) for x in values], + "last_change": float(abs(values[-1]-values[-2]))} + + +def gap_flux(velocity, center_a, center_b, radius, *, samples=2001): + """Oriented flux across the shortest open gap, normal=left(tangent).""" + a = np.asarray(center_a, dtype=float); b = np.asarray(center_b, dtype=float) + if a.shape != (2,) or b.shape != (2,) or not np.isfinite([*a,*b,radius]).all(): + raise ValueError("invalid gap geometry") + d = b-a; length = float(np.linalg.norm(d)) + if radius <= 0 or length <= 2*radius: + raise ValueError("gap must be positive") + if isinstance(samples, (bool, np.bool_)) or not isinstance(samples, (int, np.integer)) or samples < 3: + raise ValueError("samples must be an integer >= 3") + tangent = d/length; normal = np.array([-tangent[1], tangent[0]]) + t = np.linspace(radius, length-radius, int(samples)) + points = a + t[:, None]*tangent + trace = np.asarray(velocity(points), dtype=float) @ normal + return {"flux": float(_trapezoid(trace, t)), "normal": normal.tolist(), + "gap_length": length-2*radius, "samples": int(samples)} + + + + +def tensor_trapezoid_weights(x, y): + """Physical composite-trapezoid weights for a rectilinear tensor grid.""" + x=np.asarray(x,dtype=float); y=np.asarray(y,dtype=float) + if x.ndim!=1 or y.ndim!=1 or len(x)<2 or len(y)<2 or np.any(np.diff(x)<=0) or np.any(np.diff(y)<=0) or not np.isfinite(x).all() or not np.isfinite(y).all(): + raise ValueError("x and y must be finite increasing axes") + def widths(a): + w=np.empty_like(a); w[0]=(a[1]-a[0])/2; w[-1]=(a[-1]-a[-2])/2 + w[1:-1]=(a[2:]-a[:-2])/2 + return w + return np.outer(widths(y),widths(x)) + + +def quadrature_l2(field, mask, weights, *, normalizer=None): + """Explicit weighted L2 integral norm, never an RMS.""" + q=np.asarray(field,dtype=float); m=np.asarray(mask,dtype=bool); w=np.asarray(weights,dtype=float) + if q.ndim!=3 or q.shape[-1]!=2 or m.shape!=q.shape[:2] or w.shape!=m.shape or not np.isfinite(w).all() or np.any(w<0): + raise ValueError("invalid aligned L2 field, mask, or weights") + if not m.any() or float(np.sum(w[m]))<=0: raise ValueError("L2 mask retains no positive area") + if not np.isfinite(q[m]).all(): raise ValueError("L2 field is nonfinite on mask") + value=float(np.sqrt(np.sum(w[m]*np.sum(q[m]*q[m],axis=1)))) + result={"L2":value,"retained_measure":float(np.sum(w[m])),"points":int(m.sum()),"definition":"sqrt(integral |q|^2)"} + if normalizer is not None: + n=np.asarray(normalizer,dtype=float) + if n.shape!=q.shape or not np.isfinite(n[m]).all(): raise ValueError("invalid L2 normalizer") + scale=float(np.sqrt(np.sum(w[m]*np.sum(n[m]*n[m],axis=1)))) + if scale<=0: raise ValueError("L2 normalizer is zero") + result.update(normalizer_L2=scale,normalized_L2=value/scale) + return result + + +def conservative_masked_vorticity(x, y, ux, uy, valid_mask): + """Centered curl only where all four axial neighbors are valid.""" + x=np.asarray(x,dtype=float); y=np.asarray(y,dtype=float); ux=np.asarray(ux,dtype=float); uy=np.asarray(uy,dtype=float); valid=np.asarray(valid_mask,dtype=bool) + if ux.shape!=(len(y),len(x)) or uy.shape!=ux.shape or valid.shape!=ux.shape or len(x)<3 or len(y)<3 or np.any(np.diff(x)<=0) or np.any(np.diff(y)<=0) or not np.isfinite(ux).all() or not np.isfinite(uy).all(): + raise ValueError("invalid vorticity grid") + usable=np.zeros_like(valid); usable[1:-1,1:-1]=valid[1:-1,1:-1]&valid[1:-1,:-2]&valid[1:-1,2:]&valid[:-2,1:-1]&valid[2:,1:-1] + omega=np.full(ux.shape,np.nan) + duy_dx=(uy[1:-1,2:]-uy[1:-1,:-2])/(x[2:]-x[:-2])[None,:] + dux_dy=(ux[2:,1:-1]-ux[:-2,1:-1])/(y[2:]-y[:-2])[:,None] + interior=usable[1:-1,1:-1]; values=duy_dx-dux_dy + omega[1:-1,1:-1][interior]=values[interior] + return omega,usable + + +def absolute_vorticity_moments(y, omega, mask, weights): + """Absolute-vorticity weighted transverse centroid and width.""" + y=np.asarray(y,dtype=float); o=np.asarray(omega,dtype=float); m=np.asarray(mask,dtype=bool); w=np.asarray(weights,dtype=float) + if o.shape!=m.shape or w.shape!=m.shape or o.shape[0]!=len(y): raise ValueError("vorticity moments shape mismatch") + use=m&np.isfinite(o); mass=float(np.sum(w[use]*np.abs(o[use]))) + if not use.any() or mass<=0: raise ValueError("vorticity moment mask has zero absolute vorticity") + yy=np.broadcast_to(y[:,None],o.shape); centroid=float(np.sum(w[use]*np.abs(o[use])*yy[use])/mass) + width=float(np.sqrt(np.sum(w[use]*np.abs(o[use])*(yy[use]-centroid)**2)/mass)) + return {"absolute_vorticity_integral":mass,"y_centroid":centroid,"y_width":width,"points":int(use.sum())} + + +def recirculation_observables(x, ux, mask, weights): + """Area and occupied-column streamwise extent where ux is negative.""" + x=np.asarray(x,dtype=float); u=np.asarray(ux,dtype=float); m=np.asarray(mask,dtype=bool); w=np.asarray(weights,dtype=float) + if u.shape!=m.shape or w.shape!=m.shape or u.shape[1]!=len(x) or not np.isfinite(u).all(): raise ValueError("invalid recirculation inputs") + use=m&(u<0); occupied=np.any(use,axis=0) + if not occupied.any(): return {"area":0.0,"x_min":None,"x_max":None,"streamwise_extent":0.0,"points":0} + indices=np.flatnonzero(occupied); xmin=float(x[indices[0]]); xmax=float(x[indices[-1]]) + return {"area":float(np.sum(w[use])),"x_min":xmin,"x_max":xmax,"streamwise_extent":xmax-xmin,"points":int(use.sum())} + + +def wake_deficit_observables(y, ux_profile, mask): + """Frozen station momentum-deficit proxies using line quadrature.""" + y=np.asarray(y,dtype=float); u=np.asarray(ux_profile,dtype=float); m=np.asarray(mask,dtype=bool) + if y.ndim!=1 or u.shape!=y.shape or m.shape!=y.shape or len(y)<2 or not np.isfinite(u).all(): raise ValueError("invalid wake profile") + if not m.any(): raise ValueError("wake profile mask is empty") + deficit=1-u; positive=np.maximum(deficit,0); indicator=(deficit>0).astype(float) + def segments(v): + total=0.0 + for i in range(len(y)-1): + if m[i] and m[i+1]: total+=0.5*(v[i]+v[i+1])*(y[i+1]-y[i]) + return float(total) + return {"momentum_deficit_proxy":segments(positive),"positive_deficit_measure":segments(indicator),"signed_deficit_integral":segments(deficit),"points":int(m.sum())} + +def bilinear_sample_velocity(x, y, ux, uy, points, *, valid_mask=None): + """Sample a rectilinear (y,x)-ordered velocity grid by bilinear interpolation.""" + x=np.asarray(x,dtype=float); y=np.asarray(y,dtype=float) + ux=np.asarray(ux,dtype=float); uy=np.asarray(uy,dtype=float); p=np.asarray(points,dtype=float) + if x.ndim != 1 or y.ndim != 1 or len(x)<2 or len(y)<2 or np.any(np.diff(x)<=0) or np.any(np.diff(y)<=0): raise ValueError("x and y must be strictly increasing 1-D axes") + if ux.shape != (len(y),len(x)) or uy.shape != ux.shape or p.ndim != 2 or p.shape[1] != 2: raise ValueError("fields must be (y,x) and points finite (N,2)") + if not np.isfinite(x).all() or not np.isfinite(y).all() or not np.isfinite(ux).all() or not np.isfinite(uy).all() or not np.isfinite(p).all(): raise ValueError("sampling inputs must be finite") + if np.any((p[:,0]x[-1]) | (p[:,1]y[-1])): raise ValueError("sampling point outside grid") + ix=np.clip(np.searchsorted(x,p[:,0],side="right")-1,0,len(x)-2); iy=np.clip(np.searchsorted(y,p[:,1],side="right")-1,0,len(y)-2) + tx=(p[:,0]-x[ix])/(x[ix+1]-x[ix]); ty=(p[:,1]-y[iy])/(y[iy+1]-y[iy]) + def interp(a): return ((1-tx)*(1-ty)*a[iy,ix]+tx*(1-ty)*a[iy,ix+1]+(1-tx)*ty*a[iy+1,ix]+tx*ty*a[iy+1,ix+1]) + if valid_mask is not None: + m=np.asarray(valid_mask,dtype=bool) + if m.shape != ux.shape: raise ValueError("valid_mask shape mismatch") + if not (m[iy,ix]&m[iy,ix+1]&m[iy+1,ix]&m[iy+1,ix+1]).all(): raise ValueError("bilinear stencil intersects invalid cells") + return np.column_stack((interp(ux),interp(uy))) + + +def ccw_contour_circulation(x, y, ux, uy, center, radii, *, samples=2048, valid_mask=None): + """Geometric-CCW circular line integrals on explicitly ordered contours.""" + center=np.asarray(center,dtype=float); radii=np.asarray(radii,dtype=float) + if center.shape!=(2,) or radii.ndim!=1 or len(radii)==0 or np.any(~np.isfinite(radii)) or np.any(radii<=0): raise ValueError("center and radii must be finite and positive") + if isinstance(samples,(bool,np.bool_)) or not isinstance(samples,(int,np.integer)) or samples<16: raise ValueError("samples must be an integer >= 16") + theta=2*np.pi*np.arange(int(samples))/int(samples); normal=np.column_stack((np.cos(theta),np.sin(theta))); tangent=np.column_stack((-np.sin(theta),np.cos(theta))) + values=[] + for radius in radii: + velocity=bilinear_sample_velocity(x,y,ux,uy,center+radius*normal,valid_mask=valid_mask) + values.append(float(radius*(2*np.pi/int(samples))*np.sum(np.einsum("ij,ij->i",velocity,tangent)))) + return {"orientation":"geometric-CCW","radii":radii.tolist(),"circulation":values,"samples":int(samples)} + + +def preregistered_outer_mask(x, y, centers, radius, *, bounds, exclusion_factor=1.5, wall_margin=2.0): + """Frozen common-exterior point mask for endpoint-field WLS.""" + x=np.asarray(x,dtype=float); y=np.asarray(y,dtype=float); c=np.asarray(centers,dtype=float) + if len(bounds)!=4 or bounds[0]>=bounds[1] or bounds[2]>=bounds[3] or exclusion_factor<=1 or wall_margin<0: raise ValueError("invalid preregistered mask parameters") + xx,yy=np.meshgrid(x,y,indexing="xy"); mask=(xx>=bounds[0])&(xx<=bounds[1])&(yy>=bounds[2])&(yy<=bounds[3]) + mask &= (yy>=y[0]+wall_margin)&(yy<=y[-1]-wall_margin) + for center in c: mask &= (xx-center[0])**2+(yy-center[1])**2 >= (exclusion_factor*radius)**2 + return mask + + +def outer_wls_effective_circulation(observed_delta, unit_model_delta, mask, *, weights=None): + """Origin-constrained vector WLS for one geometric-circulation amplitude.""" + obs=np.asarray(observed_delta,dtype=float); model=np.asarray(unit_model_delta,dtype=float); mask=np.asarray(mask,dtype=bool) + if obs.shape!=model.shape or obs.ndim!=3 or obs.shape[-1]!=2 or mask.shape!=obs.shape[:2]: raise ValueError("WLS arrays must be aligned (y,x,2) with a (y,x) mask") + w=np.ones(mask.shape) if weights is None else np.asarray(weights,dtype=float) + if w.shape!=mask.shape or np.any(~np.isfinite(w)) or np.any(w<0) or not np.isfinite(obs).all() or not np.isfinite(model).all(): raise ValueError("invalid WLS arrays or weights") + use=mask&(w>0); denominator=float(np.sum(w[use]*np.sum(model[use]**2,axis=1))) + if not use.any() or denominator<=0: raise ValueError("WLS mask has no model information") + gamma=float(np.sum(w[use]*np.sum(obs[use]*model[use],axis=1))/denominator); residual=obs[use]-gamma*model[use] + rms=float(np.sqrt(np.sum(w[use]*np.sum(residual**2,axis=1))/np.sum(w[use]))); data_rms=float(np.sqrt(np.sum(w[use]*np.sum(obs[use]**2,axis=1))/np.sum(w[use]))) + return {"gamma_eff":gamma,"weighted_RMS":rms,"relative_RMS":rms/data_rms if data_rms>0 else float("nan"),"points":int(use.sum()),"weight_sum":float(w[use].sum()),"denominator":denominator} + + +def outer_wls_total_model(observed_delta, base_model, unit_model_delta, mask, *, weights=None): + """Fit observed=base+gamma*direction and return the complete prediction.""" + observed=np.asarray(observed_delta,dtype=float); base=np.asarray(base_model,dtype=float) + if observed.shape!=base.shape: + raise ValueError("observed and base model must have identical shapes") + fit=outer_wls_effective_circulation(observed-base,unit_model_delta,mask,weights=weights) + fit["fit_model"]="observed = base_model + gamma_eff * unit_model_delta" + fit["prediction"]=base+fit["gamma_eff"]*np.asarray(unit_model_delta,dtype=float) + return fit + + +def fit_two_point_affine_closure(s_train, gamma_train): + """Exact affine closure from the preregistered two distinct endpoints.""" + s=np.asarray(s_train,dtype=float); g=np.asarray(gamma_train,dtype=float) + if s.shape!=(2,) or g.shape!=(2,) or not np.isfinite(s).all() or not np.isfinite(g).all() or s[0]==s[1]: raise ValueError("closure requires two finite distinct training endpoints") + slope=float((g[1]-g[0])/(s[1]-s[0])); return {"intercept":float(g[0]-slope*s[0]),"slope":slope,"train_s":s.tolist(),"train_gamma":g.tolist()} + + +def predict_affine_closure(closure, s): return float(closure["intercept"]+closure["slope"]*float(s)) + + +def strip_modal_projection(y, velocity, H, *, modes): + """Project a station onto exact downstream Neumann-strip velocity modes.""" + y=np.asarray(y,dtype=float); v=np.asarray(velocity,dtype=float) + if y.ndim!=1 or v.shape!=(len(y),2) or len(y)<3 or not np.isfinite(v).all() or H<=0 or y[0] < -H-1e-12 or y[-1] > H+1e-12: raise ValueError("invalid strip station") + modes=int(modes) + if modes<1: raise ValueError("modes must be positive") + rows=[] + for n in range(1,modes+1): + k=n*np.pi/(2*H); c=np.cos(k*(y+H)); sn=np.sin(k*(y+H)) + rows.append((n,k,float(_trapezoid(v[:,0]*c,y)/H),float(_trapezoid(v[:,1]*sn,y)/H))) + return {"through_flow_zero_mode":float(_trapezoid(v[:,0],y)/(2*H)),"modes":np.asarray(rows),"normalization":"integral/H"} + + +def strip_mode_parity_sector(name): + """Return the allowed Neumann-mode parity for each affine field part.""" + sectors={"base":"even","rear_opposite":"even","common_rear":"odd","front_only":"odd"} + if name not in sectors: raise ValueError(f"unknown strip parity sector {name!r}") + return sectors[name] + + +def propagate_strip_modes(projection, dx): + rows=np.asarray(projection["modes"],dtype=float).copy() + if dx<0: raise ValueError("downstream propagation requires dx >= 0") + rows[:,2:4] *= np.exp(-rows[:,1]*float(dx))[:,None] + return {"through_flow_zero_mode":projection["through_flow_zero_mode"],"modes":rows,"normalization":projection["normalization"]} + + + +def _karman_labels(strengths): + k=np.asarray(strengths,dtype=float) + if k.ndim!=1 or len(k)<4 or not np.isfinite(k).all() or not np.any(k<0) or not np.any(k>0): + raise ValueError("Karman metrics require finite opposite-sign rows") + return k<0,k>0 + + +def karman_observer_mask(initial_positions, spacing, *, half_width=2.5): + """Frozen initial-label mask for a central two-row observer.""" + x=np.asarray(initial_positions,dtype=float) + if x.ndim!=2 or x.shape[1]!=2 or not np.isfinite(x).all() or spacing<=0 or half_width<=0: + raise ValueError("invalid Karman observer inputs") + mask=np.abs(x[:,0])<=float(half_width)*float(spacing)+1e-14 + if mask.sum()<4: raise ValueError("central observer retains too few vortices") + return mask + + +def aligned_position_l2(reference, candidate, mask): + """RMS position mismatch after one best global translation.""" + a=np.asarray(reference,dtype=float); b=np.asarray(candidate,dtype=float); m=np.asarray(mask,dtype=bool) + if a.shape!=b.shape or a.ndim!=2 or a.shape[1]!=2 or m.shape!=(len(a),) or not m.any() or not np.isfinite(a).all() or not np.isfinite(b).all(): + raise ValueError("invalid aligned-position inputs") + delta=b[m]-a[m]; translation=np.mean(delta,axis=0); residual=delta-translation + return {"translation":translation.tolist(),"L2":float(np.sqrt(np.mean(np.sum(residual*residual,axis=1))))} + + +def karman_propagation_metrics(initial, final, strengths, observer_mask, *, spacing, separation): + """Frozen central-window geometry metrics after best global translation.""" + x0=np.asarray(initial,dtype=float); x1=np.asarray(final,dtype=float); k=np.asarray(strengths,dtype=float); m=np.asarray(observer_mask,dtype=bool) + if x0.shape!=x1.shape or x0.ndim!=2 or x0.shape[1]!=2 or k.shape!=(len(x0),) or m.shape!=(len(x0),) or not m.any() or spacing<=0 or separation<=0 or not np.isfinite(x0).all() or not np.isfinite(x1).all(): + raise ValueError("invalid Karman propagation inputs") + lower,upper=_karman_labels(k); fit=aligned_position_l2(x0,x1,m); translation=np.asarray(fit["translation"]); aligned=x1-translation + def row_spacing(points,row): + values=np.sort(points[m&row,0]); + if len(values)<2: raise ValueError("observer row retains too few vortices") + return float(np.mean(np.diff(values))) + lower_spacing=row_spacing(aligned,lower); upper_spacing=row_spacing(aligned,upper) + h0=float(np.mean(x0[m&upper,1])-np.mean(x0[m&lower,1])); h1=float(np.mean(aligned[m&upper,1])-np.mean(aligned[m&lower,1])) + phase0=float(np.mean(x0[m&upper,0])-np.mean(x0[m&lower,0])); phase1=float(np.mean(aligned[m&upper,0])-np.mean(aligned[m&lower,0])) + center0=np.array([np.mean(x0[m&lower,1]),np.mean(x0[m&upper,1])]); center1=np.array([np.mean(aligned[m&lower,1]),np.mean(aligned[m&upper,1])]) + delta=x1[:,None,:]-x1[None,:,:]; distance=np.linalg.norm(delta,axis=2); np.fill_diagonal(distance,np.inf) + return {"best_translation":translation.tolist(),"vortex_position_L2":fit["L2"], + "lower_spacing_drift":(lower_spacing-spacing)/spacing,"upper_spacing_drift":(upper_spacing-spacing)/spacing, + "a_over_h_drift":float(spacing/h1-spacing/h0),"phase_stagger_drift":float((phase1-phase0)/spacing), + "row_center_shift":(center1-center0).tolist(),"minimum_pair_distance":float(np.min(distance))} + + +def normalized_invariant_drift(values, *, scale): + v=np.asarray(values,dtype=float) + if v.ndim!=1 or not len(v) or not np.isfinite(v).all() or not np.isfinite(scale) or scale<0: + raise ValueError("invalid invariant drift inputs") + denominator=max(abs(float(v[0])),float(scale),np.finfo(float).eps) + return float(np.max(np.abs(v-v[0]))/denominator) + + +def _adjacent_fluid_to_bodies(fluid_mask, body_id, body_ids): + """Boolean mask of fluid cells with a four-neighbor listed body cell.""" + fluid=np.asarray(fluid_mask,dtype=bool); body=np.asarray(body_id) + if fluid.shape!=body.shape or fluid.ndim!=2: raise ValueError("fluid_mask/body_id shape mismatch") + ids=tuple(int(v) for v in body_ids) + if not ids: raise ValueError("body_ids must be nonempty") + solid=np.zeros_like(fluid) + for registry_id in ids: solid |= body==registry_id + near=np.zeros_like(fluid) + near[:,1:] |= fluid[:,1:]&solid[:,:-1]; near[:,:-1] |= fluid[:,:-1]&solid[:,1:] + near[1:,:] |= fluid[1:,:]&solid[:-1,:]; near[:-1,:] |= fluid[:-1,:]&solid[1:,:] + return near + + +def near_wall_tangential_speed(x, y, ux, uy, fluid_mask, body_id, centers, radius, *, + body_ids=(1, 2), body_labels=None): + """Sample fluid tangential speed on cells adjacent to listed body interiors.""" + x=np.asarray(x,dtype=float); y=np.asarray(y,dtype=float) + ux=np.asarray(ux,dtype=float); uy=np.asarray(uy,dtype=float) + centers=np.asarray(centers,dtype=float) + if ux.shape!=(len(y),len(x)) or uy.shape!=ux.shape or centers.ndim!=2 or centers.shape[1]!=2: + raise ValueError("invalid near-wall velocity grid or centers") + if not np.isfinite(radius) or radius<=0: raise ValueError("radius must be positive") + near=_adjacent_fluid_to_bodies(fluid_mask,body_id,body_ids) + labels=list(body_labels) if body_labels is not None else [f"body_{i}" for i in body_ids] + if len(labels)!=len(body_ids): raise ValueError("body_labels length mismatch") + xx,yy=np.meshgrid(x,y,indexing="xy"); report={} + for registry_id,label in zip(body_ids,labels): + solid=np.asarray(body_id)==int(registry_id) + mask=np.zeros_like(near) + mask[:,1:] |= near[:,1:]&solid[:,:-1]; mask[:,:-1] |= near[:,:-1]&solid[:,1:] + mask[1:,:] |= near[1:,:]&solid[:-1,:]; mask[:-1,:] |= near[:-1,:]&solid[1:,:] + if not mask.any(): + report[label]={"availability":"unavailable_no_adjacent_fluid","points":0} + continue + cx,cy=centers[int(registry_id)]; dx=xx[mask]-cx; dy=yy[mask]-cy + rr=np.hypot(dx,dy); usable=rr>0 + if not np.any(usable): + report[label]={"availability":"unavailable_degenerate_radius","points":int(mask.sum())} + continue + tx=-dy[usable]/rr[usable]; ty=dx[usable]/rr[usable] + speed=ux[mask][usable]*tx+uy[mask][usable]*ty + report[label]={"availability":"available","points":int(usable.sum()), + "mean_tangential_speed":float(np.mean(speed)), + "max_abs_tangential_speed":float(np.max(np.abs(speed))), + "rms_tangential_speed":float(np.sqrt(np.mean(speed*speed)))} + return {"definition":"fluid cells adjacent to body; geometric-CCW tangent (-dy,dx)/r", + "radius":float(radius),"bodies":report} + + +def wall_vorticity_production_proxy(x, y, ux, uy, fluid_mask, body_id, centers, radius, *, + body_ids=(1, 2), body_labels=None, min_pairs=8): + """Fail-closed wall-vorticity proxy from radial tangential gradient when supported.""" + x=np.asarray(x,dtype=float); y=np.asarray(y,dtype=float) + ux=np.asarray(ux,dtype=float); uy=np.asarray(uy,dtype=float) + centers=np.asarray(centers,dtype=float); fluid=np.asarray(fluid_mask,dtype=bool) + if isinstance(min_pairs,(bool,np.bool_)) or not isinstance(min_pairs,(int,np.integer)) or min_pairs<1: + raise ValueError("min_pairs must be a positive integer") + near=_adjacent_fluid_to_bodies(fluid,body_id,body_ids) + labels=list(body_labels) if body_labels is not None else [f"body_{i}" for i in body_ids] + xx,yy=np.meshgrid(x,y,indexing="xy"); report={} + for registry_id,label in zip(body_ids,labels): + solid=np.asarray(body_id)==int(registry_id) + mask=np.zeros_like(near) + mask[:,1:] |= near[:,1:]&solid[:,:-1]; mask[:,:-1] |= near[:,:-1]&solid[:,1:] + mask[1:,:] |= near[1:,:]&solid[:-1,:]; mask[:-1,:] |= near[:-1,:]&solid[1:,:] + iy,ix=np.nonzero(mask); pairs=[] + cx,cy=centers[int(registry_id)] + for i,j in zip(iy,ix): + dx=xx[i,j]-cx; dy=yy[i,j]-cy; rr=float(np.hypot(dx,dy)) + if rr<=0: continue + nx,ny=dx/rr,dy/rr; tx,ty=-ny,nx + # One lattice step outward along the discrete neighbor closest to +n. + candidates=((i,j+1,1.,0.),(i,j-1,-1.,0.),(i+1,j,0.,1.),(i-1,j,0.,-1.)) + best=None; best_dot=-np.inf + for ii,jj,sx,sy in candidates: + if ii<0 or jj<0 or ii>=fluid.shape[0] or jj>=fluid.shape[1] or not fluid[ii,jj]: continue + dot=sx*nx+sy*ny + if dot>best_dot: best_dot=dot; best=(ii,jj,float(np.hypot(xx[ii,jj]-xx[i,j],yy[ii,jj]-yy[i,j]))) + if best is None or best_dot<=0 or best[2]<=0: continue + ii,jj,ds=best + u_theta0=ux[i,j]*tx+uy[i,j]*ty; u_theta1=ux[ii,jj]*tx+uy[ii,jj]*ty + pairs.append((u_theta1-u_theta0)/ds) + if len(pairs)= 8") + near=_adjacent_fluid_to_bodies(fluid,body_id,body_ids) + labels=list(body_labels) if body_labels is not None else [f"body_{i}" for i in body_ids] + xx,yy=np.meshgrid(x,y,indexing="xy"); report={} + for registry_id,label in zip(body_ids,labels): + solid=np.asarray(body_id)==int(registry_id) + mask=np.zeros_like(near) + mask[:,1:] |= near[:,1:]&solid[:,:-1]; mask[:,:-1] |= near[:,:-1]&solid[:,1:] + mask[1:,:] |= near[1:,:]&solid[:-1,:]; mask[:-1,:] |= near[:-1,:]&solid[1:,:] + if mask.sum()6: + report[label]={"availability":"unavailable_ambiguous_topology","points":int(mask.sum()), + "sign_changes":len(flips),"angles":flips} + continue + report[label]={"availability":"available","points":int(mask.sum()),"sign_changes":len(flips), + "angles":flips,"observable":"near-wall ux zero crossings; not proved separation line"} + return {"definition":"fail-closed separation/reattachment estimator from near-wall ux","bodies":report} + + +def control_volume_streamwise_momentum_ledger(x, y, ux, uy, rho, fluid_mask, *, + x_left, x_right, force_history=None, + viscosity=None, cs2=1.0/3.0): + """Incomplete streamwise momentum ledger between two stations; never a closed balance.""" + x=np.asarray(x,dtype=float); y=np.asarray(y,dtype=float) + ux=np.asarray(ux,dtype=float); uy=np.asarray(uy,dtype=float); rho=np.asarray(rho,dtype=float) + fluid=np.asarray(fluid_mask,dtype=bool) + if ux.shape!=(len(y),len(x)) or uy.shape!=ux.shape or rho.shape!=ux.shape or fluid.shape!=ux.shape: + raise ValueError("invalid control-volume fields") + if not np.isfinite([x_left,x_right,cs2]).all() or x_right<=x_left or cs2<=0: + raise ValueError("invalid control-volume stations or cs2") + def station(xq): + ix=int(np.argmin(np.abs(x-xq))); rows=fluid[:,ix].copy(); rows[[0,-1]]=False + if rows.sum()<3: raise ValueError("control-volume station retains too few fluid rows") + yy=y[rows]; uu=ux[rows,ix]; vv=uy[rows,ix]; rr=rho[rows,ix] + pressure=cs2*(rr-1.0) + return {"x":float(x[ix]),"points":int(rows.sum()), + "mass_flux":float(_trapezoid(rr*uu,yy)), + "momentum_flux":float(_trapezoid(rr*uu*uu,yy)), + "pressure_force_proxy":float(_trapezoid(-pressure,yy)), + "pressure_model":"LBM weak-compressible p~cs2(rho-1); not incompressible NS pressure"} + left=station(x_left); right=station(x_right) + body_force={"availability":"unavailable_no_force_history","total_Fx_mean":None} + if force_history is not None: + force=np.asarray(force_history,dtype=float) + if force.ndim!=2 or force.shape[1]<8 or not np.isfinite(force).all(): + raise ValueError("force_history must be finite with Fx columns") + tail=force[-min(10,len(force)):,2:] + total_fx=float(np.mean(tail[:,0]+tail[:,2]+tail[:,4])) + body_force={"availability":"available_from_force_history_tail", + "tail_samples":int(len(tail)),"total_Fx_mean":total_fx, + "normalization":"Celeris force-history mean; not certified CV body integral"} + viscous={"availability":"unavailable_gradient_unsupported", + "reason":"face viscous stress requires supported wall-normal gradients on both stations"} + if viscosity is not None: + if not np.isfinite(viscosity) or float(viscosity)<=0: + raise ValueError("viscosity must be finite and positive when provided") + # Even with nu known, this ledger does not assemble a complete NS stress integral. + viscous={"availability":"unavailable_incomplete_stress_tensor", + "viscosity":float(viscosity), + "note":"viscosity present but full face/wall viscous stress closure is absent"} + residual_proxy=None + if body_force["total_Fx_mean"] is not None: + residual_proxy=float((right["momentum_flux"]+right["pressure_force_proxy"]) + -(left["momentum_flux"]+left["pressure_force_proxy"]) + -body_force["total_Fx_mean"]) + return {"definition":"streamwise momentum ledger between rear-gap plane and observer; incomplete", + "balance_status":"incomplete_not_closed", + "left":left,"right":right,"body_force":body_force,"viscous_stress":viscous, + "residual_proxy_if_partial":residual_proxy, + "claim_limit":"NEVER a closed momentum balance; pressure is weak-compressible proxy"} + + +def torque_power_availability(force_history=None, *, torque_history=None): + """Torque/power are unavailable unless an explicit torque history exists.""" + if torque_history is not None: + tau=np.asarray(torque_history,dtype=float) + if tau.ndim!=2 or tau.shape[1]<1 or not np.isfinite(tau).all(): + raise ValueError("torque_history must be finite 2-D") + return {"availability":"available_torque_history","samples":int(len(tau)), + "mean_torque":np.mean(tau,axis=0).tolist()} + if force_history is not None: + return {"availability":"unavailable_no_torque_history", + "note":"force_history provides Fx/Fy only; torque/power not inferred"} + return {"availability":"unavailable_no_torque_history","note":"no force or torque history provided"} + + +def fit_linear_composite(observed, components, mask, *, names=None): + """Unweighted vector least squares on listed component fields. + + Each component must share the observed field shape (...,2). Returns + coefficients, predicted field, residual, condition number, and dof count. + """ + obs = np.asarray(observed, dtype=float) + m = np.asarray(mask, dtype=bool) + if obs.ndim != 3 or obs.shape[-1] != 2 or m.shape != obs.shape[:2] or not m.any(): + raise ValueError("invalid composite fit inputs") + cols = [] + comp_names = [] + for item in components: + if isinstance(item, tuple): + name, field = item + else: + name, field = None, item + field = np.asarray(field, dtype=float) + if field.shape != obs.shape or not np.isfinite(field[m]).all(): + raise ValueError("component shape or values invalid on mask") + cols.append(field[m].reshape(-1)) + comp_names.append(name) + if names is not None and list(names) != comp_names: + raise ValueError("names must match components") + y = obs[m].reshape(-1) + A = np.column_stack(cols) + coeff, _, rank, sv = np.linalg.lstsq(A, y, rcond=1e-12) + pred = np.tensordot(A, coeff, axes=(1, 0)).reshape(obs[m].shape) + residual = obs[m] - pred + full = np.zeros_like(obs) + full[m] = pred.reshape(obs[m].shape) + res_full = np.zeros_like(obs) + res_full[m] = residual.reshape(obs[m].shape) + cond = float(sv[0] / sv[-1]) if sv[-1] > 0 else float("inf") + return { + "names": comp_names, + "coefficients": {n: float(v) for n, v in zip(comp_names, coeff)}, + "rank": int(rank), + "condition_number": cond, + "dof": int(len(coeff)), + "prediction": full, + "residual": res_full, + "weighted_RMS": float(np.sqrt(np.mean(np.sum(residual * residual, axis=1)))), + "relative_RMS": float(np.sqrt(np.mean(np.sum(residual * residual, axis=1))) / + max(float(np.sqrt(np.mean(np.sum(y * y)))), np.finfo(float).eps)), + } + + +def profile_station_errors(delta, x, y, station, *, fluid_mask=None, exclude_outer_rows=2): + """Full-profile E_inf/L2 at one x/D station on common fluid rows.""" + x = np.asarray(x, dtype=float) + ix = int(np.argmin(np.abs(x - float(station)))) + d = np.asarray(delta, dtype=float)[:, ix, :] + if fluid_mask is not None: + rows = np.asarray(fluid_mask, dtype=bool)[:, ix].copy() + if exclude_outer_rows: + rows[:exclude_outer_rows] = False + rows[-exclude_outer_rows:] = False + d = d[rows] + if d.size == 0: + raise ValueError("empty profile at station") + return profile_errors(d[:, 0], d[:, 1], u_inf=1.0) + + +def held_out_improvement(baseline_residual, candidate_residual, mask): + """Relative held-out L2 improvement of candidate over baseline.""" + m = np.asarray(mask, dtype=bool) + b = np.asarray(baseline_residual, dtype=float) + c = np.asarray(candidate_residual, dtype=float) + if b.shape != c.shape or m.shape != b.shape[:2]: + raise ValueError("held-out fields must align") + # unit weights for relative comparison on same mask + w = np.ones(m.shape, dtype=float) + lb = quadrature_l2(b, m, w)["L2"] + lc = quadrature_l2(c, m, w)["L2"] + return {"baseline_L2": lb, "candidate_L2": lc, + "relative_improvement": float((lb - lc) / max(lb, np.finfo(float).eps)), + "significant": bool(lc < 0.9 * lb)} + + +# NS-first dimensional diagnostics: resolved CPU arrays only. +def torque_to_actuator_power(torque, angular_velocity, *, torque_ownership, rho_ref, u_ref, diameter): + """Convert raw 2-D per-span torque and return actuator-to-fluid power.""" + from .contract import NondimensionalContract + tau=np.asarray(torque,float); omega=np.asarray(angular_velocity,float) + if tau.ndim not in (1,2) or tau.shape!=omega.shape or not tau.size or not np.isfinite(tau).all() or not np.isfinite(omega).all(): raise ValueError("torque/angular_velocity must be finite aligned samples[,bodies]") + if torque_ownership not in ("fluid_on_body","actuator_on_fluid"): raise ValueError("invalid torque_ownership") + contract=NondimensionalContract(float(diameter),float(u_ref),float(rho_ref)) + actuator_tau=-tau if torque_ownership=="fluid_on_body" else tau + power=actuator_tau*omega + total=power if power.ndim==1 else power.sum(axis=1) + torque_scale=.5*rho_ref*u_ref**2*diameter**2 + power_scale=.5*rho_ref*u_ref**3*diameter + raw_c_tau=tau/torque_scale; actuator_c_tau=actuator_tau/torque_scale + return {"torque_ownership":torque_ownership,"raw_torque":tau, + "raw_torque_interpretation":f"{torque_ownership}; Celeris reads are lattice cut-link sums, mean per accumulated LBM step when normalize=True", + "sampling_semantics":{"normalize_true":"mean per accumulated LBM step exactly once","kernel_reduction":"sum of cut-link lattice loads","normalizations_not_applied":["force/torque coefficient","body count","density","dynamic pressure","span"],"span":"two-dimensional per-unit-span"}, + "sign_contract":"omega>0 geometric CCW; power>0 actuator-to-fluid", + "actuator_torque":actuator_tau,"raw_C_tau":raw_c_tau,"actuator_C_tau":actuator_c_tau, + "power_per_body":power,"total_power":total,"mean_total_power":float(total.mean()), + "torque_scale":float(torque_scale),"power_scale":float(power_scale), + "C_P_samples":total/power_scale,"C_P":float(total.mean()/power_scale), + "nondimensional_reference":contract.convert()["metadata"], + "dimensions":{"torque":"M L^2 T^-2/span","power":"M L^2 T^-3/span","C_tau":"1","C_P":"1"}} + + +def _masked_line_trapezoid(y, value, mask): + y=np.asarray(y,float); v=np.asarray(value,float); m=np.asarray(mask,bool) + if y.ndim!=1 or v.shape[0]!=len(y) or m.shape!=y.shape or len(y)<2: raise ValueError("line fields must align") + use=m[:-1]&m[1:] + if not use.any(): raise ValueError("station mask retains no complete segment") + shape=(len(y)-1,)+(1,)*(v.ndim-1); factor=(np.diff(y)*use).reshape(shape) + return np.sum(.5*(v[:-1]+v[1:])*factor,axis=0) + + +def station_flux_metrics(y, ux, uy, rho, pressure, mask, *, normal=(1.,0.), q_in=None): + """Mass, vector momentum, kinetic and mechanical-energy flux across a frozen station normal.""" + y=np.asarray(y,float); ux=np.asarray(ux,float); uy=np.asarray(uy,float); rho=np.asarray(rho,float); pressure=np.asarray(pressure,float); mask=np.asarray(mask,bool); n=np.asarray(normal,float) + if y.ndim!=1 or any(a.shape!=y.shape for a in (ux,uy,rho,pressure,mask)): raise ValueError("station profiles must be aligned 1-D") + if n.shape!=(2,) or not np.isfinite(n).all() or not np.isclose(np.linalg.norm(n),1,atol=1e-12,rtol=0): raise ValueError("normal must be a finite unit vector") + if np.any(np.diff(y)<=0) or np.any(rho[mask]<=0) or not all(np.isfinite(a[mask]).all() for a in (ux,uy,rho,pressure)): raise ValueError("invalid station values") + u=np.column_stack((ux,uy)); un=u@n; speed2=ux**2+uy**2; momentum=rho[:,None]*u*un[:,None]+pressure[:,None]*n + out={"mass_flux":float(_masked_line_trapezoid(y,rho*un,mask)),"momentum_flux":np.asarray(_masked_line_trapezoid(y,momentum,mask)), + "kinetic_energy_flux":float(_masked_line_trapezoid(y,.5*rho*speed2*un,mask)),"pressure_work_flux":float(_masked_line_trapezoid(y,pressure*un,mask)), + "mechanical_energy_flux":float(_masked_line_trapezoid(y,(pressure+.5*rho*speed2)*un,mask)),"normal":n.tolist(),"retained_points":int(mask.sum()), + "dimensions":{"mass_flux":"M T^-1/span","momentum_flux":"M L T^-2/span","energy_flux":"M L^2 T^-3/span"}} + if q_in is not None: + keys=("mass_flux","momentum_flux","kinetic_energy_flux","pressure_work_flux","mechanical_energy_flux") + if not isinstance(q_in,dict) or any(k not in q_in for k in keys+("normal",)) or not np.allclose(q_in["normal"],n,atol=1e-12,rtol=0): raise ValueError("q_in must be matched with the same frozen normal") + out["matched_q_in"]={k:q_in[k] for k in keys}; out["delta_from_q_in"]={k:out[k]-q_in[k] for k in keys} + return out + + +def volume_viscous_dissipation(x,y,ux,uy,viscosity,mask,*,density=None): + """Integrate 2*mu*S:S over valid centered stencils of a masked rectilinear grid.""" + x=np.asarray(x,float); y=np.asarray(y,float); ux=np.asarray(ux,float); uy=np.asarray(uy,float); m=np.asarray(mask,bool) + if ux.shape!=(len(y),len(x)) or uy.shape!=ux.shape or m.shape!=ux.shape or min(len(x),len(y))<3: raise ValueError("invalid masked rectilinear grid") + if np.any(np.diff(x)<=0) or np.any(np.diff(y)<=0) or not np.isfinite(ux[m]).all() or not np.isfinite(uy[m]).all() or not np.isfinite(viscosity) or viscosity<=0: raise ValueError("invalid grid, field, or viscosity") + use=np.zeros_like(m); use[1:-1,1:-1]=m[1:-1,1:-1]&m[1:-1,:-2]&m[1:-1,2:]&m[:-2,1:-1]&m[2:,1:-1] + if not use.any(): raise ValueError("dissipation mask retains no centered stencil") + uxx=(ux[1:-1,2:]-ux[1:-1,:-2])/(x[2:]-x[:-2])[None,:]; uyx=(uy[1:-1,2:]-uy[1:-1,:-2])/(x[2:]-x[:-2])[None,:] + uxy=(ux[2:,1:-1]-ux[:-2,1:-1])/(y[2:]-y[:-2])[:,None]; uyy=(uy[2:,1:-1]-uy[:-2,1:-1])/(y[2:]-y[:-2])[:,None] + if density is None: mu=np.full(ux.shape,float(viscosity)); kind="dynamic" + else: + density=np.asarray(density,float) + if density.shape!=ux.shape or np.any(density[use]<=0) or not np.isfinite(density[use]).all(): raise ValueError("density must be finite positive and aligned") + mu=viscosity*density; kind="kinematic_with_density" + phi=np.full(ux.shape,np.nan); core=2*uxx**2+2*uyy**2+(uxy+uyx)**2; core_use=use[1:-1,1:-1] + phi[1:-1,1:-1][core_use]=mu[1:-1,1:-1][core_use]*core[core_use]; w=tensor_trapezoid_weights(x,y) + requested_area=float(w[m].sum()); usable_area=float(w[use].sum()) + return {"viscous_dissipation":float(np.sum(w[use]*phi[use])),"dissipation_density":phi,"usable_mask":use, + "retained_area":usable_area,"requested_fluid_area":requested_area,"usable_stencil_area":usable_area, + "usable_stencil_fraction":usable_area/requested_area,"omitted_fluid_area":requested_area-usable_area, + "near_body_omission":"partial_centered_stencil_omission_at_mask_boundaries", + "points":int(use.sum()),"requested_fluid_points":int(m.sum()),"viscosity_kind":kind, + "definition":"partial CV-fluid integral 2*mu*S:S on usable centered stencils", + "balance_status":"partial_not_closed_energy","dimensions":"M L^2 T^-3/span"} + + +def gap_mass_momentum_flux(velocity,density,center_a,center_b,radius,*,samples=2001): + """Frozen a-to-b orientation; Q_g=int u.n, mass=int rho*u.n, J_g=int rho*(u.n)^2.""" + base=gap_flux(velocity,center_a,center_b,radius,samples=samples); a=np.asarray(center_a,float); b=np.asarray(center_b,float); length=float(np.linalg.norm(b-a)) + t=np.linspace(radius,length-radius,int(samples)); points=a+t[:,None]*(b-a)[None,:]/length; v=np.asarray(velocity(points),float); rho=np.asarray(density(points),float) + if v.shape!=points.shape or rho.shape!=(len(points),) or np.any(rho<=0) or not np.isfinite(rho).all(): raise ValueError("density must return finite positive gap samples") + un=v@np.asarray(base["normal"]); base.update(Q_g=base.pop("flux"),mass_flux=float(_trapezoid(rho*un,t)),J_g=float(_trapezoid(rho*un**2,t)),density_min=float(rho.min()),density_max=float(rho.max()),orientation="center_a to center_b; normal=left(tangent), frozen by argument order",dimensions={"Q_g":"L^2 T^-1","mass_flux":"M T^-1/span","J_g":"M L T^-2/span"}) + return base + + +def control_volume_mechanical_energy_ledger(left_station,right_station,*,viscous_dissipation=None,actuator_power_to_fluid=None,lateral_mechanical_energy_flux=None,storage_rate=None): + """Report resolved energy terms; compute residual only when every signed term exists.""" + def e(q,label): + if not isinstance(q,dict) or "mechanical_energy_flux" not in q or not np.isfinite(q["mechanical_energy_flux"]): raise ValueError(f"{label} station lacks finite mechanical_energy_flux") + return float(q["mechanical_energy_flux"]) + left=e(left_station,"left"); right=e(right_station,"right"); supplied={"viscous_dissipation":viscous_dissipation,"actuator_power_to_fluid":actuator_power_to_fluid,"lateral_outward_mechanical_energy_flux":lateral_mechanical_energy_flux,"storage_rate":storage_rate} + for v in supplied.values(): + if v is not None and not np.isfinite(v): raise ValueError("ledger terms must be finite") + complete=all(v is not None for v in supplied.values()); residual=None if not complete else float(right-left+lateral_mechanical_energy_flux+viscous_dissipation+storage_rate-actuator_power_to_fluid) + resolved={"left_mechanical_energy_flux":left,"right_mechanical_energy_flux":right}; resolved.update({k:{"availability":"available" if v is not None else "unavailable_not_supplied","value":None if v is None else float(v)} for k,v in supplied.items()}) + return {"definition":"right-left + lateral_out + dissipation + storage - actuator_power_to_fluid = residual","resolved_terms":resolved,"closure_available":complete,"balance_status":"residual_available" if complete else "incomplete_not_closed","residual":residual,"claim_limit":"No closure/residual unless every signed term is supplied."} + + +def fit_conservation_model(features,target,*,feature_names,feature_dimensions,target_dimension,feature_scales,target_scale,held_out=None): + """Dimension-audited low-dimensional scalar closure fit; never fits velocity fields.""" + X=np.asarray(features,float); y=np.asarray(target,float); names=list(feature_names); dims=list(feature_dimensions); scales=np.asarray(feature_scales,float) + if X.ndim!=2 or y.shape!=(X.shape[0],) or X.shape[1]!=len(names) or len(dims)!=len(names): raise ValueError("features/target metadata dimensions mismatch") + if X.shape[0]<=X.shape[1] or not np.isfinite(X).all() or not np.isfinite(y).all(): raise ValueError("finite overdetermined scalar data required") + if len(set(names))!=len(names) or any(not isinstance(d,str) or not d for d in dims) or not isinstance(target_dimension,str) or not target_dimension: raise ValueError("explicit names and dimensions required") + if scales.shape!=(X.shape[1],) or np.any(scales<=0) or not np.isfinite(scales).all() or not np.isfinite(target_scale) or target_scale<=0: raise ValueError("positive dimensional scales required") + A=X/scales; z=y/target_scale; beta,_,rank,sv=np.linalg.lstsq(A,z,rcond=1e-12); coef=target_scale*beta/scales; pred=X@coef; residual=y-pred; dof=len(y)-rank + sigma2=float(residual@residual/dof) if dof>0 and rank==X.shape[1] else None; cov=None if sigma2 is None else sigma2*np.linalg.inv(X.T@X) + result={"feature_names":names,"feature_dimensions":dims,"target_dimension":target_dimension,"coefficient_dimensions":[f"({target_dimension})/({d})" for d in dims],"coefficients":coef,"rank":int(rank),"condition_number":float(sv[0]/sv[-1]) if sv[-1]>0 else float("inf"),"prediction":pred,"residual":residual,"residual_RMS":float(np.sqrt(np.mean(residual**2))),"coefficient_covariance":cov,"uncertainty_available":cov is not None,"model_kind":"scalar low-dimensional conservation closure"} + if held_out is not None: + if not isinstance(held_out,(tuple,list)) or len(held_out)!=2: raise ValueError("held_out must be (features,target)") + Xh=np.asarray(held_out[0],float); yh=np.asarray(held_out[1],float) + if Xh.ndim!=2 or Xh.shape[1]!=X.shape[1] or yh.shape!=(len(Xh),) or not np.isfinite(Xh).all() or not np.isfinite(yh).all(): raise ValueError("held-out dimensions mismatch") + ph=Xh@coef; result["held_out"]={"prediction":ph,"target":yh,"residual":yh-ph,"RMS":float(np.sqrt(np.mean((yh-ph)**2))),"samples":int(len(yh))} + return result + + +def predict_conservation_model(model,features,*,feature_names,feature_dimensions): + """Predict scalar observables after exact feature-name and dimension validation.""" + if list(feature_names)!=model.get("feature_names") or list(feature_dimensions)!=model.get("feature_dimensions"): raise ValueError("prediction feature names/dimensions do not match model") + X=np.asarray(features,float); c=np.asarray(model["coefficients"],float) + if X.ndim not in (1,2) or X.shape[-1]!=len(c) or not np.isfinite(X).all(): raise ValueError("invalid prediction features") + return X@c + + +def weak_compressible_pressure_proxy(rho, *, rho_ref, cs2=1.0/3.0): + """LBM weak-compressible pressure proxy p'=cs2*(rho-rho_ref); never a missing-pressure sentinel.""" + density=np.asarray(rho,float) + if not np.isfinite(density).all() or np.any(density<=0) or not np.isfinite([rho_ref,cs2]).all() or rho_ref<=0 or cs2<=0: + raise ValueError("pressure proxy requires finite positive density, rho_ref, and cs2") + return {"values":cs2*(density-float(rho_ref)),"model":"weak-compressible pressure proxy p'=cs2*(rho-rho_ref)", + "cs2":float(cs2),"rho_ref":float(rho_ref),"availability":"available_weak_compressible_proxy", + "claim_limit":"Not incompressible Navier-Stokes pressure; zero values mean rho=rho_ref, never unavailable pressure."} + + +def rectangular_control_volume_fluxes(x,y,ux,uy,rho,fluid_mask,front_center,diameter,*, + rho_ref,cs2=1.0/3.0,viscosity=None): + """Four-face endpoint spatial flux ledger on the nearest body-enclosing lattice rectangle.""" + x=np.asarray(x,float); y=np.asarray(y,float); ux=np.asarray(ux,float); uy=np.asarray(uy,float) + rho=np.asarray(rho,float); fluid=np.asarray(fluid_mask,bool); center=np.asarray(front_center,float) + shape=(len(y),len(x)) + if any(a.shape!=shape for a in (ux,uy,rho,fluid)) or center.shape!=(2,) or min(len(x),len(y))<3: + raise ValueError("invalid control-volume grid or front center") + if np.any(np.diff(x)<=0) or np.any(np.diff(y)<=0) or not np.isfinite([*x,*y,*center,diameter,rho_ref,cs2]).all() or diameter<=0: + raise ValueError("control-volume coordinates and references must be finite and valid") + targets=(center[0]-2*diameter,center[0]+10*diameter,center[1]-3*diameter,center[1]+3*diameter) + il,ir,jb,jt=(int(np.argmin(abs(x-targets[0]))),int(np.argmin(abs(x-targets[1]))), + int(np.argmin(abs(y-targets[2]))),int(np.argmin(abs(y-targets[3])))) + if not (0=1: raise ValueError("invalid branch margin/hysteresis") + den=dr*dr+da*da + if np.any(den<=0): raise ValueError("branch order undefined when both endpoint distances vanish") + value=(dr*dr-da*da)/den + state=np.zeros(value.shape,dtype=np.int8) + prior=0 if previous is None else int(previous) + if prior not in (-1,0,1): raise ValueError("previous branch state must be -1, 0, or 1") + for i,v in enumerate(value.flat): + threshold=margin+hysteresis if prior==0 else max(0.,margin-hysteresis) + if prior==1: prior=1 if v>=-threshold else -1 + elif prior==-1: prior=-1 if v<=threshold else 1 + else: prior=1 if v>threshold else (-1 if v<-threshold else 0) + state.flat[i]=prior + return {"m":value,"state":state,"state_meaning":{"1":"accepted-nearer","-1":"reverse-nearer","0":"unresolved"}, + "margin":float(margin),"hysteresis":float(hysteresis),"definition":"m=(dR^2-dA^2)/(dR^2+dA^2); state uses margin and Schmitt hysteresis"} diff --git a/src/steady_pinball_theory/plot_results.py b/src/steady_pinball_theory/plot_results.py new file mode 100644 index 0000000..46a1a74 --- /dev/null +++ b/src/steady_pinball_theory/plot_results.py @@ -0,0 +1,229 @@ +#!/usr/bin/env python3 +"""CPU-only, lattice-exact reader plots from authenticated steady evidence.""" +from __future__ import annotations +import argparse,csv,hashlib,json,os,shutil,tempfile +from dataclasses import dataclass +from pathlib import Path +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt +from matplotlib.colorbar import ColorbarBase +from matplotlib.colors import BoundaryNorm,ListedColormap +from matplotlib.patches import Circle +import numpy as np +from PIL import Image +from steady_pinball_theory.metrics import conservative_masked_vorticity,tensor_trapezoid_weights,profile_errors +from steady_pinball_theory.runner import load_validate_artifact +from steady_pinball_theory.theory import affine_velocity,strip_basis_affine + +HERE=Path(__file__).resolve().parent +DEFAULT_STEADY=Path("/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-contract-v5-torque-d20-20260808") +DEFAULT_STRIP=Path("/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/steady-strip-modal-analysis-20260804-v4/analysis.json") +DEFAULT_LEDGER=Path("/home/frank14f/optane/DynamisLab/steady_pinball_theory/authoritative/ns-ledger-v2-oracle-bound-d20-20260809/analysis.json") +DEFAULT_OUTPUT=HERE/"figures"; STATIONS=(2.,4.,6.,10.); DPI=100; PRIMARY=0.0231672176752314 +@dataclass +class Case: + id:str; label:str; family:str; pname:str; parameter:float|None + ux:np.ndarray; uy:np.ndarray; fluid:np.ndarray; vort:np.ndarray; vort_mask:np.ndarray + source_path:str; source_hash:str + +def sha(path): + h=hashlib.sha256() + with Path(path).open("rb") as f: + for b in iter(lambda:f.read(1<<20),b""): h.update(b) + return h.hexdigest() +def discrete_colormap(name,lo,hi,bins,*,center_white=False): + if not lo=1.8)&(X<=10)&(abs(Y)<=1.5)&(c.ux/U<0); near=c.vort_mask&(X>=1.8)&(X<4)&(abs(Y)<=3); diag.append({"case":c.id,"label":c.label,"s":c.parameter,"recirculation_area_D2":float(np.sum(weights[rec])),"immediate_wake_abs_vorticity_integral":float(np.sum(weights[near]*np.abs(c.vort[near]))),"definition":"ux/U<0 on 1.8<=x/D<=10, |y/D|<=1.5; vorticity on 1.8<=x/D<4, |y/D|<=3","source_sha256":c.source_hash}) + write_csv(root/"near_wake_diagnostics.csv",diag); f,aa=plt.subplots(1,2,figsize=(9,4.4),constrained_layout=True); labs=["accepted\ns=3.55","reverse\ns=5.2"]; aa[0].bar(labs,[r["recirculation_area_D2"] for r in diag],color=("#4477AA","#AA6655")); aa[0].set(title="Recirculation area",ylabel=r"area/$D^2$"); aa[1].bar(labs,[r["immediate_wake_abs_vorticity_integral"] for r in diag],color=("#4477AA","#AA6655")); aa[1].set(title="Immediate-wake vorticity",ylabel=r"$\int|\omega^*|dA^*$"); f.suptitle("Selected endpoint diagnostics (amplitudes differ; partial ledger)"); summary_save(f,root,"near_wake_diagnostics") + sources={"strip_analysis":{"path":str(strip),"sha256":sha(strip)},"ledger":{"path":str(ledger),"sha256":sha(ledger)},"steady_root":{"path":str(steady),"files":{}}} + for n in loaded: + for fn in ("manifest.json","endpoint.npz"): p=steady/n/fn; sources["steady_root"]["files"][f"{n}/{fn}"]={"path":str(p),"sha256":sha(p),"bytes":p.stat().st_size} + command=f'PYTHONPATH="$PWD/src" conda run -n pinball_math python src/steady_pinball_theory/plot_results.py --steady "{steady}" --strip "{strip}" --ledger "{ledger}" --output "{out}"' + readme=f"""# Unified steady-pinball figures + +Regenerable reader-facing visualization, not new evidence. CPU-only; no CFD/CUDA ran. + +## Redraw +```bash +{command} +``` +Defaults permit omitting all flags. Existing output fails unless `--overwrite` is supplied; replacement uses atomic staging and affects only this generated root. + +## Contents and definitions +- `fields/error`: six raw `|q_case-q_in|/U_inf` canvases (dimensionless, not percent). +- `fields/vorticity`: six raw `omega D/U_inf` canvases. Potential exterior values are the analytical irrotational value zero; CFD retains conservative masked numerical curl. +- `fields/streamlines`: total-velocity streamlines, arrows enabled. +- `colorbars` and `annotations`: family-named standalone legends and separate metric assets. +- `plates/{{error,vorticity,streamlines}}`: publication-friendly PNG/PDF companions with titles and framed metrics. Plates are presentation assets, not pixel-exact arrays. +- `field_metrics.csv`, `profiles_long.csv`, and `summary`: direct redraw data; every summary PNG/PDF has a same-basename CSV. + +Crop indices x={ix[0]}..{ix[-1]}, y={iy[0]}..{iy[-1]}; exact x/D=[{x[0]:.12g},{x[-1]:.12g}], y/D=[{y[0]:.12g},{y[-1]:.12g}], canvas={len(x)}x{len(y)} pixels. Arrays are yx, x is horizontal, y is up, origin is the front center. Potential uses these exact CFD lattice coordinates and analytic cylinders; CFD uses solver fluid masks. Scalar images use nearest mapping, one pixel/cell, no axes/titles/padding. Bodies are white with thin black outlines. Streamline paths are vector-rendered, but their PNG canvas has the same exact dimensions and lattice-edge extent. + +Potential and CFD errors use separate pooled-family 97.5-percentile limits: potential `{elims["potential"]:.16g}`, CFD `{elims["CFD"]:.16g}`. Both use the same discrete Greys style, but grayscale darkness is only comparable within its named family colorbar. Shared CFD-only symmetric vorticity limit is `+/-{vlim:.16g}`. Potential displayed/exported vorticity is analytical zero. Values beyond limits map to end bins and raw maxima remain in CSV. Vorticity uses discrete RdBu_r with a forced-white center and no zero contour. + +Crop L2 is `sqrt(integral_common |q_case-q_in|^2 dA / integral_common dA)/U_inf` with tensor trapezoid weights. Profiles are direct differences, not deltas misused with a uniform-reference helper. Accepted x/D=10 direct vector E_inf is `{PRIMARY}`. + +Potential `g_opt={g['theoretical_rear_opposite_g_opt_layer40']}` and fitted `g={g['actual_wls_g']}` have opposite signs: do not infer a potential mechanism. Body order is front, rear_y_plus, rear_y_minus; accepted is `[0,+Omega,-Omega]`. Stationary is an unsteady reference. Accepted s=3.55 and reverse s=5.2 have mismatched amplitudes. The NS ledger is partial. No mechanism, causality, stability, or closure is established; no CCD numbers are used. + +## Sources +```json +{json.dumps(sources,indent=2,sort_keys=True)} +``` +"""; (stage/"README.md").write_text(readme) + man={"schema":"steady-pinball-unified-figures/v2","scientific_scope":"CPU-only regenerable visualization; no CFD/CUDA; not evidence","crop":{"requested_x_over_D":[-2,10],"requested_y_over_D":[-3,3],"x_indices_inclusive":[int(ix[0]),int(ix[-1])],"y_indices_inclusive":[int(iy[0]),int(iy[-1])],"x_lattice":[float(q["x"][ix[0]]),float(q["x"][ix[-1]])],"y_lattice":[float(q["y"][iy[0]]),float(q["y"][iy[-1]])],"x_over_D":[float(x[0]),float(x[-1])],"y_over_D":[float(y[0]),float(y[-1])],"pixel_dimensions_xy":[len(x),len(y)],"array_order":"yx"},"render":{"one_output_pixel_per_lattice_cell":True,"scalar_interpolation":"nearest","raw_axes_titles":False,"plates":"presentation companions; not pixel-exact raw arrays","streamline_arrowheads":True},"masks":{"potential":"analytic cylinder exterior; displayed/exported vorticity analytically zero","CFD":"case/q_in common solver FLUID bits; conservative centered curl stencil"},"colormaps":{"error":{"name":"Greys","bins":12,"family_scales":{family:{"edges":color[0].tolist(),"limits":[0,elims[family]],"limit_statistic":"family-pooled 97.5 percentile","colorbars":[f"colorbars/error_{family.lower()}_horizontal.png",f"colorbars/error_{family.lower()}_vertical.png"]} for family,color in ecs.items()},"comparison_warning":"grayscale values compare only within the named family scale","clipping":"end bins; raw values retained"},"vorticity":{"name":"RdBu_r","bins":21,"edges":vc[0].tolist(),"limits":[-vlim,vlim],"limit_statistic":"CFD-only pooled absolute 97.5 percentile","potential_value":"analytical irrotational zero on valid exterior","center_bin":"white","zero_contour":False,"clipping":"end bins; raw values retained"}},"definitions":{"error":"hypot(ux-qin_ux,uy-qin_uy)/U_inf","vorticity":"potential analytical zero; CFD conservative omega D/U_inf","crop_L2":"sqrt(integral common-fluid |q_case-q_in|^2 dA / integral common-fluid dA)/U_inf; tensor trapezoid weights"},"geometry":{"origin":"front center","coordinates":"x-right_y-up","body_order":["front","rear_y_plus","rear_y_minus"],"centers_over_D":centers.tolist(),"radius_over_D":radius},"cases":[{"case":c.id,"label":c.label,"family":c.family,"parameter_name":c.pname,"parameter":c.parameter,"error_scale_family":c.family,"source_sha256":c.source_hash} for c in cases],"primary_identity":{"case":"cfd-accepted-s3p55","x_over_D":10,"E_inf_vector":PRIMARY},"sources":sources,"exact_command":command,"overwrite_contract":"default fail; explicit --overwrite atomically replaces only output root"} + files={} + for p in sorted(stage.rglob("*")): + if p.is_file(): files[str(p.relative_to(stage))]={"sha256":sha(p),"bytes":p.stat().st_size} + man["files"]=files; man["payload_sha256"]=hashlib.sha256(json.dumps(man,sort_keys=True,separators=(",",":")).encode()).hexdigest(); (stage/"manifest.json").write_text(json.dumps(man,indent=2,sort_keys=True)+"\n"); publish(stage,out,a.overwrite) + except Exception: shutil.rmtree(stage,ignore_errors=True); raise + return out + +def main(argv=None): + p=argparse.ArgumentParser(description=__doc__); p.add_argument("--steady",type=Path,default=DEFAULT_STEADY); p.add_argument("--strip",type=Path,default=DEFAULT_STRIP); p.add_argument("--ledger",type=Path,default=DEFAULT_LEDGER); p.add_argument("--output",type=Path,default=DEFAULT_OUTPUT); p.add_argument("--overwrite",action="store_true"); a=p.parse_args(argv); print(f"wrote unified figures to {build(a)}"); return 0 +if __name__=="__main__": raise SystemExit(main()) diff --git a/src/steady_pinball_theory/runner.py b/src/steady_pinball_theory/runner.py index ae7e82f..9e9d574 100644 --- a/src/steady_pinball_theory/runner.py +++ b/src/steady_pinball_theory/runner.py @@ -1,67 +1,2676 @@ -"""Serial Celeris diagnostic/scan runner; outputs live outside this package.""" +"""Strict serial Celeris endpoint campaign; artifacts remain external.""" from __future__ import annotations -import argparse, json, os, tempfile +import argparse, csv, hashlib, importlib.metadata, json, os, platform, socket, subprocess, sys, tempfile, time +from contextlib import contextmanager from pathlib import Path import numpy as np -from .contract import CanonicalContract -from .metrics import profile_errors +from .contract import CanonicalContract, NondimensionalContract, REVERSE_PRODUCTION_S +from .metrics import profile_errors, two_window_change, conservative_masked_vorticity + +SCHEMA="steady-pinball-endpoint/v5" +LEGACY_FORCE_SCHEMAS=("steady-pinball-endpoint/v3","steady-pinball-endpoint/v4") +FLUID_BIT=np.uint16(0x0001) +FLUID_BODY_ID=np.int16(-1) +STATIC_NONFLUID_BODY_ID=np.int16(-2) +PRODUCTION_T_END=250.0 +PRODUCTION_SAMPLE_DT=2.0 +PRODUCTION_SETTLING_WINDOWS=10 +SETTLING_THRESHOLD=1e-4 +ACCEPTED_S=(3.45,3.55,3.65) +STEADY_ROLES=("qin","stationary","accepted","reverse") +PROFILE_HISTORY_COLUMNS=("lattice_step","tU_over_D","E_inf_vector","E_L2_vector") +FORCE_HISTORY_COLUMNS=("lattice_step","tU_over_D","Fx_front","Fy_front","Fx_rear_y_plus","Fy_rear_y_plus","Fx_rear_y_minus","Fy_rear_y_minus") +TORQUE_HISTORY_COLUMNS=("lattice_step","tU_over_D","Tz_front","Tz_rear_y_plus","Tz_rear_y_minus") +MIN_LAUNCH_COOLDOWN_SECONDS=30.0 +RUNTIME_ROOT=Path(__file__).resolve().parents[2]/".runtime" +LEASE_PATH=RUNTIME_ROOT/"steady-pinball-cfd.lock" +COOLDOWN_PATH=RUNTIME_ROOT/"steady-pinball-cfd-cooldown.json" +ARRAY_FILE="endpoint.npz" +MANIFEST_FILE="manifest.json" + +def _canonical_json(value): return json.dumps(value,sort_keys=True,separators=(",",":"),allow_nan=False).encode() +def _sha256(path): + h=hashlib.sha256() + with Path(path).open("rb") as f: + for block in iter(lambda:f.read(1024*1024),b""): h.update(block) + return h.hexdigest() +def _git_value(root, *args): + try: return subprocess.check_output(["git",*args],cwd=root,text=True,stderr=subprocess.DEVNULL).strip() + except Exception: return None -def _cfg(c: CanonicalContract, D: float): - scale=D/c.diameter; nx=int(round(c.nx*scale)); ny=int(round(c.ny*scale)) - return {"grid":{"lattice_model":"D2Q9","nx":nx,"ny":ny,"nz":1}, - "physics":{"data_type":"FP32","viscosity":c.u_inf*D/c.re_d,"velocity":c.u_inf,"rho":1.0}, - "method":{"collision":"MRT","streaming":"double_buffer","store_precision":"FP32","ddf_shifting":False, - "les":{"enabled":False,"cs":0.16,"closed_form":True},"trt":{"magic_param":0.1875}, - "inlet":{"profile":"uniform","scheme":"regularized","trt_neq_damp":0.5,"regularized_neq_damp":0.5}, - "outlet":{"mode":"neq_extrap","backflow_clamp":True,"blend_alpha":0.7,"srt_neq_damp":0.5}, - "y_wall_bc":"free_slip","omega_guard":{"min":0.01,"max":1.99}}, +def _source_identity(*, celeris_module=None, intended_celeris_root=None): + root=Path(__file__).resolve().parents[2] + identity={"git_commit":_git_value(root,"rev-parse","HEAD"), + "git_status_porcelain":_git_value(root,"status","--porcelain","--","src/steady_pinball_theory"), + "runner_sha256":_sha256(__file__),"python":sys.version,"executable":sys.executable, + "platform":platform.platform(),"numpy_version":np.__version__} + if celeris_module is None: + identity.update(celeris_import_file=None,celeris_import_root=None, + celeris_intended_root=None,celeris_version=_package_version("CelerisLab"), + celeris_git_commit=None,celeris_git_dirty=None,celeris_source_hashes={}) + return identity + import_file=Path(celeris_module.__file__).resolve() + intended=Path(intended_celeris_root).expanduser().resolve(strict=True) + try: import_file.relative_to(intended) + except ValueError as exc: raise RuntimeError(f"Celeris import {import_file} is outside intended root {intended}") from exc + source_root=intended + source_paths=[import_file,source_root/"src/CelerisLab/simulation.py"] + source_paths.extend(sorted((source_root/"src/CelerisLab/lbm/kernels/config").glob("config_*.h"))) + status=_git_value(source_root,"status","--porcelain") + identity.update(celeris_import_file=str(import_file),celeris_import_root=str(source_root), + celeris_intended_root=str(intended),celeris_version=getattr(celeris_module,"__version__",None), + celeris_distribution_version=_package_version("CelerisLab"), + celeris_git_commit=_git_value(source_root,"rev-parse","HEAD"), + celeris_git_dirty=None if status is None else bool(status),celeris_git_status_porcelain=status, + celeris_source_hashes={str(path.relative_to(source_root)):_sha256(path) for path in source_paths if path.is_file()}) + return identity +def _package_version(name): + try: return importlib.metadata.version(name) + except importlib.metadata.PackageNotFoundError: return None + +def _cfg(c): + return {"grid":{"lattice_model":"D2Q9","nx":c.nx,"ny":c.ny,"nz":1},"physics":{"data_type":"FP32","viscosity":c.viscosity,"velocity":c.u_inf,"rho":1.0}, + "method":{"collision":"MRT","streaming":"double_buffer","store_precision":"FP32","ddf_shifting":False,"les":{"enabled":False,"cs":0.16,"closed_form":True}, + "trt":{"magic_param":0.1875},"inlet":{"profile":"uniform","scheme":"regularized","trt_neq_damp":0.5,"regularized_neq_damp":0.5}, + "outlet":{"mode":"neq_extrap","backflow_clamp":True,"blend_alpha":0.7,"srt_neq_damp":0.5},"y_wall_bc":"free_slip","omega_guard":{"min":0.01,"max":1.99}}, "cuda":{"threads_per_block":256,"compute_capability":"auto"}} +def case_spec(kind,s=None,*,branch=None,D=20.0,t_end=250.0,sample_dt=2.0,settling_windows=10): + roles={ + "qin":("inflow_reference",None,False), + "stationary":("unsteady_stationary_reference",None,True), + "accepted":("accepted_controlled_endpoint","plus-minus",True), + "reverse":("reversed_controlled_endpoint","minus-plus",True), + "diagnostic":("nonproduction_diagnostic",branch or "plus-minus",True), + } + if kind not in roles: raise ValueError("kind must be qin, stationary, accepted, reverse, or diagnostic") + scientific_role,expected_branch,controlled=roles[kind] + if kind in ("qin","stationary") and s is not None: raise ValueError(f"{kind} has no s") + if kind=="accepted" and (s is None or float(s) not in ACCEPTED_S): raise ValueError("accepted production s must be 3.45, 3.55, or 3.65") + if kind=="reverse" and (s is None or float(s) not in REVERSE_PRODUCTION_S): raise ValueError("reverse production s must be 3.55 or 5.2") + if kind=="diagnostic" and (s is None or not np.isfinite(s)): raise ValueError("diagnostic requires finite s") + if branch is not None and branch!=expected_branch: raise ValueError(f"{kind} branch must be {expected_branch}") + if kind in STEADY_ROLES and (float(t_end)!=PRODUCTION_T_END or float(sample_dt)!=PRODUCTION_SAMPLE_DT or int(settling_windows)!=PRODUCTION_SETTLING_WINDOWS): + raise ValueError("production endpoints require t_end=250, sample_dt=2, settling_windows=10") + c=CanonicalContract(diameter=float(D)) + if kind in ("qin","stationary"): + action=np.zeros(0 if kind=="qin" else 3); selected_oracle=None + else: + action=c.action(float(s),expected_branch); selected_oracle=c.oracle(float(s))[expected_branch] + branch_value="none" if expected_branch is None else expected_branch + qualification_role="unsteady_reference" if kind=="stationary" else ("required_steady_endpoint" if kind in ("qin","accepted","reverse") else "diagnostic") + body_ids=[] if not controlled else [0,1,2] + return {"schema":SCHEMA,"kind":kind,"scientific_role":scientific_role,"qualification_role":qualification_role, + "branch":branch_value,"s":None if s is None else float(s),"D":float(D),"t_end_U_over_D":float(t_end),"sample_dt_U_over_D":float(sample_dt), + "settling_window_count":int(settling_windows),"settling_acceptance_threshold":SETTLING_THRESHOLD, + "body_ids":body_ids,"body_labels":[] if not controlled else list(c.body_order),"body_order":"front,rear_y_plus,rear_y_minus" if controlled else None, + "centers_xy":[] if not controlled else np.asarray(c.centers).tolist(),"radius":None if not controlled else c.radius, + "action":{"scientific_role":scientific_role,"branch":branch_value,"omega":action.tolist(),"body_order":None if not controlled else list(c.body_order)}, + "action_omega":action.tolist(),"wall_oracle":{"scientific_role":scientific_role,"branch":branch_value,"selected":selected_oracle}, + "history_schema":{"profile":{"array":"history","columns":list(PROFILE_HISTORY_COLUMNS)}, + "force":{"availability":"unavailable_no_bodies" if kind=="qin" else "available_celeris_cut_link_force_mean_per_accumulated_lbm_step", + "array":None if kind=="qin" else "force_history","columns":None if kind=="qin" else list(FORCE_HISTORY_COLUMNS)}, + "torque":{"availability":"unavailable_no_bodies" if kind=="qin" else "available_celeris_cut_link_actuator_on_fluid_torque_mean_per_accumulated_lbm_step", + "ownership":None if kind=="qin" else "actuator_on_fluid", + "array":None if kind=="qin" else "torque_history","columns":None if kind=="qin" else list(TORQUE_HISTORY_COLUMNS)}}, + "celeris_read_semantics":{"normalize_true":"mean per accumulated LBM step only; do not divide by stride again", + "kernel_reduction":"sum of cut-link lattice loads", + "not_applied":["force/torque/body normalization","density normalization","dynamic-pressure normalization","span normalization"], + "scope":"two-dimensional per-unit-span"}, + "nondimensional_contract":NondimensionalContract(float(D),c.u_inf,1.0).convert()["metadata"], + "array_axes":"yx","coordinates":"x-right_y-up", + "topology":{"controlled":controlled,"solver_flags_dtype":"uint16","fluid_bit":int(FLUID_BIT),"fluid_body_id":int(FLUID_BODY_ID),"static_nonfluid_body_id":int(STATIC_NONFLUID_BODY_ID),"body_id_assignment":"none" if not controlled else "registry order 0,1,2 reconstructed on solver-nonfluid circle interiors"}, + "primary_metric":"direct q_case-vs-q_in full two-component profiles at x/D=2,4,6,10", + "config_lbm":_cfg(c),"source_environment":_source_identity()} -def run_case(out: Path, *, branch: str, s: float, D: float, t_end: float, sample_dt: float, half_height_d: float = 15.0, upstream_d: float = 50.0, downstream_d: float = 50.0): +def _reshape_exact(name, value, ny, nx, *, dtype=None): + """Reshape solver storage to exact (ny,nx), rejecting size drift.""" + array=np.asarray(value) + if array.size != ny*nx: + raise ValueError(f"{name} size does not match ny*nx") + array=array.reshape(ny,nx) + return np.asarray(array,dtype=dtype) if dtype is not None else array + + +def topology_from_solver_flags(raw_flags, *, nx, ny, centers, radius, controlled): + """Decode solver FLUID bit and reconstruct registry IDs on nonfluid cells.""" + flags=np.asarray(raw_flags) + if flags.dtype != np.uint16: + raise ValueError("raw solver flags must have dtype uint16") + flags=_reshape_exact("raw solver flags",flags,ny,nx) + fluid=(flags & FLUID_BIT) != 0 + if not fluid.any(): + raise ValueError("solver FLUID-bit mask is empty") + body_id=np.full((ny,nx),STATIC_NONFLUID_BODY_ID,dtype=np.int16) + body_id[fluid]=FLUID_BODY_ID + if controlled: + c=np.asarray(centers,dtype=float) + if c.shape!=(3,2) or not np.isfinite(c).all() or not np.isfinite(radius) or radius<=0: + raise ValueError("controlled topology requires three finite circles") + yy,xx=np.mgrid[:ny,:nx] + for registry_id,(cx,cy) in enumerate(c): + inside=(xx-cx)**2+(yy-cy)**2 < float(radius)**2 + cells=(~fluid)&inside + if not cells.any(): + raise ValueError(f"controlled body ID {registry_id} has no solver-nonfluid cells") + overlap=cells&(body_id>=0) + if overlap.any(): + raise ValueError("reconstructed body geometries overlap") + body_id[cells]=registry_id + return np.ascontiguousarray(flags),np.ascontiguousarray(fluid),body_id + + +def _validate_arrays(arrays,spec): + required=("x","y","ux","uy","rho","solver_flags","fluid_mask","body_id","history") + if any(k not in arrays for k in required): raise ValueError("endpoint missing required arrays") + force_expected=spec["history_schema"]["force"]["array"] + torque_schema=spec["history_schema"].get("torque") + torque_expected=None if torque_schema is None else torque_schema["array"] + if force_expected is None and "force_history" in arrays: raise ValueError("qin force history must be absent") + if force_expected is not None and "force_history" not in arrays: raise ValueError("body case missing force_history") + if torque_expected is None and "torque_history" in arrays: raise ValueError("torque_history must be absent") + if torque_expected is not None and "torque_history" not in arrays: raise ValueError("body case missing torque_history") + x=np.asarray(arrays["x"]); y=np.asarray(arrays["y"]); shape=(len(y),len(x)) + expected=(int(spec["config_lbm"]["grid"]["ny"]),int(spec["config_lbm"]["grid"]["nx"])) + if x.ndim!=1 or y.ndim!=1 or np.any(np.diff(x)<=0) or np.any(np.diff(y)<=0): raise ValueError("invalid coordinate axes") + if shape!=expected: raise ValueError("coordinate axes do not match configured (ny,nx)") + for k in ("ux","uy","rho","solver_flags","fluid_mask","body_id"): + if np.asarray(arrays[k]).shape!=shape: raise ValueError(f"{k} shape does not match (y,x)") + if not np.isfinite(arrays["ux"]).all() or not np.isfinite(arrays["uy"]).all() or not np.isfinite(arrays["rho"]).all(): raise ValueError("nonfinite endpoint field") + flags=np.asarray(arrays["solver_flags"]); fluid=np.asarray(arrays["fluid_mask"]); body=np.asarray(arrays["body_id"]) + if flags.dtype != np.uint16: raise ValueError("solver_flags must be uint16") + if fluid.dtype != np.bool_: raise ValueError("fluid_mask must be boolean") + if body.dtype != np.int16: raise ValueError("body_id must be int16") + decoded=(flags & FLUID_BIT)!=0 + if not np.array_equal(fluid,decoded): raise ValueError("fluid_mask does not equal solver FLUID-bit mask") + if np.any(body[fluid] != FLUID_BODY_ID): raise ValueError("fluid cells must have body_id -1") + if np.any(body[~fluid] == FLUID_BODY_ID): raise ValueError("nonfluid cells cannot have body_id -1") + history=np.asarray(arrays["history"]) + if history.ndim!=2 or history.shape[1]!=len(PROFILE_HISTORY_COLUMNS) or not np.isfinite(history).all(): raise ValueError("history must match finite profile history schema") + if force_expected is not None: + force=np.asarray(arrays["force_history"]) + if force.ndim!=2 or force.shape[1]!=len(FORCE_HISTORY_COLUMNS) or len(force)!=len(history) or not np.isfinite(force).all(): raise ValueError("force_history must match finite force history schema") + if not np.array_equal(force[:,:2],history[:,:2]): raise ValueError("force and profile history clocks differ") + if torque_expected is not None: + torque=np.asarray(arrays["torque_history"]) + if torque.ndim!=2 or torque.shape[1]!=len(TORQUE_HISTORY_COLUMNS) or len(torque)!=len(history) or not np.isfinite(torque).all(): raise ValueError("torque_history must match finite torque history schema") + if not np.array_equal(torque[:,:2],history[:,:2]): raise ValueError("torque and profile history clocks differ") + if force_expected is not None and not np.array_equal(torque[:,:2],np.asarray(arrays["force_history"])[:,:2]): raise ValueError("force and torque history clocks differ") + ids=set(np.unique(body).tolist()) + allowed={-2,-1} if not spec["topology"]["controlled"] else {-2,-1,0,1,2} + if not ids <= allowed: raise ValueError("unexpected body ID") + if spec["topology"]["controlled"]: + for registry_id in (0,1,2): + if not np.any(body==registry_id): raise ValueError(f"controlled body ID {registry_id} is empty") + + + +def _publish_directory_no_replace(temporary, out): + """Atomically publish a sibling directory without replacing an existing path.""" + temporary=Path(temporary); out=Path(out) + if sys.platform.startswith("linux"): + import ctypes + libc=ctypes.CDLL(None,use_errno=True) + renameat2=getattr(libc,"renameat2",None) + if renameat2 is not None: + result=renameat2(-100,os.fsencode(temporary),-100,os.fsencode(out),1) + if result==0: return + error=ctypes.get_errno() + if error==17: raise FileExistsError(f"refusing to clobber {out}") + raise OSError(error,os.strerror(error),str(out)) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + temporary.rename(out) + +def write_artifact(out,spec,arrays,result): + """Validate and publish one artifact atomically from a temporary sibling.""" + out=Path(out) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"artifact parent does not exist: {out.parent}") + if spec.get("schema")!=SCHEMA: raise ValueError("writer requires current endpoint schema") + _validate_arrays(arrays,spec) + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + np.savez_compressed(temporary/ARRAY_FILE,**arrays) + manifest={"schema":SCHEMA,"immutable":True,"spec":spec,"result":result,"files":{ARRAY_FILE:{"sha256":_sha256(temporary/ARRAY_FILE),"bytes":(temporary/ARRAY_FILE).stat().st_size}}} + manifest["manifest_payload_sha256"]=hashlib.sha256(_canonical_json(manifest)).hexdigest() + (temporary/MANIFEST_FILE).write_text(json.dumps(manifest,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(temporary,out) + return manifest + finally: + if temporary.exists(): + import shutil + shutil.rmtree(temporary) + + +def _load_manifest_arrays(out, *, require_payload=True): + out=Path(out); manifest=json.loads((out/MANIFEST_FILE).read_text()) + if not manifest.get("immutable"): raise ValueError("mutable artifact") + payload=manifest.pop("manifest_payload_sha256",None) + if payload is None: + if require_payload: raise ValueError("manifest payload hash missing") + elif payload!=hashlib.sha256(_canonical_json(manifest)).hexdigest(): raise ValueError("manifest payload hash mismatch") + entry=manifest["files"][ARRAY_FILE] + if _sha256(out/ARRAY_FILE)!=entry["sha256"] or (out/ARRAY_FILE).stat().st_size!=entry["bytes"]: raise ValueError("endpoint file hash mismatch") + with np.load(out/ARRAY_FILE,allow_pickle=False) as loaded: arrays={k:loaded[k].copy() for k in loaded.files} + if payload is not None: manifest["manifest_payload_sha256"]=payload + return manifest,arrays + + +def load_validate_artifact(out): + """Load only the current torque-capable endpoint schema.""" + manifest,arrays=_load_manifest_arrays(out) + if manifest.get("schema")!=SCHEMA or manifest.get("spec",{}).get("schema")!=SCHEMA: + raise ValueError("current loader requires torque-capable endpoint schema v5") + _validate_arrays(arrays,manifest["spec"]) + return manifest,arrays + + +def load_legacy_force_artifact(out): + """Explicitly load and validate a force-only v3/v4 endpoint.""" + raw=json.loads((Path(out)/MANIFEST_FILE).read_text()); schema=raw.get("schema") + if schema not in LEGACY_FORCE_SCHEMAS: raise ValueError("not an explicitly supported legacy force-only schema") + manifest,arrays=_load_manifest_arrays(out,require_payload=(schema=="steady-pinball-endpoint/v4")) + if "torque_history" in arrays: raise ValueError("legacy force-only artifact unexpectedly contains torque_history") + if schema=="steady-pinball-endpoint/v4": + if manifest.get("spec",{}).get("schema")!=schema: raise ValueError("legacy manifest/spec schema mismatch") + _validate_arrays(arrays,manifest["spec"]) + else: + if any(k not in arrays for k in ("ux","uy")): raise ValueError("legacy endpoint missing velocity arrays") + if np.asarray(arrays["ux"]).shape!=np.asarray(arrays["uy"]).shape or not np.isfinite(arrays["ux"]).all() or not np.isfinite(arrays["uy"]).all(): raise ValueError("legacy endpoint velocity arrays must be matching and finite") + return manifest,arrays + + +def load_endpoint_arrays(out): + """Load current endpoint arrays; legacy callers must use load_legacy_force_artifact.""" + return load_validate_artifact(out) + + +def _assert_cfd_environment(*, intended_celeris_root, env=None): + env=os.environ if env is None else env + if env.get("CONDA_DEFAULT_ENV")!="pycuda_3_10": raise RuntimeError("actual CFD requires conda environment pycuda_3_10") + visible=env.get("CUDA_VISIBLE_DEVICES") + if visible is None or not visible.strip() or "," in visible: raise RuntimeError("CUDA_VISIBLE_DEVICES must expose exactly one GPU") + if intended_celeris_root is None: raise RuntimeError("production CFD requires an explicit intended Celeris root") + return visible.strip(),Path(intended_celeris_root).expanduser().resolve(strict=True) + + +@contextmanager +def exclusive_cfd_lease(path=LEASE_PATH, *, role="endpoint"): + path=Path(path); path.parent.mkdir(parents=True,exist_ok=True) + payload={"schema":"steady-pinball-cfd-lease/v1","pid":os.getpid(),"host":socket.gethostname(),"role":role} + try: fd=os.open(path,os.O_WRONLY|os.O_CREAT|os.O_EXCL,0o600) + except FileExistsError: raise RuntimeError(f"CFD lease already exists; refusing concurrent launch: {path}") from None + with os.fdopen(fd,"w") as stream: + json.dump(payload,stream,sort_keys=True); stream.write("\n"); stream.flush(); os.fsync(stream.fileno()) + try: yield payload + finally: + if not path.exists() or json.loads(path.read_text())!=payload: raise RuntimeError("CFD lease ownership changed or disappeared") + path.unlink() + + +def enforce_launch_cooldown(path=COOLDOWN_PATH, *, delay_seconds=MIN_LAUNCH_COOLDOWN_SECONDS, monotonic=time.monotonic, sleep=time.sleep): + if float(delay_seconds)=4)") + if isinstance(window_count,(bool,np.bool_)) or not isinstance(window_count,(int,np.integer)) or window_count<2: + raise ValueError("settling window_count must be an integer >= 2") + required=2*int(window_count); actual=int(len(samples)) + record={"method":"two adjacent equal windows; RMS change of E_inf_vector and E_L2_vector means", + "window_count":int(window_count),"actual_samples":actual,"required_samples":required, + "value":None,"computed":False,"qualified":False,"acceptance_threshold":SETTLING_THRESHOLD} + if actual=-2)&(x<=10))[::2]; iy_fit=np.flatnonzero((y>=-6)&(y<=6))[::2] + xx,yy=np.meshgrid(x[ix_fit],y[iy_fit],indexing="xy"); points=np.column_stack((xx.ravel(),yy.ravel())) + geometry=np.ones(xx.shape,dtype=bool) + for c in centers: geometry &= (xx-c[0])**2+(yy-c[1])**2 >= .75**2 + qfluid=q["fluid_mask"][np.ix_(iy_fit,ix_fit)] + model=(affine["unit"].velocity(points)-affine["zero"].velocity(points)).reshape(*xx.shape,2) + cases={}; fitted=[] + qvel=np.stack((q["ux"],q["uy"]),axis=-1)/U + for name,svalue in zip(names[1:],(3.45,3.55,3.65)): + manifest,a=loaded[name]; velocity=np.stack((a["ux"],a["uy"]),axis=-1)/U; delta=velocity-qvel + common=a["fluid_mask"]&q["fluid_mask"] + contours={} + for body_id in (1,2): + result=ccw_contour_circulation(x,y,delta[...,0],delta[...,1],centers[body_id],radii, + samples=contour_samples,valid_mask=common) + result["Gamma_over_UD"]=result.pop("circulation") + contours[spec["body_labels"][body_id]]=result + fitmask=geometry&qfluid&a["fluid_mask"][np.ix_(iy_fit,ix_fit)] + obs=delta[np.ix_(iy_fit,ix_fit)] + zero_model=(affine["zero"].velocity(points)-np.array([1.,0.])).reshape(*xx.shape,2) + fit_observation=obs-zero_model + fit=outer_wls_total_model(obs,zero_model,model,fitmask); fit.pop("prediction") + use=fitmask + numerator=float(np.sum(fit_observation[use]*model[use])) + fit["cosine_similarity_to_unit_direction"]=numerator/float(np.linalg.norm(fit_observation[use])*np.linalg.norm(model[use])) + fit["per_rear_Gamma_over_UD"]=fit["gamma_eff"]/np.sqrt(2) + profiles={} + for station in (2.,4.,6.,10.): + ix=int(np.argmin(np.abs(x-station))); rows=common[:,ix].copy(); rows[[0,-1]]=False + d=delta[rows,ix]; profiles[str(int(station))]={"x_over_D":float(x[ix]),"points":int(rows.sum()), + "E_inf_vector":float(np.max(np.linalg.norm(d,axis=1))), + "E_L2_vector":float(np.sqrt(np.mean(np.sum(d*d,axis=1))))} + cases[f"{svalue:.2f}"]={"artifact":name,"endpoint_sha256":manifest["files"][ARRAY_FILE]["sha256"], + "settling":manifest["result"]["settling"],"contours":contours,"wls":fit,"profiles":profiles} + fitted.append(fit["gamma_eff"]) + closure=fit_two_point_affine_closure([3.45,3.65],[fitted[0],fitted[2]]) + predicted=predict_affine_closure(closure,3.55); observed=fitted[1] + held=loaded["accepted-s3.55"][1]; delta=np.stack((held["ux"]-q["ux"],held["uy"]-q["uy"]),axis=-1)/U + prediction=predicted*model; fitmask=geometry&qfluid&held["fluid_mask"][np.ix_(iy_fit,ix_fit)] + zero_model=(affine["zero"].velocity(points)-np.array([1.,0.])).reshape(*xx.shape,2) + prediction=zero_model+prediction + obs=delta[np.ix_(iy_fit,ix_fit)]; residual=obs-prediction + weights=fitmask.astype(float); wrms=lambda z: float(np.sqrt(np.sum(weights*np.sum(z*z,axis=2))/np.sum(weights))) + ix10=int(np.argmin(np.abs(x-10))); rows=(q["fluid_mask"][:,ix10]&held["fluid_mask"][:,ix10]); rows[[0,-1]]=False + profile_points=np.column_stack((np.full(rows.sum(),x[ix10]),y[rows])); pred_profile=affine_velocity(affine,predicted,profile_points)-np.array([1.,0.]) + obs_profile=delta[rows,ix10]; profile_residual=obs_profile-pred_profile + # Reflection residual parity on paired common fit rows. + parity=[] + for iy0 in range(len(iy_fit)): + iy1=int(np.argmin(np.abs(y[iy_fit]+y[iy_fit[iy0]]))) + valid=fitmask[iy0]&fitmask[iy1] + if valid.any(): parity.append(np.column_stack((residual[iy0,valid,0]-residual[iy1,valid,0],residual[iy0,valid,1]+residual[iy1,valid,1]))) + parity=np.concatenate(parity) if parity else np.empty((0,2)) + upper=np.array([cases[k]["contours"]["rear_y_plus"]["Gamma_over_UD"] for k in cases]); lower=np.array([cases[k]["contours"]["rear_y_minus"]["Gamma_over_UD"] for k in cases]) + wls_upper=np.asarray(fitted)/np.sqrt(2) + sign_pass=bool(np.all(upper*lower<0)&np.all(np.sign(upper)==np.sign(wls_upper))&np.all(np.sign(lower)==-np.sign(wls_upper))) + analysis={"schema":"steady-pinball-finite-re-analysis/v2","fit_model":"observed_delta - (MFS_zero-uniform) = g*(MFS_unit-MFS_zero)","campaign":str(campaign),"common_identity":identities[0], + "preregistration":{"contour_radii_D":radii.tolist(),"contour_samples":contour_samples,"fit_bounds_D":[-2,10,-6,6],"fit_stride_lattice":2, + "exclusion_D":.75,"wall_margin_D":1,"model":{"centers_D":centers.tolist(),"radius_D":.5,"H_D":15,"u_inf":1,"basis":"rear_opposite unit L2","n_boundary":32,"source_ratio":.65,"image_layers":40}}, + "cases":cases,"closure":{"train_s":[3.45,3.65],"held_out_s":3.55,**closure,"predicted_g":predicted,"observed_g":observed, + "error_g":predicted-observed,"predicted_per_rear_Gamma_over_UD":predicted/np.sqrt(2),"observed_per_rear_Gamma_over_UD":observed/np.sqrt(2)}, + "held_out":{"common_points":int(fitmask.sum()),"observed_weighted_RMS":wrms(obs),"prediction_weighted_RMS":wrms(prediction),"residual_weighted_RMS":wrms(residual), + "relative_residual":wrms(residual)/wrms(obs),"profile_points":int(rows.sum()),"profile_residual_E_inf_vector":float(np.max(np.linalg.norm(profile_residual,axis=1))), + "profile_residual_E_L2_vector":float(np.sqrt(np.mean(np.sum(profile_residual**2,axis=1)))), + "residual_parity_Linf":float(np.max(np.abs(parity))),"residual_parity_RMS":float(np.sqrt(np.mean(parity**2)))}, + "classification":{"sign_gate":"PASS" if sign_pass else "FAIL","closure":"BOUNDED","material_usefulness":"NOT_PREREGISTERED", + "reversed_sign_control_needed":not sign_pass,"notes":"Contour radius variation is viscous enclosed-vorticity evidence, not a required plateau or topological potential period."}} + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + np.savez_compressed(temporary/"analysis_arrays.npz",x_over_D=x,y_over_D=y,fit_x_over_D=x[ix_fit],fit_y_over_D=y[iy_fit],fit_mask=fitmask, + held_out_observed=obs,held_out_prediction=prediction,held_out_residual=residual,profile_y_over_D=y[rows],profile_observed=obs_profile,profile_prediction=pred_profile) + analysis["files"]={"analysis_arrays.npz":{"sha256":_sha256(temporary/"analysis_arrays.npz"),"bytes":(temporary/"analysis_arrays.npz").stat().st_size}} + analysis["payload_sha256"]=hashlib.sha256(_canonical_json(analysis)).hexdigest() + (temporary/"analysis.json").write_text(json.dumps(analysis,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(temporary,out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + return analysis + + + +def _assert_steady_mechanism_roles(loaded): + expected={"qin":("qin","none",None),"stationary":("stationary","none",None), + "accepted-s3.55":("accepted","plus-minus",3.55),"reverse-s5.2":("reverse","minus-plus",5.2)} + identities=[] + for name,(kind,branch,svalue) in expected.items(): + manifest,_=loaded[name]; spec=manifest["spec"] + if spec["kind"]!=kind or spec["branch"]!=branch or spec["s"]!=svalue: + raise ValueError(f"{name} role/branch/s contract mismatch") + if spec["action"]["branch"]!=branch or spec["wall_oracle"]["branch"]!=branch: + raise ValueError(f"{name} branch provenance mismatch") + if kind in ("accepted","reverse"): + selected=spec["wall_oracle"]["selected"] + if selected is None or not np.array_equal(np.asarray(selected["action"]),np.asarray(spec["action"]["omega"])): + raise ValueError(f"{name} action/oracle mismatch") + if kind in ("qin","accepted","reverse") and not manifest["result"].get("qualification_passed",False): + raise ValueError(f"{name} is not a qualified steady endpoint") + if kind=="stationary" and manifest["result"].get("qualification_role")!="unsteady_reference": + raise ValueError("stationary must be an unsteady reference") + identities.append(_campaign_common_identity(manifest)) + settings=[{k:v for k,v in identity.items() if k!="source_environment"} for identity in identities] + if any(setting!=settings[0] for setting in settings[1:]): + raise ValueError("steady-contract artifacts do not share exact CFD settings") + return settings[0],{name:loaded[name][0]["spec"]["source_environment"] for name in expected} + + +def analyze_steady_contract(campaign, out): + """Analyze frozen S2 endpoint residuals without launching CFD.""" + from .metrics import (absolute_vorticity_moments, bilinear_sample_velocity, + ccw_contour_circulation, conservative_masked_vorticity, + control_volume_streamwise_momentum_ledger, gap_flux, + near_wall_tangential_speed, outer_wls_total_model, quadrature_l2, + recirculation_observables, separation_reattachment_estimator, + tensor_trapezoid_weights, torque_power_availability, + wake_deficit_observables, wall_vorticity_production_proxy) + from .theory import strip_basis_affine + campaign=Path(campaign); out=Path(out) + names=("qin","stationary","accepted-s3.55","reverse-s5.2") + loaded={name:load_validate_artifact(campaign/name) for name in names} + identity,source_provenance=_assert_steady_mechanism_roles(loaded) + negative_name="reverse-s3.55"; negative=None + if (campaign/negative_name).exists(): + negative=load_validate_artifact(campaign/negative_name); manifest=negative[0]; spec=manifest["spec"] + if spec["kind"]!="reverse" or spec["branch"]!="minus-plus" or spec["s"]!=3.55: raise ValueError("reverse-s3.55 negative-control role/branch/s contract mismatch") + if {k:v for k,v in _campaign_common_identity(manifest).items() if k!="source_environment"}!=identity: raise ValueError("reverse-s3.55 does not share exact CFD settings") + source_provenance[negative_name]=spec["source_environment"] + qmanifest,q=loaded["qin"]; spec=loaded["accepted-s3.55"][0]["spec"] + D=float(spec["D"]); U=float(spec["config_lbm"]["physics"]["velocity"]); center0=np.asarray(spec["centers_xy"][0],float) + centers_lat=np.asarray(spec["centers_xy"],float); radius_lat=float(spec["radius"]) + centers=(centers_lat-center0)/D; x=(q["x"]-center0[0])/D; y=(q["y"]-center0[1])/D + weights=tensor_trapezoid_weights(x,y); qvel=np.stack((q["ux"],q["uy"]),axis=-1)/U + affine=strip_basis_affine(centers,.5,"rear_opposite",H=15,u_inf=1,n_boundary=32,source_ratio=.65,image_layers=40) + radii=np.array([.60,.65,.70]); ix_fit=np.flatnonzero((x>=-2)&(x<=10))[::2]; iy_fit=np.flatnonzero((y>=-6)&(y<=6))[::2] + fxx,fyy=np.meshgrid(x[ix_fit],y[iy_fit],indexing="xy"); fit_points=np.column_stack((fxx.ravel(),fyy.ravel())) + fit_geometry=np.ones(fxx.shape,dtype=bool) + for center in centers: fit_geometry &= (fxx-center[0])**2+(fyy-center[1])**2>=.75**2 + fit_geometry &= (fyy>=y[0]+1)&(fyy<=y[-1]-1) + zero_fit=np.zeros((*fxx.shape,2)); direction_fit=np.zeros_like(zero_fit) + safe_fit=fit_geometry.ravel(); safe_points=fit_points[safe_fit] + safe_zero=affine["zero"].velocity(safe_points) + zero_fit.reshape(-1,2)[safe_fit]=safe_zero-np.array([1.,0.]) + direction_fit.reshape(-1,2)[safe_fit]=affine["unit"].velocity(safe_points)-safe_zero + region_defs={"near_gap":(-.5,1.8,1.5,False),"immediate_wake":(1.8,4.,3.,False),"recovery":(4.,10.,3.,True)} + xx,yy=np.meshgrid(x,y,indexing="xy") + model_domain=(xx>=-.5)&(xx<=10)&(np.abs(yy)<=3) + for center in centers: model_domain &= (xx-center[0])**2+(yy-center[1])**2>=.75**2 + model_points=np.column_stack((xx[model_domain],yy[model_domain])) + zero_domain=np.empty((len(model_points),2)); direction_domain=np.empty_like(zero_domain) + for start in range(0,len(model_points),20000): + sl=slice(start,start+20000); p0=model_points[sl] + z=affine["zero"].velocity(p0); zero_domain[sl]=z-[1.,0.]; direction_domain[sl]=affine["unit"].velocity(p0)-z + cases={}; station_metrics={} + rear_labels=[spec["body_labels"][1],spec["body_labels"][2]] + for name in ("accepted-s3.55","reverse-s5.2"): + manifest,a=loaded[name]; velocity=np.stack((a["ux"],a["uy"]),axis=-1)/U; delta=velocity-qvel; common=a["fluid_mask"]&q["fluid_mask"] + fitmask=fit_geometry&common[np.ix_(iy_fit,ix_fit)]; obs=delta[np.ix_(iy_fit,ix_fit)] + fit=outer_wls_total_model(obs,zero_fit,direction_fit,fitmask); fit.pop("prediction") + centered=obs-zero_fit; numerator=float(np.sum(centered[fitmask]*direction_fit[fitmask])); fit["cosine_similarity_to_unit_direction"]=numerator/float(np.linalg.norm(centered[fitmask])*np.linalg.norm(direction_fit[fitmask])); fit["per_rear_Gamma_over_UD"]=fit["gamma_eff"]/np.sqrt(2) + residual=np.full_like(velocity,np.nan); residual[model_domain]=delta[model_domain]-(zero_domain+fit["gamma_eff"]*direction_domain) + regions={} + for rname,(xmin,xmax,ymax,closed) in region_defs.items(): + horizontal=(xx>=xmin)&((xx<=xmax) if closed else (xx=xmin)&(xx=1.8)&(xx<=10)&(np.abs(yy)<=1.5) + recirc=recirculation_observables(x,velocity[...,0],recmask,weights) + wake={} + for station in (2.,4.,6.,10.): + ix=int(np.argmin(np.abs(x-station))); rows=common[:,ix].copy(); rows[[0,-1]]=False + wake[str(int(station))]={"x_over_D":float(x[ix]),**wake_deficit_observables(y,velocity[:,ix,0],rows)} + tail=np.asarray(a["force_history"],float)[-10:,2:]; mean=np.mean(tail,axis=0); std=np.std(tail,axis=0,ddof=0) + total=np.column_stack((tail[:,0]+tail[:,2]+tail[:,4],tail[:,1]+tail[:,3]+tail[:,5])) + forces={"normalization":"Celeris average force per accumulated stride; not pressure drag","tail_samples":10,"body_columns":list(FORCE_HISTORY_COLUMNS[2:]),"body_mean":mean.tolist(),"body_tail_std":std.tolist(),"total_mean":np.mean(total,axis=0).tolist(),"total_tail_std":np.std(total,axis=0,ddof=0).tolist()} + near_wall=near_wall_tangential_speed(a["x"],a["y"],a["ux"],a["uy"],a["fluid_mask"],a["body_id"],centers_lat,radius_lat,body_ids=(1,2),body_labels=rear_labels) + wall_prod=wall_vorticity_production_proxy(a["x"],a["y"],a["ux"],a["uy"],a["fluid_mask"],a["body_id"],centers_lat,radius_lat,body_ids=(1,2),body_labels=rear_labels) + separation=separation_reattachment_estimator(a["x"],a["y"],a["ux"],a["fluid_mask"],a["body_id"],centers_lat,radius_lat,body_ids=(1,2),body_labels=rear_labels) + x_gap=float(centers[1][0]); ledger=control_volume_streamwise_momentum_ledger( + x,y,velocity[...,0],velocity[...,1],a["rho"],common,x_left=x_gap,x_right=10.0, + force_history=a["force_history"],viscosity=float(spec["config_lbm"]["physics"]["viscosity"])) + torque_history=a.get("torque_history"); torque=torque_power_availability(a.get("force_history"),torque_history=None if torque_history is None else np.asarray(torque_history)[:,2:]) + cases[name]={"s":spec["s"] if name=="accepted-s3.55" else loaded[name][0]["spec"]["s"],"endpoint_sha256":manifest["files"][ARRAY_FILE]["sha256"],"settling":manifest["result"]["settling"],"wls":fit,"contours":contours,"residual_regions":regions,"observer_profile":observer,"gap_flux":gaps,"vorticity_moments":vort,"recirculation":recirc,"wake_deficit":wake,"forces":forces, + "near_wall_tangential_speed":near_wall,"wall_vorticity_production_proxy":wall_prod, + "separation_reattachment":separation,"control_volume_momentum_ledger":ledger,"torque_power":torque} + station_metrics[name]=wake + candidates=[] + for metric in ("momentum_deficit_proxy","positive_deficit_measure","signed_deficit_integral"): + av=[station_metrics["accepted-s3.55"][str(s)][metric] for s in (2,4,6,10)]; rv=[station_metrics["reverse-s5.2"][str(s)][metric] for s in (2,4,6,10)] + signs=np.sign(np.asarray(rv)-np.asarray(av)); nonzero=signs!=0 + if nonzero.sum()>=2 and (np.all(signs[nonzero]>0) or np.all(signs[nonzero]<0)): + candidates.append({"observable":metric,"stations_x_over_D":[2,4,6,10],"accepted":av,"reverse":rv,"reverse_minus_accepted_sign":int(signs[nonzero][0])}) + acc,rev=cases["accepted-s3.55"],cases["reverse-s5.2"] + local_gap={"accepted_flux":acc["gap_flux"]["rear_rear"]["flux"],"reverse_flux":rev["gap_flux"]["rear_rear"]["flux"], + "discriminates":abs(acc["gap_flux"]["rear_rear"]["flux"]-rev["gap_flux"]["rear_rear"]["flux"])>1e-6} + near_wake={"accepted_abs_omega":acc["vorticity_moments"]["immediate_wake"]["absolute_vorticity_integral"], + "reverse_abs_omega":rev["vorticity_moments"]["immediate_wake"]["absolute_vorticity_integral"], + "accepted_width":acc["vorticity_moments"]["immediate_wake"]["y_width"], + "reverse_width":rev["vorticity_moments"]["immediate_wake"]["y_width"], + "accepted_recirc_extent":acc["recirculation"]["streamwise_extent"], + "reverse_recirc_extent":rev["recirculation"]["streamwise_extent"], + "accepted_Fx":acc["forces"]["total_mean"][0],"reverse_Fx":rev["forces"]["total_mean"][0], + "discriminates":(abs(acc["vorticity_moments"]["immediate_wake"]["absolute_vorticity_integral"] + -rev["vorticity_moments"]["immediate_wake"]["absolute_vorticity_integral"])>1e-6 + and abs(acc["recirculation"]["streamwise_extent"]-rev["recirculation"]["streamwise_extent"])>1e-6)} + downstream={"qualifying_observables":candidates,"discriminates":bool(candidates)} + near_wall_status={role:{"availability":{body:info.get("availability") for body,info in cases[role]["near_wall_tangential_speed"]["bodies"].items()}, + "wall_vorticity":{body:info.get("availability") for body,info in cases[role]["wall_vorticity_production_proxy"]["bodies"].items()}, + "separation":{body:info.get("availability") for body,info in cases[role]["separation_reattachment"]["bodies"].items()}, + "cv_balance":cases[role]["control_volume_momentum_ledger"]["balance_status"], + "torque":cases[role]["torque_power"]["availability"]} + for role in ("accepted-s3.55","reverse-s5.2")} + s3="PASS" if (local_gap["discriminates"] and near_wake["discriminates"] and downstream["discriminates"]) else "BOUNDED" + verdict="PASS" if candidates else "BOUNDED" + neg={"present":negative is not None,"use":"negative/nonsteady context only"} + if negative is not None: neg.update(qualification_passed=bool(negative[0]["result"].get("qualification_passed",False)),settling=negative[0]["result"]["settling"],endpoint_sha256=negative[0]["files"][ARRAY_FILE]["sha256"]) + source_files=[Path(__file__),Path(__file__).with_name("metrics.py"),Path(__file__).with_name("theory.py"),Path(__file__).with_name("DERIVATION.md")] + analysis={"schema":"steady-pinball-steady-residual/v2","campaign":str(campaign),"common_cfd_settings":identity,"source_provenance_by_role":source_provenance,"preregistration":{"outer_fit":"corrected total strip rear-opposite affine model; uniform WLS","fit_bounds_D":[-2,10,-6,6],"fit_stride_lattice":2,"fit_exclusion_D":.75,"contour_radii_D":radii.tolist(),"regions":{"near_gap":"-0.5<=x/D<1.8, |y/D|<=1.5","immediate_wake":"1.8<=x/D<4, |y/D|<=3","recovery":"4<=x/D<=10, |y/D|<=3","observer":"nearest x/D=10 column, outermost two rows excluded"},"recirculation_window":"1.8<=x/D<=10, |y/D|<=1.5, ux/U_inf<0","gap_endpoint_exclusion_D":.05,"mechanism_chain":"wall→gap/shear→recirculation/force→downstream","control_volume":"rear-gap plane to x/D=10; incomplete ledger never closed"},"cases":cases,"reverse_s3.55_negative_control":neg,"spatial_sequence":{"interpretation":"ordered spatial coexistence/association only; endpoints do not establish temporal causality","qualifying_observables":candidates,"preregistered_chain":"wall→gap/shear→recirculation/force→downstream","local_gap":local_gap,"near_wake_force":near_wake,"downstream":downstream,"near_wall_availability":near_wall_status},"classification":{"S2":verdict,"S3_mechanism":s3,"common_outer_potential_explanation":"descriptive fits only; favorable circulation cancellation remains rejected by known sign contradiction","mechanism_association":s3,"causality":"NOT_ESTABLISHED","comparison":"different s; not equal-amplitude intervention","incomplete_ledgers":"control-volume/torque terms remain unavailable or incomplete and are not closed balances"},"source_hashes":{str(path.relative_to(Path(__file__).resolve().parents[2])):_sha256(path) for path in source_files},"reproduce_command":f'PYTHONPATH="$PWD/src" conda run -n pinball_math python -m steady_pinball_theory.runner analyze-steady {campaign} --out {out}'} + analysis["endpoint_hashes"]={name:loaded[name][0]["files"][ARRAY_FILE]["sha256"] for name in names} + if negative is not None: analysis["endpoint_hashes"][negative_name]=negative[0]["files"][ARRAY_FILE]["sha256"] + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"analysis parent does not exist: {out.parent}") + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + analysis["payload_sha256"]=hashlib.sha256(_canonical_json(analysis)).hexdigest() + (temporary/"analysis.json").write_text(json.dumps(analysis,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(temporary,out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + return analysis + + +def _strict_json_value(value): + """Convert numerical output to strict finite JSON-native values.""" + if isinstance(value,np.ndarray): return _strict_json_value(value.tolist()) + if isinstance(value,np.generic): return _strict_json_value(value.item()) + if isinstance(value,dict): return {str(k):_strict_json_value(v) for k,v in value.items()} + if isinstance(value,(list,tuple)): return [_strict_json_value(v) for v in value] + if isinstance(value,float) and not np.isfinite(value): raise ValueError("NS ledger contains a nonfinite scalar") + return value + + +def analyze_ns_ledger(campaign,out): + """CPU-only endpoint spatial partial ledger for a torque-capable v5 campaign.""" + from .metrics import (bilinear_sample_velocity,gap_mass_momentum_flux, + rectangular_control_volume_fluxes,station_flux_metrics,torque_to_actuator_power, + volume_viscous_dissipation,weak_compressible_pressure_proxy) + campaign,out=Path(campaign),Path(out); required=("qin","stationary","accepted-s3.55","reverse-s5.2") + missing=[n for n in required if not (campaign/n).is_dir()] + if missing: raise FileNotFoundError("analyze-ns-ledger requires torque-capable v5 campaign roles; missing: "+", ".join(missing)+"; v4 torque-free data are not accepted") + loaded={n:load_validate_artifact(campaign/n) for n in required}; identity,sources=_assert_steady_mechanism_roles(loaded) + negative=None + if (campaign/"reverse-s3.55").exists(): + negative=load_validate_artifact(campaign/"reverse-s3.55"); m,_=negative; sp=m["spec"] + if (sp.get("kind"),sp.get("branch"),sp.get("s")) != ("reverse","minus-plus",3.55): raise ValueError("reverse-s3.55 optional role/branch/s contract mismatch") + if {k:v for k,v in _campaign_common_identity(m).items() if k!="source_environment"}!=identity: raise ValueError("reverse-s3.55 does not share exact CFD settings") + sources["reverse-s3.55"]=sp["source_environment"] + _,q=loaded["qin"]; ref=loaded["accepted-s3.55"][0]["spec"]; D=float(ref["D"]); physics=ref["config_lbm"]["physics"] + U,rho_ref,nu=float(physics["velocity"]),float(physics["rho"]),float(physics["viscosity"]); centers=np.asarray(ref["centers_xy"],float); radius=float(ref["radius"]) + contract=NondimensionalContract(D,U,rho_ref); x_D=(np.asarray(q["x"],float)-centers[0,0])/D + indices={str(int(z)):int(np.argmin(abs(x_D-z))) for z in (2.,4.,6.,10.)}; cases={} + qin_cv=rectangular_control_volume_fluxes(q["x"],q["y"],q["ux"],q["uy"],q["rho"],q["fluid_mask"],centers[0],D,rho_ref=rho_ref,viscosity=nu) + def nondimensional_cv(cv): + totals=cv["outward_totals"] + converted=contract.convert(mass_flux=totals["mass_flux"],momentum_flux=totals["momentum_convective"]+totals["momentum_pressure"], + energy_flux=totals["kinetic_energy_flux"]+totals["pressure_work"]+totals.get("viscous_work",0.)) + return {"mass_flux_star":converted["mass_flux_star"],"momentum_flux_star":converted["momentum_flux_star"], + "mechanical_spatial_flux_star":converted["energy_flux_star"],"reference":converted["metadata"]} + qin_cv["dimensionless_outward_totals"]=nondimensional_cv(qin_cv) + for name in ("stationary","accepted-s3.55","reverse-s5.2"): + manifest,a=loaded[name]; spec=manifest["spec"]; action=np.asarray(spec["action_omega"],float) + if not np.array_equal(action,np.asarray(spec["action"]["omega"],float)): raise ValueError(f"{name} exact action provenance mismatch") + for clock in ("force_history","torque_history"): + if not np.array_equal(np.asarray(a[clock])[:,:2],np.asarray(a["history"])[:,:2]): raise ValueError(f"{name} {clock} clock mismatch") + stations={} + for label,ix in indices.items(): + rows=np.asarray(a["fluid_mask"],bool)[:,ix]&np.asarray(q["fluid_mask"],bool)[:,ix]; rows=rows.copy(); rows[[0,-1]]=False + qp=weak_compressible_pressure_proxy(q["rho"][:,ix],rho_ref=rho_ref); ap=weak_compressible_pressure_proxy(a["rho"][:,ix],rho_ref=rho_ref) + qin=station_flux_metrics(q["y"],q["ux"][:,ix],q["uy"][:,ix],q["rho"][:,ix],qp["values"],rows) + station=station_flux_metrics(a["y"],a["ux"][:,ix],a["uy"][:,ix],a["rho"][:,ix],ap["values"],rows,q_in=qin) + station.update(x_over_D=float(x_D[ix]),pressure_term={k:v for k,v in ap.items() if k!="values"}); stations[label]=station + torque=np.asarray(a["torque_history"],float); tail=torque[-min(10,len(torque)):,2:] + power=torque_to_actuator_power(tail,np.broadcast_to(action,tail.shape),torque_ownership="actuator_on_fluid",rho_ref=rho_ref,u_ref=U,diameter=D) + power["qualification_status"]="runtime_oracle_qualified_actuator_on_fluid" + velocity=lambda p,a=a: bilinear_sample_velocity(a["x"],a["y"],a["ux"],a["uy"],p,valid_mask=a["fluid_mask"]) + density=lambda p,a=a: bilinear_sample_velocity(a["x"],a["y"],a["rho"],a["rho"],p,valid_mask=a["fluid_mask"])[:,0] + er=1.1*radius; pairs={"rear_rear":(1,2),"front_upper_rear":(0,1),"front_lower_rear":(0,2)} + gaps={k:gap_mass_momentum_flux(velocity,density,centers[i],centers[j],er,samples=1001) for k,(i,j) in pairs.items()} + for gap in gaps.values(): + gap["endpoint_exclusion_radius_over_D"]=er/D + nd=contract.convert(Q=gap["Q_g"],J=gap["J_g"],mass_flux=gap["mass_flux"]) + gap["dimensionless"]={k:nd[k] for k in ("Q_star","J_star","mass_flux_star")} + cv=rectangular_control_volume_fluxes(a["x"],a["y"],a["ux"],a["uy"],a["rho"],a["fluid_mask"],centers[0],D,rho_ref=rho_ref,viscosity=nu) + cv["dimensionless_outward_totals"]=nondimensional_cv(cv) + xx,yy=np.meshgrid(a["x"],a["y"],indexing="xy"); b=cv["bounds"]["actual"] + cv_fluid=np.asarray(a["fluid_mask"],bool)&(xx>=b["x"][0])&(xx<=b["x"][1])&(yy>=b["y"][0])&(yy<=b["y"][1]) + diss=volume_viscous_dissipation(a["x"],a["y"],a["ux"],a["uy"],nu,cv_fluid,density=a["rho"]); dv=diss["viscous_dissipation"] + diss["dimensionless_energy_flux_star"]=contract.convert(energy_flux=dv)["energy_flux_star"] + partial={"definition":"same-CV endpoint spatial partial ledger; no residual closure", + "outward_face_fluxes":cv["outward_totals"],"cv_fluid_viscous_dissipation":dv, + "actuator_power_diagnostic":power["mean_total_power"], + "storage_rate":{"availability":"unavailable_endpoint_only","value":None}, + "body_adjacent_gradient_terms":{"availability":"partially_omitted_centered_stencil_mask","value":None}, + "time_consistent_terms":{"availability":"unavailable_endpoint_arrays_only","value":None}, + "residual":None,"balance_status":"endpoint_spatial_partial_not_closed", + "claim_limit":"Same rectangular CV for four-face fluxes and dissipation, but storage and body-adjacent gradients are unavailable."} + cases[name]={"scientific_role":spec["scientific_role"],"branch":spec["branch"],"s":spec["s"],"exact_action_omega":action, + "endpoint_sha256":manifest["files"][ARRAY_FILE]["sha256"],"qualification_passed":manifest["result"].get("qualification_passed"), + "clock_verification":"profile/force/torque clocks exactly equal","torque_and_actuator_power":power, + "legacy_station_fluxes_vs_matching_qin":stations,"control_volume":cv,"gap_fluxes_separate_orientations":gaps, + "control_volume_viscous_dissipation":{k:v for k,v in diss.items() if k not in ("dissipation_density","usable_mask")}, + "same_cv_partial_ledger":partial} + neg={"present":negative is not None,"use":"optional negative/nonsteady context only"} + if negative is not None: neg.update(qualification_passed=bool(negative[0]["result"].get("qualification_passed",False)),endpoint_sha256=negative[0]["files"][ARRAY_FILE]["sha256"]) + analysis={"schema":"steady-pinball-ns-ledger/v2","campaign":str(campaign),"execution":"CPU analysis of existing endpoint arrays only; no CFD or GPU", + "common_cfd_settings":identity,"source_provenance_by_role":sources,"control_volume_contract":qin_cv["bounds"], + "matching_qin_control_volume":qin_cv,"legacy_station_x_over_D":[2,4,6,10],"cases":cases,"reverse_s3.55_negative_control":neg, + "claim_classification":{"same_cv_endpoint_spatial_ledger":"AVAILABLE_PARTIAL","mechanical_energy_closure":"NOT_CLOSED", + "pressure_work":"AVAILABLE_WEAK_COMPRESSIBLE_PROXY","storage_rate":"UNAVAILABLE","body_adjacent_gradients":"PARTIALLY_OMITTED", + "torque_ownership":"ACTUATOR_ON_FLUID_RUNTIME_ORACLE","causality":"NOT_ESTABLISHED"}, + "claim_limit":"Stage 2 supplies a same-CV endpoint spatial partial ledger. Missing storage/time-consistent and body-adjacent gradient terms prohibit a closed mechanical-energy balance or residual.", + "endpoint_hashes":{n:loaded[n][0]["files"][ARRAY_FILE]["sha256"] for n in required}, + "reproduce_command":f'PYTHONPATH="$PWD/src" python -m steady_pinball_theory.runner analyze-ns-ledger {campaign} --out {out}'} + if negative is not None: analysis["endpoint_hashes"]["reverse-s3.55"]=negative[0]["files"][ARRAY_FILE]["sha256"] + analysis=_strict_json_value(analysis) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"analysis parent does not exist: {out.parent}") + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + analysis["payload_sha256"]=hashlib.sha256(_canonical_json(analysis)).hexdigest(); (temporary/"analysis.json").write_text(json.dumps(analysis,indent=2,sort_keys=True,allow_nan=False)+"\n"); _publish_directory_no_replace(temporary,out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + return analysis + + +def _evidence_root(): + return Path(__file__).resolve().parent/"evidence" + + +def _load_legacy_endpoint(case): + case=Path(case); contract=json.loads((case/"contract.json").read_text()) + with np.load(case/"endpoint.npz",allow_pickle=False) as loaded: + arrays={k:loaded[k].copy() for k in loaded.files} + if "ux" not in arrays or "uy" not in arrays: raise ValueError(f"legacy endpoint missing velocity: {case}") + return contract,arrays + + +def _profile_vs_qin(ctl_ux, ctl_uy, qin_ux, qin_uy, centers, D, *, u_inf=0.01, fluid_ctl=None, fluid_qin=None): + """Full-profile E_inf/L2 of q_ctl-q_in at x/D=10 using matching-resolution qin.""" + centers=np.asarray(centers,dtype=float); cx=float(centers[0][0]); ix=int(round(cx+10.0*float(D))) + if fluid_ctl is None or fluid_qin is None: + rows=slice(2,-2) + dux=(np.asarray(ctl_ux)[rows,ix]-np.asarray(qin_ux)[rows,ix])/float(u_inf) + duy=(np.asarray(ctl_uy)[rows,ix]-np.asarray(qin_uy)[rows,ix])/float(u_inf) + else: + common=np.asarray(fluid_ctl,dtype=bool)[:,ix]&np.asarray(fluid_qin,dtype=bool)[:,ix] + common=common.copy(); common[[0,-1]]=False + if not common.any(): raise ValueError("profile mask empty at x/D=10") + dux=(np.asarray(ctl_ux)[common,ix]-np.asarray(qin_ux)[common,ix])/float(u_inf) + duy=(np.asarray(ctl_uy)[common,ix]-np.asarray(qin_uy)[common,ix])/float(u_inf) + vec=np.hypot(dux,duy) + return {"E_inf_vector":float(np.max(vec)),"E_L2_vector":float(np.sqrt(np.mean(vec*vec))), + "points":int(len(vec)),"x_index":ix,"u_inf":float(u_inf)} + + +def _history_settling_legacy(history): + hist=np.asarray(history,dtype=float) + if hist.ndim!=2 or hist.shape[0]<4 or hist.shape[1]<3 or not np.isfinite(hist).all(): + return {"availability":"unavailable_or_short_history","value":None} + tail=hist[-min(20,len(hist)):,1:3]; value=float(two_window_change(tail)) + return {"availability":"available_legacy_profile_history","window_samples":int(len(tail)), + "value":value,"qualified":bool(value<=SETTLING_THRESHOLD)} + + +def analyze_credibility(*, out, evidence_root=None, agreement_tol=0.05): + """Stage-2 numerical credibility from promoted convergence/domain/D20 endpoints.""" + evidence=Path(evidence_root) if evidence_root is not None else _evidence_root() + out=Path(out); conv=evidence/"authoritative"/"steady-convergence-20260802" + domain=evidence/"authoritative"/"steady-domain-20260802" + bridge=evidence/"authoritative"/"steady-finite-re-bridge-d20-20260804" + contract=evidence/"authoritative"/"steady-contract-d20-20260806" + u_inf=0.01; resolution={}; status_flags=[] + + def mark(name, state, detail=None): + entry={"name":name,"status":state} + if detail is not None: entry["detail"]=detail + status_flags.append(entry); return entry + + grid_summary=json.loads((conv/"grid_summary.json").read_text()) + d30_local=json.loads((conv/"D30_local_summary.json").read_text()) + domain_summary=json.loads((domain/"summary.json").read_text()) + mark("grid_summary.json","reused"); mark("D30_local_summary.json","reused"); mark("domain/summary.json","reused") + + for D,ctl_name,qin_name in ((10,"D10-s3.55","D10-qin"),(30,"D30-s3.55","D30-qin")): + ctl_path=conv/ctl_name; qin_path=conv/qin_name + if not ctl_path.exists() or not qin_path.exists(): + mark(f"D{D}-s3.55","missing"); resolution[str(D)]={"availability":"missing"}; continue + c_ctl,a_ctl=_load_legacy_endpoint(ctl_path); _,a_qin=_load_legacy_endpoint(qin_path) + metrics=_profile_vs_qin(a_ctl["ux"],a_ctl["uy"],a_qin["ux"],a_qin["uy"],c_ctl["centers"],D,u_inf=u_inf) + settling=_history_settling_legacy(a_ctl["history"]) + resolution[str(D)]={"availability":"recomputed_from_endpoints","source":str(ctl_path.relative_to(evidence)), + "qin_source":str(qin_path.relative_to(evidence)),"s":float(c_ctl["s"]), + "profiles_xD10_vs_qin":metrics,"settling":settling, + "endpoint_sha256":_sha256(ctl_path/"endpoint.npz")} + mark(f"D{D}-s3.55","recomputed") + + d20_metrics=None; d20_meta=None + for label,root in (("contract",contract),("bridge",bridge)): + ctl=root/"accepted-s3.55"; qin=root/"qin" + if not ctl.exists() or not qin.exists(): continue + m_ctl,a_ctl=load_legacy_force_artifact(ctl); _,a_qin=load_legacy_force_artifact(qin) + metrics=_profile_vs_qin(a_ctl["ux"],a_ctl["uy"],a_qin["ux"],a_qin["uy"],m_ctl["spec"]["centers_xy"],20.0,u_inf=u_inf, + fluid_ctl=a_ctl.get("fluid_mask"),fluid_qin=a_qin.get("fluid_mask")) + d20_metrics=metrics; d20_meta={"label":label,"ctl":str(ctl),"qin":str(qin), + "endpoint_sha256":m_ctl["files"][ARRAY_FILE]["sha256"], + "settling":m_ctl.get("result",{}).get("settling")} + mark(f"D20-s3.55-{label}","recomputed"); break + if d20_metrics is None: + mark("D20-s3.55","missing"); resolution["20"]={"availability":"missing"} + else: + resolution["20"]={"availability":"recomputed_from_endpoints","source":d20_meta["ctl"], + "qin_source":d20_meta["qin"],"campaign":d20_meta["label"],"s":3.55, + "profiles_xD10_vs_qin":d20_metrics,"settling":d20_meta["settling"], + "endpoint_sha256":d20_meta["endpoint_sha256"]} + + order_block={"availability":"missing"} + if resolution.get("20",{}).get("availability")=="recomputed_from_endpoints" and resolution.get("30",{}).get("availability")=="recomputed_from_endpoints": + e20=resolution["20"]["profiles_xD10_vs_qin"]["E_inf_vector"]; e30=resolution["30"]["profiles_xD10_vs_qin"]["E_inf_vector"] + l20=resolution["20"]["profiles_xD10_vs_qin"]["E_L2_vector"]; l30=resolution["30"]["profiles_xD10_vs_qin"]["E_L2_vector"] + rel_inf=abs(e30-e20)/max(abs(e20),np.finfo(float).eps); rel_l2=abs(l30-l20)/max(abs(l20),np.finfo(float).eps) + observed_order=None + if resolution.get("10",{}).get("availability")=="recomputed_from_endpoints": + e10=resolution["10"]["profiles_xD10_vs_qin"]["E_inf_vector"] + d_coarse=abs(e10-e20); d_fine=abs(e20-e30) + if d_coarse>0 and d_fine>0: + observed_order={"note":"unequal refinement; not a single Richardson order", + "log_ratio_D10_D20":float(np.log(d_coarse)/np.log(2.0)), + "log_ratio_D20_D30":float(np.log(d_fine)/np.log(1.5)), + "D10_underresolved_expected":True} + order_block={"availability":"computed","E_inf_D20":e20,"E_inf_D30":e30,"E_L2_D20":l20,"E_L2_D30":l30, + "relative_change_E_inf":float(rel_inf),"relative_change_E_L2":float(rel_l2), + "observed_order":observed_order} + + strip={} + for H in (12,18): + ctl=domain/f"H{H}-D20-s3.55"; qin=domain/f"H{H}-D20-qin" + if not ctl.exists() or not qin.exists(): + mark(f"H{H}","missing"); strip[str(H)]={"availability":"missing"}; continue + c_ctl,a_ctl=_load_legacy_endpoint(ctl); _,a_qin=_load_legacy_endpoint(qin) + metrics=_profile_vs_qin(a_ctl["ux"],a_ctl["uy"],a_qin["ux"],a_qin["uy"],c_ctl["centers"],20.0,u_inf=u_inf) + strip[str(H)]={"availability":"recomputed_from_endpoints","H_over_D":H,"profiles_xD10_vs_qin":metrics, + "endpoint_sha256":_sha256(ctl/"endpoint.npz")} + mark(f"H{H}-D20-s3.55","recomputed") + strip_delta=None + if strip.get("12",{}).get("availability")=="recomputed_from_endpoints" and strip.get("18",{}).get("availability")=="recomputed_from_endpoints": + e12=strip["12"]["profiles_xD10_vs_qin"]["E_inf_vector"]; e18=strip["18"]["profiles_xD10_vs_qin"]["E_inf_vector"] + strip_delta={"E_inf_H12":e12,"E_inf_H18":e18,"abs_change":float(abs(e18-e12)), + "relative_change":float(abs(e18-e12)/max(abs(e12),np.finfo(float).eps))} + + neighborhood={"D20":{},"D30":{}} + for svalue in (3.45,3.55,3.65): + key=f"{svalue:.2f}" + path=conv/f"D30-s{key}"; qin_path=conv/"D30-qin" + if path.exists() and qin_path.exists(): + c_ctl,a_ctl=_load_legacy_endpoint(path); _,a_qin=_load_legacy_endpoint(qin_path) + neighborhood["D30"][key]={"availability":"recomputed_from_endpoints", + "profiles_xD10_vs_qin":_profile_vs_qin(a_ctl["ux"],a_ctl["uy"],a_qin["ux"],a_qin["uy"],c_ctl["centers"],30.0,u_inf=u_inf), + "endpoint_sha256":_sha256(path/"endpoint.npz")} + mark(f"D30-s{key}","recomputed") + else: + neighborhood["D30"][key]={"availability":"missing"}; mark(f"D30-s{key}","missing") + if svalue==3.55 and resolution.get("20",{}).get("availability")=="recomputed_from_endpoints": + neighborhood["D20"][key]={"availability":"recomputed_from_endpoints", + "profiles_xD10_vs_qin":resolution["20"]["profiles_xD10_vs_qin"], + "endpoint_sha256":resolution["20"]["endpoint_sha256"], + "source":resolution["20"]["source"]} + else: + bpath=bridge/f"accepted-s{key}"; bqin=bridge/"qin" + cpath=conv/f"D20-s{key}" + if bpath.exists() and bqin.exists(): + m_ctl,a_ctl=load_legacy_force_artifact(bpath); _,a_qin=load_legacy_force_artifact(bqin) + neighborhood["D20"][key]={"availability":"recomputed_from_endpoints", + "profiles_xD10_vs_qin":_profile_vs_qin(a_ctl["ux"],a_ctl["uy"],a_qin["ux"],a_qin["uy"],m_ctl["spec"]["centers_xy"],20.0,u_inf=u_inf,fluid_ctl=a_ctl.get("fluid_mask"),fluid_qin=a_qin.get("fluid_mask")), + "endpoint_sha256":m_ctl["files"][ARRAY_FILE]["sha256"],"source":str(bpath)} + mark(f"D20-s{key}-bridge","recomputed") + elif cpath.exists(): + neighborhood["D20"][key]={"availability":"bounded_missing_matching_qin", + "note":"D20 endpoint present in convergence but matching D20-qin absent there", + "legacy_result":json.loads((cpath/"result.json").read_text())} + mark(f"D20-s{key}","bounded") + else: + neighborhood["D20"][key]={"availability":"missing"}; mark(f"D20-s{key}","missing") + + def _neighborhood_coherent(block): + vals=[] + for key in ("3.45","3.55","3.65"): + item=block.get(key,{}) + if item.get("availability")!="recomputed_from_endpoints": return False,"incomplete" + vals.append(item["profiles_xD10_vs_qin"]["E_inf_vector"]) + e345,e355,e365=vals + ok=bool(e365>max(e345,e355) and abs(e345-e355)/max(e355,np.finfo(float).eps)<=0.1) + return ok,{"E_inf":vals,"side_degrades_at_3.65":bool(e365>max(e345,e355)),"flat_3.45_3.55":bool(abs(e345-e355)/max(e355,np.finfo(float).eps)<=0.1)} + d20_ok,d20_coh=_neighborhood_coherent(neighborhood["D20"]); d30_ok,d30_coh=_neighborhood_coherent(neighborhood["D30"]) + + missing_tests=[{"name":"outlet_boundary_sensitivity","status":"BOUNDED","detail":"not present in promoted evidence"}, + {"name":"final_window_length_sensitivity","status":"BOUNDED","detail":"not present in promoted evidence"}, + {"name":"initial_condition_perturbation","status":"BOUNDED","detail":"not present in promoted evidence"}, + {"name":"D10_underresolved","status":"BOUNDED","detail":"expected; D10 retained only as coarse diagnostic"}] + for item in missing_tests: mark(item["name"],item["status"],item["detail"]) + + agree=order_block.get("relative_change_E_inf") + if isinstance(agree,(int,float)) and agree<=float(agreement_tol) and d20_ok and d30_ok: numerical="PASS" + elif isinstance(agree,(int,float)) and agree<=float(agreement_tol): numerical="BOUNDED" + else: numerical="BOUNDED" + classification={"numerical_observation":numerical,"mechanism":"NOT_CLAIMED", + "agreement_tol_E_inf":float(agreement_tol),"D20_D30_relative_E_inf":agree, + "neighborhood_coherent_D20":d20_ok,"neighborhood_coherent_D30":d30_ok, + "notes":"PASS/BOUNDED applies only to numerical observation of profile credibility; no viscous mechanism claim"} + + analysis={"schema":"steady-pinball-credibility-analysis/v1", + "primary_metric":"full-profile E_inf_vector of q_ctl-q_in at x/D=10", + "secondary_metric":"full-profile E_L2_vector", + "evidence_root":str(evidence), + "resolution_s3.55":resolution,"D20_D30_change":order_block, + "strip_height":{"cases":strip,"delta":strip_delta,"summary_reused":domain_summary}, + "s_neighborhood":neighborhood,"neighborhood_coherence":{"D20":d20_coh,"D30":d30_coh}, + "settling_repeatability":{k:resolution[k].get("settling") for k in resolution if isinstance(resolution[k],dict)}, + "reused_summaries":{"grid_summary":grid_summary,"D30_local_summary":d30_local}, + "status_flags":status_flags,"missing_or_bounded_tests":missing_tests, + "classification":classification, + "reproduce_command":f'PYTHONPATH="$PWD/src" conda run -n pinball_math python -m steady_pinball_theory.runner analyze-credibility --out {out}'} + source_files=[Path(__file__),Path(__file__).with_name("metrics.py"),Path(__file__).with_name("RESULTS.md")] + analysis["source_hashes"]={str(path.relative_to(Path(__file__).resolve().parents[2])):_sha256(path) for path in source_files if path.exists()} + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"analysis parent does not exist: {out.parent}") + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + analysis["payload_sha256"]=hashlib.sha256(_canonical_json(analysis)).hexdigest() + (temporary/"analysis.json").write_text(json.dumps(analysis,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(temporary,out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + return analysis + + +def promote_evidence(source, dest, *, scientific_question, notes=""): + """Atomically promote a /tmp analysis into evidence/authoritative with PROMOTION.json.""" + import shutil + source=Path(source); dest=Path(dest) + if not source.is_dir(): raise FileNotFoundError(f"promotion source missing: {source}") + if dest.exists(): raise FileExistsError(f"refusing to clobber {dest}") + if not dest.parent.is_dir(): raise FileNotFoundError(f"promotion parent missing: {dest.parent}") + files={} + for path in sorted(p for p in source.rglob("*") if p.is_file()): + rel=str(path.relative_to(source)); files[rel]={"sha256":_sha256(path),"bytes":path.stat().st_size} + promotion={"schema":"steady-pinball-evidence-promotion/v1","immutable":True,"role":"authoritative", + "scientific_question":scientific_question,"source_tmp":str(source),"notes":notes,"files":files} + temporary=Path(tempfile.mkdtemp(prefix=f".{dest.name}.tmp-",dir=dest.parent)) + try: + for rel in files: + target=temporary/rel; target.parent.mkdir(parents=True,exist_ok=True); shutil.copy2(source/rel,target) + (temporary/"PROMOTION.json").write_text(json.dumps(promotion,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(temporary,dest) + finally: + if temporary.exists(): shutil.rmtree(temporary) + index=_evidence_root()/"INDEX.json" + if index.exists(): + payload=json.loads(index.read_text()); name=dest.name + auth=list(payload.get("authoritative",[])) + if name not in auth: + auth.append(name); auth.sort(); payload["authoritative"]=auth + index.write_text(json.dumps(payload,indent=2,sort_keys=True,allow_nan=False)+"\n") + return promotion + + +def analyze_strip(out, *, finite_analysis=None): + """Run the frozen Stage-4 free-slip strip modal qualification.""" + from .metrics import (affine_profile_sensitivity, profile_errors, strip_modal_projection, + strip_mode_parity_sector) + from .theory import affine_velocity, circulation_basis, solve_mfs, strip_basis_affine + out=Path(out); centers=np.array([[0.,0.],[1.3,.75],[1.3,-.75]]) + H=15.; radius=.5; stations=(4.,6.,8.,10.,12.,14.,16.); layers_set=(20,40,80); modes=12 + y=np.linspace(-H,H,3001); names=("rear_opposite","common_rear","front_only") + results={}; saved={"y":y} + for layers in layers_set: + layer={} + for name in names: + affine=strip_basis_affine(centers,radius,name,H=H,u_inf=1,n_boundary=32,source_ratio=.65,image_layers=layers) + station_rows={}; base_projections=[]; direction_projections=[] + for station in stations: + points=np.column_stack((np.full_like(y,station),y)) + base=affine["zero"].velocity(points)-np.array([1.,0.]) + direction=affine["unit"].velocity(points)-affine["zero"].velocity(points) + pb=strip_modal_projection(y,base,H,modes=modes); pd=strip_modal_projection(y,direction,H,modes=modes) + base_projections.append(pb["modes"]); direction_projections.append(pd["modes"]) + def summary(projection, parity): + rows=projection["modes"] + abs_disagreement=np.abs(rows[:,2]-rows[:,3]) + amplitude=np.sqrt(np.sum(rows[:,2:4]**2,axis=1)) + floor=max(float(np.max(amplitude))*1e-8,1e-12) + parity_allowed=(rows[:,0].astype(int)%2==(0 if parity=="even" else 1)) + significant=(amplitude>=floor)&parity_allowed + relative=np.full(len(rows),np.nan) + relative[significant]=abs_disagreement[significant]/amplitude[significant] + return {"through_flow_zero_mode":projection["through_flow_zero_mode"], + "modes":rows.tolist(),"ux_uy_absolute_disagreement":abs_disagreement.tolist(), + "significance_floor":floor,"parity_sector":parity,"parity_allowed":parity_allowed.tolist(), + "significant":significant.tolist(),"ux_uy_relative_disagreement_significant_only":[None if np.isnan(v) else float(v) for v in relative]} + station_rows[str(int(station))]={"base":summary(pb,strip_mode_parity_sector("base")),"direction":summary(pd,strip_mode_parity_sector(name))} + base_projections=np.asarray(base_projections); direction_projections=np.asarray(direction_projections) + def collapse(data, parity): + k=data[0,:,1]; scaled=data[:,:,2:4]*np.exp((np.asarray(stations)[:,None]-stations[0])*k[None,:])[:,:,None] + mean=np.mean(scaled,axis=0); spread=np.max(np.abs(scaled-mean),axis=0) + amplitude=np.sqrt(np.sum(mean*mean,axis=1)); floor=max(float(amplitude.max())*1e-8,1e-12) + allowed=(np.arange(1,len(amplitude)+1)%2==(0 if parity=="even" else 1)) + significant=(amplitude>=floor)&allowed + return {"reference_station":stations[0],"collapsed_mean":mean.tolist(),"collapsed_max_abs_spread":spread.tolist(), + "significance_floor":floor,"parity_sector":parity,"significant":significant.tolist(), + "significant_modes_absolute_spread":spread[significant].tolist(),"significant_modes":(np.flatnonzero(significant)+1).astype(int).tolist()} + points10=np.column_stack((np.full_like(y,10.),y)); base10=affine["zero"].velocity(points10); direction10=affine["unit"].velocity(points10)-base10 + objective=affine_profile_sensitivity(base10,direction10,u_inf=1); optimum=base10+objective["g_opt"]*direction10 + errors=profile_errors(optimum[:,0],optimum[:,1],u_inf=1) + direct,_=solve_mfs(centers,radius,0.5*objective["g_opt"]*circulation_basis(name),u_inf=1,n_boundary=32,source_ratio=.65,H=H,image_layers=layers) + held_affine=base10+0.5*objective["g_opt"]*direction10 + held_error=float(np.max(np.abs(held_affine-direct.velocity(points10)))) + layer[name]={"basis":affine["basis"].tolist(),"parity":{"base":"even","direction":strip_mode_parity_sector(name)},"stations":station_rows,"base_collapse":collapse(base_projections,"even"), + "direction_collapse":collapse(direction_projections,strip_mode_parity_sector(name)),"objective":{"J0":objective["J0"],"g_opt":objective["g_opt"], + "J_opt":objective["J_opt"],"E_inf_vector_opt":errors["E_inf_vector"],"E_L2_vector_opt":errors["E_L2_vector"], + "held_amplitude":0.5*objective["g_opt"],"held_affine_direct_Linf":held_error}} + if layers==40: + saved[f"{name}_base_x10"]=base10; saved[f"{name}_direction_x10"]=direction10; saved[f"{name}_optimum_x10"]=optimum + results[str(layers)]=layer + convergence={} + for name in names: + opts=np.array([results[str(L)][name]["objective"]["g_opt"] for L in layers_set]) + mode_arrays=np.array([results[str(L)][name]["stations"]["10"]["direction"]["modes"] for L in layers_set]) + convergence[name]={"g_opt":opts.tolist(),"g_opt_successive_abs_change":np.abs(np.diff(opts)).tolist(), + "x10_direction_mode_successive_Linf":np.max(np.abs(np.diff(mode_arrays[:,:,2:4],axis=0)),axis=(1,2)).tolist()} + actual_g=None + if finite_analysis is not None: + finite=json.loads(Path(finite_analysis).read_text()); actual_g=float(finite["closure"]["observed_g"]) + favorable=[results["40"][name]["objective"]["J_opt"] for name in names] + rear_unique=bool(favorable[0]0.2*h)} + core="PASS" if all(checks.values()) else "FAIL"; overall="BOUNDED" if core=="PASS" else "FAIL" + return {"schema":config["schema"],"expected_self_advection":expected,"runs":runs,"window_refinement":window,"time_refinement":time, + "perturbed_geometry_sensitivity":{"initial_aligned_L2":initial_sensitivity,"final_aligned_L2":final_sensitivity,"amplification":final_sensitivity/max(initial_sensitivity,np.finfo(float).eps),"interpretation":config["perturbation"]["label"]}, + "checks":checks,"classification":{"mathematical_core":core,"K1":overall,"K2_authorized":False,"K2_gate":"NO-GO: required source-verified Mowlavi growth/impulse oracle remains publication-held"}} + + +def write_karman_baseline(out): + out=Path(out); config=_karman_config(); result=_karman_run(config) + # Re-run before publication: canonical payload equality is the reproducibility gate. + repeat=_karman_run(config); reproducible=_canonical_json(result)==_canonical_json(repeat) + result["checks"]["byte_reproducible_payload"]=reproducible + if not reproducible: + result["classification"].update(mathematical_core="FAIL",K1="FAIL",K2_authorized=False,K2_gate="NO-GO: non-reproducible payload") + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"artifact parent does not exist: {out.parent}") + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + (temporary/"config.json").write_text(json.dumps(config,indent=2,sort_keys=True,allow_nan=False)+"\n") + (temporary/"result.json").write_text(json.dumps(result,indent=2,sort_keys=True,allow_nan=False)+"\n") + source_files=[Path(__file__),Path(__file__).with_name("theory.py"),Path(__file__).with_name("metrics.py"),Path(__file__).with_name("DERIVATION.md")] + manifest={"schema":config["schema"],"immutable":True,"files":{name:{"sha256":_sha256(temporary/name),"bytes":(temporary/name).stat().st_size} for name in ("config.json","result.json")}, + "source_hashes":{str(path.relative_to(Path(__file__).resolve().parents[2])):_sha256(path) for path in source_files}} + manifest["manifest_payload_sha256"]=hashlib.sha256(_canonical_json(manifest)).hexdigest() + (temporary/"manifest.json").write_text(json.dumps(manifest,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(temporary,out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + return result + +def _json_safe(value): + if isinstance(value, dict): + return {k: _json_safe(v) for k, v in value.items()} + if isinstance(value, list): + return [_json_safe(v) for v in value] + if isinstance(value, (float, np.floating)): + x = float(value) + if not np.isfinite(x): + return None + return x + if isinstance(value, (np.integer,)): + return int(value) + if isinstance(value, (np.bool_,)): + return bool(value) + return value + + +def analyze_semi_analytic(*, out, evidence_root=None): + """Layered semi-analytic composite fit with spatial/s/direction held-out gates.""" + from .metrics import (fit_linear_composite, fit_two_point_affine_closure, + held_out_improvement, predict_affine_closure, + profile_errors, profile_station_errors) + from .theory import composite_model_fields, strip_basis_affine + evidence = Path(evidence_root) if evidence_root is not None else _evidence_root() + out = Path(out) + bridge = evidence / "authoritative" / "steady-finite-re-bridge-d20-20260804" + contract = evidence / "authoritative" / "steady-contract-d20-20260806" + names = ("qin", "accepted-s3.45", "accepted-s3.55", "accepted-s3.65") + loaded = {name: load_legacy_force_artifact(bridge / name) for name in names} + rev = load_legacy_force_artifact(contract / "reverse-s5.2") + qmanifest, q = loaded["qin"] + U = float(qmanifest["spec"]["config_lbm"]["physics"]["velocity"]) + D = float(qmanifest["spec"]["D"]) + center0 = np.asarray(qmanifest["spec"]["centers_xy"][0], float) + centers = (np.asarray(qmanifest["spec"]["centers_xy"], float) - center0) / D + radius = 0.5 + x = (q["x"] - center0[0]) / D + y = (q["y"] - center0[1]) / D + qvel = np.stack((q["ux"], q["uy"]), axis=-1) / U + affine = strip_basis_affine(centers, radius, "rear_opposite", H=15, u_inf=1, + n_boundary=32, source_ratio=0.65, image_layers=40) + ix_fit = np.flatnonzero((x >= -2.0) & (x <= 2.0))[::2] + iy_fit = np.flatnonzero((np.abs(y) <= 6.0))[::2] + ix_held = np.flatnonzero(x > 2.0)[::2] + xx_fit, yy_fit = np.meshgrid(x[ix_fit], y[iy_fit], indexing="xy") + fit_pts = np.column_stack((xx_fit.ravel(), yy_fit.ravel())) + geometry = np.ones(xx_fit.shape, dtype=bool) + for c in centers: + geometry &= (xx_fit - c[0]) ** 2 + (yy_fit - c[1]) ** 2 >= 0.75 ** 2 + + def _component_block(omega_abs, branch): + block = composite_model_fields( + fit_pts, centers=centers, radius=radius, omega=omega_abs, branch=branch, + H=15, u_inf=1.0, n_boundary=32, source_ratio=0.65, image_layers=40, + coeffs={"alpha_vi": 1.0, "alpha_gap": 1.0, "wake_amplitude": 0.0, + "wake_width": 0.5, "gamma": 0.0}) + shape = xx_fit.shape + (2,) + uniform = np.array([1.0, 0.0]) + q0 = block["q_mfs0"].reshape(shape) - uniform + qvi = block["q_vi"].reshape(shape) + qgap = block["q_gap"].reshape(shape) + qwake = block["q_wake"].reshape(shape) + qgamma = (affine["unit"].velocity(fit_pts) - + affine["zero"].velocity(fit_pts)).reshape(shape) + return q0, qvi, qgap, qwake, qgamma, block["gaps"] + + def _predict(coeffs, q0, qvi, qgap, qwake, qgamma): + pred = np.zeros_like(q0) + pred += coeffs.get("q_mfs0", coeffs.get("intercept", 0.0)) * q0 + pred += coeffs.get("alpha_vi", 0.0) * qvi + pred += coeffs.get("alpha_gap", 0.0) * qgap + pred += coeffs.get("wake", 0.0) * qwake + pred += coeffs.get("gamma", 0.0) * qgamma + return pred + + def _case_analysis(name, manifest, arrays, *, branch, svalue): + if not manifest.get("result", {}).get("settling", {}).get("qualified", False): + raise ValueError(f"{name} is not a qualified endpoint") + velocity = np.stack((arrays["ux"], arrays["uy"]), axis=-1) / U + delta = velocity - qvel + common = q["fluid_mask"] & arrays["fluid_mask"] + fitmask = geometry & common[np.ix_(iy_fit, ix_fit)] + obs = delta[np.ix_(iy_fit, ix_fit)] + omega_abs = abs(float(manifest["spec"]["action_omega"][1])) + q0, qvi, qgap, qwake, qgamma, gaps = _component_block(omega_abs, branch) + fit_mfs0 = fit_linear_composite(obs, [("q_mfs0", q0)], fitmask) + fit_gamma = fit_linear_composite(obs, [("q_mfs0", q0), ("gamma", qgamma)], fitmask) + fit_full = fit_linear_composite( + obs, [("q_mfs0", q0), ("alpha_vi", qvi), ("alpha_gap", qgap), + ("wake", qwake), ("gamma", qgamma)], fitmask) + pred_mfs0 = fit_mfs0["prediction"] + pred_gamma = fit_gamma["prediction"] + pred_full = fit_full["prediction"] + xx_held, yy_held = np.meshgrid(x[ix_held], y[iy_fit], indexing="xy") + held_pts = np.column_stack((xx_held.ravel(), yy_held.ravel())) + held_geom = np.ones(xx_held.shape, dtype=bool) + for c in centers: + held_geom &= (xx_held - c[0]) ** 2 + (yy_held - c[1]) ** 2 >= 0.75 ** 2 + held_mask = held_geom & common[np.ix_(iy_fit, ix_held)] + held_obs = delta[np.ix_(iy_fit, ix_held)] + hshape = xx_held.shape + (2,) + hblock = composite_model_fields( + held_pts, centers=centers, radius=radius, omega=omega_abs, branch=branch, + H=15, u_inf=1.0, n_boundary=32, source_ratio=0.65, image_layers=40, + coeffs={"alpha_vi": 1.0, "alpha_gap": 1.0, "wake_amplitude": 0.0, + "wake_width": 0.5, "gamma": 0.0}) + hq0 = hblock["q_mfs0"].reshape(hshape) - np.array([1.0, 0.0]) + hqvi = hblock["q_vi"].reshape(hshape) + hqgap = hblock["q_gap"].reshape(hshape) + hqwake = hblock["q_wake"].reshape(hshape) + hqgamma = (affine["unit"].velocity(held_pts) - affine["zero"].velocity(held_pts)).reshape(hshape) + held_pred_mfs0 = fit_mfs0["coefficients"]["q_mfs0"] * hq0 + held_pred_gamma = _predict(fit_gamma["coefficients"], hq0, hqvi, hqgap, hqwake, hqgamma) + held_pred_full = _predict(fit_full["coefficients"], hq0, hqvi, hqgap, hqwake, hqgamma) + stations = {} + for station in (2, 4, 6, 10): + stations[str(station)] = { + "observed": profile_station_errors(delta, x, y, station, fluid_mask=common), + } + ix = int(np.argmin(np.abs(x - float(station)))) + rows = common[:, ix].copy() + rows[[0, -1]] = False + if rows.any(): + pts = np.column_stack((np.full(rows.sum(), x[ix]), y[rows])) + blk = composite_model_fields( + pts, centers=centers, radius=radius, omega=omega_abs, branch=branch, + H=15, u_inf=1.0, n_boundary=32, source_ratio=0.65, image_layers=40, + coeffs={"alpha_vi": 1.0, "alpha_gap": 1.0, "wake_amplitude": 0.0, + "wake_width": 0.5, "gamma": 0.0}) + g0 = blk["q_mfs0"] - np.array([1.0, 0.0]) + gvi = blk["q_vi"] + ggap = blk["q_gap"] + gwake = blk["q_wake"] + ggamma = affine["unit"].velocity(pts) - affine["zero"].velocity(pts) + obs_prof = delta[rows, ix] + for label, coeffs, use_full in ( + ("mfs0", fit_mfs0["coefficients"], False), + ("mfs0_gamma", fit_gamma["coefficients"], True), + ("composite", fit_full["coefficients"], True)): + if label == "mfs0": + pred_prof = coeffs["q_mfs0"] * g0 + else: + pred_prof = _predict(coeffs, g0, gvi, ggap, gwake, ggamma) + resid = obs_prof - pred_prof + stations[str(station)][label] = profile_errors( + resid[:, 0], resid[:, 1], u_inf=1.0) + else: + for label in ("mfs0", "mfs0_gamma", "composite"): + stations[str(station)][label] = {"E_inf_vector": None, "availability": "empty_profile"} + return { + "artifact": name, "branch": branch, "s": float(svalue), + "endpoint_sha256": manifest["files"][ARRAY_FILE]["sha256"], + "gap_oracle": gaps, + "fit_region_points": int(fitmask.sum()), + "held_out_region_points": int(held_mask.sum()), + "baselines": { + "mfs0": {"coefficients": fit_mfs0["coefficients"], + "condition_number": fit_mfs0["condition_number"], + "near_RMS": fit_mfs0["weighted_RMS"], + "held_out": held_out_improvement( + held_obs - held_pred_mfs0, held_obs - held_pred_mfs0, held_mask)}, + "mfs0_gamma": {"coefficients": fit_gamma["coefficients"], + "condition_number": fit_gamma["condition_number"], + "near_RMS": fit_gamma["weighted_RMS"], + "held_out": held_out_improvement( + held_obs - held_pred_mfs0, held_obs - held_pred_gamma, held_mask)}, + "composite": {"coefficients": fit_full["coefficients"], + "condition_number": fit_full["condition_number"], + "near_RMS": fit_full["weighted_RMS"], + "held_out": held_out_improvement( + held_obs - held_pred_mfs0, held_obs - held_pred_full, held_mask)}, + }, + "stations": stations, + "downstream_ranking": { + "observed_E_inf_at_10": stations["10"]["observed"]["E_inf_vector"], + "composite_residual_E_inf_at_10": stations["10"]["composite"]["E_inf_vector"], + }, + } + + cases = {} + for name, svalue in zip(names[1:], (3.45, 3.55, 3.65)): + cases[f"s{svalue:.2f}"] = _case_analysis( + name, loaded[name][0], loaded[name][1], branch="plus-minus", svalue=svalue) + cases["reverse-s5.20"] = _case_analysis( + "reverse-s5.2", rev[0], rev[1], branch="minus-plus", svalue=5.2) + + # s held-out: fit composite coeffs vs s on train, predict s=3.55 + train = [cases["s3.45"]["baselines"]["composite"]["coefficients"], + cases["s3.65"]["baselines"]["composite"]["coefficients"]] + keys = sorted(train[0]) + closure = {} + for key in keys: + cfit = fit_two_point_affine_closure([3.45, 3.65], [train[0][key], train[1][key]]) + closure[key] = {**cfit, "predicted_s3.55": predict_affine_closure(cfit, 3.55), + "observed_s3.55": cases["s3.55"]["baselines"]["composite"]["coefficients"][key]} + s_held = {k: abs(closure[k]["predicted_s3.55"] - closure[k]["observed_s3.55"]) / + max(abs(closure[k]["observed_s3.55"]), 1e-12) for k in keys} + + acc = cases["s3.55"]["baselines"]["composite"]["held_out"] + imp_gamma = cases["s3.55"]["baselines"]["mfs0_gamma"]["held_out"] + imp_full = acc + ranking_ok = bool( + cases["s3.55"]["downstream_ranking"]["observed_E_inf_at_10"] < + cases["reverse-s5.20"]["downstream_ranking"]["observed_E_inf_at_10"]) + gap_sign_ok = bool( + cases["s3.55"]["gap_oracle"]["rear_rear"]["Q_g"] * + cases["reverse-s5.20"]["gap_oracle"]["rear_rear"]["Q_g"] < 0) + spatial_pass = bool(imp_full.get("significant") and (imp_full.get("relative_improvement") or 0) > 0.05) + s_pass = bool(all(v is not None and v <= 0.15 for v in s_held.values())) + direction_pass = bool(ranking_ok and gap_sign_ok) + overall = "PASS" if spatial_pass and direction_pass else ("BOUNDED" if spatial_pass or direction_pass else "FAIL") + + source_files = [Path(__file__), Path(__file__).with_name("theory.py"), + Path(__file__).with_name("metrics.py"), Path(__file__).with_name("DERIVATION.md")] + analysis = _json_safe({ + "schema": "steady-pinball-semi-analytic/v1", + "model": "q_SA = q_MFS0 + alpha_VI q_VI + alpha_gap q_gap + q_wake (+ optional gamma)", + "preregistration": { + "fit_region": "x/D<=2, |y/D|<=3, >=0.75D from bodies, common fluid", + "held_out_spatial": "x/D>2 common fluid", + "train_s": [3.45, 3.65], "held_out_s": 3.55, + "direction_case": "reverse-s5.2 with minus-plus branch", + "baselines": ["MFS0", "MFS0+Gamma", "MFS0+VI+gap+wake"], + }, + "cases": cases, + "s_held_out_closure": closure, + "s_held_out_relative_errors": s_held, + "classification": { + "spatial_held_out": "PASS" if spatial_pass else "BOUNDED", + "s_held_out": "PASS" if s_pass else "BOUNDED", + "direction_branch": "PASS" if direction_pass else "FAIL", + "gap_sign_reversal": "PASS" if gap_sign_ok else "FAIL", + "downstream_ranking": "PASS" if ranking_ok else "FAIL", + "overall": overall, + "notes": "Composite model targets accepted/DRL wall sense; prescribed circulation remains descriptive only.", + }, + "source_hashes": {str(p.relative_to(Path(__file__).resolve().parents[2])): _sha256(p) + for p in source_files}, + "reproduce_command": f'PYTHONPATH="$PWD/src" conda run -n pinball_math python -m steady_pinball_theory.runner analyze-semi-analytic --out {out}', + }) + if out.exists(): + raise FileExistsError(f"refusing to clobber {out}") + temporary = Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-", dir=out.parent)) + try: + analysis["payload_sha256"] = hashlib.sha256(_canonical_json(analysis)).hexdigest() + (temporary / "analysis.json").write_text( + json.dumps(analysis, indent=2, sort_keys=True, allow_nan=False) + "\n") + _publish_directory_no_replace(temporary, out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + return analysis + + + +PARENT_SCHEMA="steady-pinball-accepted-parent/v1" +ACQUISITION_SCHEMA="steady-pinball-branch-acquisition/v1" +STABILITY_FAMILIES=("symmetric","antisymmetric") + + +def _atomic_campaign(out, roles, run_role): + """Stage every role as a sibling and expose the campaign only when complete.""" + out=Path(out) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"campaign parent does not exist: {out.parent}") + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + for role in roles: run_role(temporary,role) + _publish_directory_no_replace(temporary,out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + + +def _load_accepted_parent(parent): + parent=Path(parent).resolve(strict=True); record=json.loads((parent/"parent.json").read_text()) + payload=record.pop("payload_sha256",None) + if record.get("schema")!=PARENT_SCHEMA or not record.get("immutable") or payload!=hashlib.sha256(_canonical_json(record)).hexdigest(): raise ValueError("invalid accepted-parent manifest") + record["payload_sha256"]=payload; endpoint,arrays=load_validate_artifact(parent/record["endpoint"]["path"]) + if endpoint["manifest_payload_sha256"]!=record["endpoint"]["manifest_payload_sha256"] or endpoint["spec"]["kind"]!="accepted" or not endpoint["result"].get("qualification_passed"): raise ValueError("parent is not exact qualified accepted endpoint") + checkpoint=parent/record["checkpoint"]["path"] + if not checkpoint.is_file() or checkpoint.stat().st_size!=record["checkpoint"]["bytes"] or _sha256(checkpoint)!=record["checkpoint"]["sha256"]: raise ValueError("accepted-parent checkpoint binding mismatch") + for key in ("action_omega","config_lbm","centers_xy","radius"): + if record[key]!=endpoint["spec"][key]: raise ValueError(f"accepted-parent {key} mismatch") + return record,endpoint,arrays,checkpoint + + +def acquire_accepted_parent(out, *, intended_celeris_root, s=3.55, D=20.0): + """Explicit prerequisite which alone may create an accepted parent checkpoint.""" + _assert_cfd_environment(intended_celeris_root=intended_celeris_root) + def build(stage,_): + checkpoint=stage/"accepted.checkpoint" + manifest=_run_case_unlocked(stage/"endpoint",kind="accepted",s=s,D=D,intended_celeris_root=intended_celeris_root,checkpoint_path=checkpoint) + if not manifest["result"].get("qualification_passed"): raise RuntimeError("accepted parent endpoint did not qualify") + record={"schema":PARENT_SCHEMA,"immutable":True,"checkpoint":{"path":checkpoint.name,"sha256":_sha256(checkpoint),"bytes":checkpoint.stat().st_size},"endpoint":{"path":"endpoint","manifest_payload_sha256":manifest["manifest_payload_sha256"]},"action_omega":manifest["spec"]["action_omega"],"config_lbm":manifest["spec"]["config_lbm"],"centers_xy":manifest["spec"]["centers_xy"],"radius":manifest["spec"]["radius"],"source_environment":manifest["spec"]["source_environment"]} + record["payload_sha256"]=hashlib.sha256(_canonical_json(record)).hexdigest(); (stage/"parent.json").write_text(json.dumps(record,indent=2,sort_keys=True,allow_nan=False)+"\n") + with exclusive_cfd_lease(role="accepted-parent"): + enforce_launch_cooldown(); _atomic_campaign(out,("parent",),build) + return _load_accepted_parent(out) + + +def _new_parent_simulation(record, checkpoint, simulation_factory): + with tempfile.TemporaryDirectory(prefix="steady_branch_cfg_") as td: + lp=Path(td)/"lbm.json"; bp=Path(td)/"body.json"; lp.write_text(json.dumps(record["config_lbm"])) + objects=[{"type":"cylinder","center":z,"radius":record["radius"],"omega":w} for z,w in zip(record["centers_xy"],record["action_omega"])] + bp.write_text(json.dumps({"objects":objects})); sim=simulation_factory(lbm_config_path=str(lp),body_config_path=str(bp)) + sim.initialize(); loader=getattr(sim,"load_checkpoint",None) + if not callable(loader): sim.close(); raise RuntimeError("Simulation lacks required load_checkpoint API") + digest=_sha256(checkpoint); loader(str(checkpoint)) + if digest!=record["checkpoint"]["sha256"] or _sha256(checkpoint)!=digest: sim.close(); raise RuntimeError("parent checkpoint changed during restore") + if sim.bodies.count!=3 or [o.obj_id for o in sim.bodies.objects]!=[0,1,2]: sim.close(); raise RuntimeError("restored body registry mismatch") + if not np.array_equal(np.asarray([o.center[:2] for o in sim.bodies.objects],float),np.asarray(record["centers_xy"],float)): sim.close(); raise RuntimeError("restored geometry/order mismatch") + return sim + + +def _set_exact_action(sim, action): + action=np.asarray(action,float) + if action.shape!=(3,) or not np.isfinite(action).all(): raise ValueError("branch action must be finite length three") + for body_id,omega in enumerate(action): sim.set_body(body_id,omega=float(omega)) + + +def _capture_branch_row(sim, record, action, step, D): + """One-clock field/torque capture; unavailable spatial metrics abort acquisition.""" + from .metrics import bilinear_sample_velocity,gap_mass_momentum_flux,near_wall_tangential_speed,recirculation_observables,tensor_trapezoid_weights,torque_to_actuator_power,wake_deficit_observables + nx=record["config_lbm"]["grid"]["nx"]; ny=record["config_lbm"]["grid"]["ny"]; m=sim.get_macroscopic() + ux=_reshape_exact("ux",m["ux"],ny,nx); uy=_reshape_exact("uy",m["uy"],ny,nx); rho=_reshape_exact("rho",m["rho"],ny,nx) + flags,fluid,body=topology_from_solver_flags(np.asarray(sim.get_flags(),np.uint16),nx=nx,ny=ny,centers=record["centers_xy"],radius=record["radius"],controlled=True) + x=np.arange(nx,dtype=float); y=np.arange(ny,dtype=float); centers=np.asarray(record["centers_xy"],float); radius=float(record["radius"]); u=.01 + velocity=lambda p: bilinear_sample_velocity(x,y,ux,uy,p,valid_mask=fluid) + density=lambda p: bilinear_sample_velocity(x,y,rho,np.zeros_like(rho),p,valid_mask=fluid)[:,0] + exclusion_radius=1.1*radius + gaps=[gap_mass_momentum_flux(velocity,density,centers[a],centers[b],exclusion_radius,samples=1001) for a,b in ((0,1),(0,2),(1,2))] + local=near_wall_tangential_speed(x,y,ux,uy,fluid,body,centers,radius); available=[v for v in local["bodies"].values() if v.get("availability")=="available"] + if len(available)!=2: raise RuntimeError("local metric unavailable from actual field") + xx=(x-centers[0,0])[None,:]/D; yy=np.abs(y-centers[0,1])[:,None]/D; mask=fluid&(xx>=1.8)&(xx<4)&(yy<=3) + near=recirculation_observables(x,ux,mask,tensor_trapezoid_weights(x,y))["area"]/(D*D); stations=[] + for xd in (2,4,6,10): + ix=int(round(centers[0,0]+xd*D)); stations.append(wake_deficit_observables((y-centers[0,1])/D,ux[:,ix]/u,fluid[:,ix])["momentum_deficit_proxy"]) + tau=np.array([np.asarray(sim.read_body(i,normalize=True).torque,float).reshape(-1)[0] for i in range(3)]); direct=np.array([np.asarray(sim.read_torque(i,normalize=True),float).reshape(-1)[0] for i in range(3)]) + if not np.array_equal(tau,direct): raise RuntimeError("torque APIs disagree") + power_record=torque_to_actuator_power(tau[None,:],np.asarray(action,float)[None,:],torque_ownership="actuator_on_fluid",rho_ref=1,u_ref=u,diameter=D) + power=float(np.asarray(power_record["total_power"],float)[0]) + row=[step,step*u/D,tau.sum(),power,sum(g["Q_g"] for g in gaps),np.mean([v["rms_tangential_speed"] for v in available]),near,*stations] + if not np.isfinite(row).all(): raise RuntimeError("nonfinite synchronized telemetry") + return row,np.stack((ux,uy),axis=-1) + + +def _write_branch(out, metadata, rows, norms): + tmp=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + data={"telemetry":np.asarray(rows,float)} + if norms is not None: data["norm_history"]=np.asarray(norms,float) + np.savez_compressed(tmp/"telemetry.npz",**data); metadata=dict(metadata,immutable=True,files={"telemetry.npz":{"sha256":_sha256(tmp/"telemetry.npz"),"bytes":(tmp/"telemetry.npz").stat().st_size}}); metadata["payload_sha256"]=hashlib.sha256(_canonical_json(metadata)).hexdigest(); (tmp/"manifest.json").write_text(json.dumps(metadata,indent=2,sort_keys=True,allow_nan=False)+"\n"); _publish_directory_no_replace(tmp,out) + finally: + if tmp.exists(): + import shutil; shutil.rmtree(tmp) + + +def _run_branch(record,checkpoint,out,role,initial_action,steps,stride,D,factory,base_field=None,pulse_steps=None): + sim=_new_parent_simulation(record,checkpoint,factory); action=np.asarray(initial_action,float); applied=action.copy(); rows=[]; norms=[] + try: + _set_exact_action(sim,action) + for stop in range(stride,steps+1,stride): + sim.run(stride,zero_obs=True); row,field=_capture_branch_row(sim,record,action,stop,D); rows.append(row) + if base_field is not None: + delta=field-base_field; norms.append([stop,row[1],np.linalg.norm(delta.ravel()),np.max(np.abs(delta))]) + if pulse_steps is not None and stop>=pulse_steps: + action=np.asarray(record["action_omega"],float); _set_exact_action(sim,action); pulse_steps=None + finally: sim.close() + _write_branch(out,{"schema":ACQUISITION_SCHEMA,"role":role,"parent_sha256":record["checkpoint"]["sha256"],"initial_action_omega":applied.tolist(),"clock_columns":["post_parent_lattice_step","tU_over_D"],"telemetry_channels":list(SWITCH_TELEMETRY_CHANNELS),"branch_indicator":float(np.sign(rows[-1][4])) if norms is not None else None},rows,norms if base_field is not None else None) + + +def _production_factory(root, factory): + if factory is not None: return factory + import CelerisLab + _source_identity(celeris_module=CelerisLab,intended_celeris_root=root); return CelerisLab.Simulation + + +def acquire_causal_switch(out, *, parent, intended_celeris_root, horizon=10., sample_dt=.1, simulation_factory=None): + """Legacy entry retained but prohibited from creating anonymous v1 telemetry.""" + raise RuntimeError("v1 transient acquisition is archived; v2 reacquisition requires authenticated accepted/reverse endpoint references and named t*=0 channels") + _assert_cfd_environment(intended_celeris_root=intended_celeris_root); record,endpoint,_,checkpoint=_load_accepted_parent(parent) + if record["source_environment"].get("celeris_intended_root")!=str(Path(intended_celeris_root).resolve()): raise RuntimeError("parent Celeris root differs from intended root") + factory=_production_factory(intended_celeris_root,simulation_factory); D=float(endpoint["spec"]["D"]); steps=int(round(horizon*D/.01)); stride=int(round(sample_dt*D/.01)); contract=causal_switch_contract(checkpoint,s=endpoint["spec"]["s"],diameter=D,sample_dt=sample_dt) + def run(stage,role): enforce_launch_cooldown(); _run_branch(record,checkpoint,stage/role,role,contract["branches"][role]["action_omega"],steps,stride,D,factory) + with exclusive_cfd_lease(role="causal-switch"): _atomic_campaign(out,CAUSAL_SWITCH_ROLES,run) + + +def acquire_stability(out, *, parent, intended_celeris_root, amplitudes, horizon=10., pulse_duration=.5, sample_dt=.1, simulation_factory=None): + _assert_cfd_environment(intended_celeris_root=intended_celeris_root); record,endpoint,arrays,checkpoint=_load_accepted_parent(parent) + if record["source_environment"].get("celeris_intended_root")!=str(Path(intended_celeris_root).resolve()): raise RuntimeError("parent Celeris root differs from intended root") + amps=tuple(float(a) for a in amplitudes) + if len(amps)<2 or len(set(amps))!=len(amps) or any(a<=0 or not np.isfinite(a) for a in amps): raise ValueError("stability requires two distinct positive amplitudes") + raise RuntimeError("v1 transient acquisition is archived; v2 nonlinear-return reacquisition requires authenticated accepted/reverse endpoint fields and common-mask distances") + factory=_production_factory(intended_celeris_root,simulation_factory); D=float(endpoint["spec"]["D"]); steps=int(round(horizon*D/.01)); stride=int(round(sample_dt*D/.01)); pulse=int(round(pulse_duration*D/.01)); baseline=np.asarray(record["action_omega"],float); base=np.stack((arrays["ux"],arrays["uy"]),axis=-1); roles=[f"{f}-a{a:.12g}" for f in STABILITY_FAMILIES for a in amps] + def run(stage,role): + family=role.split("-a",1)[0]; amplitude=float(role.split("-a",1)[1]); perturb=np.array([0,-amplitude,+amplitude]) if family=="symmetric" else np.array([0,+amplitude,+amplitude]); enforce_launch_cooldown(); _run_branch(record,checkpoint,stage/role,role,baseline+perturb,steps,stride,D,factory,base,pulse) + with exclusive_cfd_lease(role="stability"): _atomic_campaign(out,roles,run) + + +CAUSAL_SWITCH_ROLES=("continue-accepted","zero","equal-amplitude-reverse") +SWITCH_TELEMETRY_CHANNELS=("torque","power","gap","local","near_wake","station_2","station_4","station_6","station_10") + + +def causal_switch_contract(parent_checkpoint, *, s=3.55, diameter=20.0, sample_dt=0.1, + frozen_threshold=0.05, bootstrap_samples=1000, seed=0): + """Preregister exact same-parent switch branches without running CFD.""" + parent=Path(parent_checkpoint) + if not parent.is_file(): raise FileNotFoundError(f"accepted parent checkpoint missing: {parent}") + if not np.isfinite([s,diameter,sample_dt,frozen_threshold]).all() or min(s,diameter,sample_dt,frozen_threshold)<=0: raise ValueError("switch scalars must be finite and positive") + if isinstance(bootstrap_samples,(bool,np.bool_)) or int(bootstrap_samples)!=bootstrap_samples or bootstrap_samples<1: raise ValueError("bootstrap_samples must be a positive integer") + c=CanonicalContract(diameter=float(diameter)); accepted=np.asarray(c.action(float(s),"plus-minus"),float) + expected=np.asarray(c.oracle(float(s))["plus-minus"]["action"],float) + if not np.array_equal(accepted,expected): raise RuntimeError("canonical accepted action/body oracle mismatch") + digest=_sha256(parent); actions={"continue-accepted":accepted,"zero":np.zeros(3),"equal-amplitude-reverse":-accepted}; branches={} + for role in CAUSAL_SWITCH_ROLES: + branch=None if role=="zero" else ("plus-minus" if role=="continue-accepted" else "minus-plus") + branches[role]={"role":role,"parent_checkpoint":str(parent),"parent_sha256":digest,"body_order":list(c.body_order),"action_omega":actions[role].tolist(),"wall_oracle":None if branch is None else c.oracle(float(s))[branch]} + return {"schema":"steady-pinball-causal-switch/v1","immutable":True,"accepted_parent":{"path":str(parent),"sha256":digest,"qualification":"accepted checkpoint required"},"branches":branches,"s":float(s),"D":float(diameter),"telemetry":{"clock_columns":["lattice_step","tU_over_D"],"sample_dt_U_over_D":float(sample_dt),"channels":list(SWITCH_TELEMETRY_CHANNELS),"scope":"synchronized torque/power, gap/local/near-wake, stations x/D=2,4,6,10"},"analysis":{"paired_estimand":"branch minus continue-accepted at identical post-parent times","frozen_onset_threshold":float(frozen_threshold),"bootstrap_samples":int(bootstrap_samples),"seed":int(seed),"gates":["polarity","dose","sham"],"claim_boundary":"cross-correlation alone never supports a causal claim"}} + + +def _switch_matrix(name,value): + a=np.asarray(value,dtype=float) + if a.ndim==2: a=a[None,...] + if a.ndim!=3 or a.shape[1]<2 or a.shape[2]<3 or not np.isfinite(a).all(): raise ValueError(f"{name} telemetry must be finite (replicate,time,2+channels)") + if np.any(np.diff(a[:,:,1],axis=1)<=0): raise ValueError(f"{name} telemetry clock must increase") + return a + + +def analyze_paired_causal_switch(contract, telemetry, *, out=None): + """Analyze synchronized same-parent branches; correlation is never causal evidence.""" + if contract.get("schema")!="steady-pinball-causal-switch/v1": raise ValueError("wrong causal-switch contract") + if set(telemetry)!=set(CAUSAL_SWITCH_ROLES): raise ValueError("all and only preregistered switch branches are required") + arrays={r:_switch_matrix(r,telemetry[r]) for r in CAUSAL_SWITCH_ROLES}; shape=arrays[CAUSAL_SWITCH_ROLES[0]].shape; clocks=arrays[CAUSAL_SWITCH_ROLES[0]][:,:,:2] + if any(a.shape!=shape for a in arrays.values()): raise ValueError("switch telemetry shapes differ") + if any(not np.array_equal(a[:,:,:2],clocks) for a in arrays.values()): raise ValueError("switch telemetry clocks are not exactly synchronized") + channels=list(contract["telemetry"]["channels"]) + if shape[2]!=2+len(channels): raise ValueError("telemetry columns do not match frozen schema") + base=arrays["continue-accepted"][:,:,2:]; zero=arrays["zero"][:,:,2:]-base; reverse=arrays["equal-amplitude-reverse"][:,:,2:]-base + threshold=float(contract["analysis"]["frozen_onset_threshold"]); scale=np.maximum(np.max(np.abs(base),axis=1),np.finfo(float).eps) + def onset(diff): + hit=np.abs(diff)>threshold*scale[:,None,:]; values=np.full((shape[0],len(channels)),np.nan) + for r in range(shape[0]): + for j in range(len(channels)): + idx=np.flatnonzero(hit[r,:,j]) + if len(idx): values[r,j]=clocks[r,idx[0],1] + return values + oz,orr=onset(zero),onset(reverse); rng=np.random.default_rng(int(contract["analysis"]["seed"])); nboot=int(contract["analysis"]["bootstrap_samples"]); ordering=[] + for j,name in enumerate(channels): + finite=np.isfinite(oz[:,j])&np.isfinite(orr[:,j]); delta=orr[finite,j]-oz[finite,j] + if len(delta): + means=[float(np.mean(delta[rng.integers(0,len(delta),len(delta))])) for _ in range(nboot)]; ci=np.quantile(means,[.025,.975]).tolist(); observed=float(np.mean(delta)) + else: ci=[None,None]; observed=None + ordering.append({"channel":name,"reverse_minus_zero_onset":observed,"bootstrap_95_CI":ci,"replicates":int(finite.sum())}) + zmean=np.mean(zero[:,-1,:],axis=0); rmean=np.mean(reverse[:,-1,:],axis=0); polarity=bool(np.dot(zmean,rmean)>=0); dose=bool(np.linalg.norm(rmean)>=np.linalg.norm(zmean)); sham=float(np.max(np.abs(np.diff(base,axis=0)))) if shape[0]>1 else 0.; sham_pass=bool(sham<=threshold*max(float(np.max(np.abs(base))),np.finfo(float).eps)) + replicated=bool(shape[0]>=2) + local_indices=[channels.index(name) for name in ("torque","power","gap","local")] + downstream_indices=[channels.index(name) for name in ("station_2","station_4","station_6","station_10")] + def local_precedes_downstream(onsets): + rows=[] + for r in range(shape[0]): + local=onsets[r,local_indices]; downstream=onsets[r,downstream_indices] + rows.append(bool(np.isfinite(local).any() and np.isfinite(downstream).all() and np.nanmin(local)<=np.min(downstream))) + return bool(all(rows)),rows + zero_order,zero_rows=local_precedes_downstream(oz); reverse_order,reverse_rows=local_precedes_downstream(orr); temporal_order=zero_order and reverse_order + gates={"polarity":{"pass":polarity},"dose":{"pass":dose},"sham":{"pass":sham_pass,"max_continue_replicate_difference":sham},"replication":{"pass":replicated,"replicates":int(shape[0]),"minimum":2},"local_before_downstream":{"pass":temporal_order,"zero_by_replicate":zero_rows,"reverse_by_replicate":reverse_rows}} + passed=all(item["pass"] for item in gates.values()) + result={"schema":"steady-pinball-causal-switch-analysis/v2","parent_sha256":contract["accepted_parent"]["sha256"],"paired_differences":{"zero_minus_continue":zero.tolist(),"reverse_minus_continue":reverse.tolist()},"onset":{"definition":"first frozen-threshold crossing","ordering":ordering},"gates":gates,"classification":"PASS" if passed else "BOUNDED","claim_boundary":"same-parent intervention evidence; PASS requires replicated local-before-downstream onset, and cross-correlation alone cannot establish causality"} + if out is not None: + out=Path(out) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"analysis parent does not exist: {out.parent}") + tmp=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: (tmp/"analysis.json").write_text(json.dumps(result,indent=2,sort_keys=True,allow_nan=False)+"\n"); _publish_directory_no_replace(tmp,out) + finally: + if tmp.exists(): + import shutil; shutil.rmtree(tmp) + return result + + +def analyze_nonlinear_return(times, families, *, decay_ratio=0.1, growth_limit=2.0, switch_ratio=1.0): + """Classify finite-amplitude symmetric/antisymmetric return families.""" + t=np.asarray(times,dtype=float) + if t.ndim!=1 or len(t)<3 or not np.isfinite(t).all() or np.any(np.diff(t)<=0): raise ValueError("times must be finite and increasing") + if set(families)!={"symmetric","antisymmetric"}: raise ValueError("both perturbation families are required") + report={}; labels=[] + for family,runs in families.items(): + rows=[] + for amplitude,values in sorted(runs.items(),key=lambda z:float(z[0])): + a=float(amplitude); q=np.asarray(values,dtype=float) + if a<=0 or q.shape!=t.shape or not np.isfinite(q).all() or np.any(q<0): raise ValueError("invalid nonlinear-return trajectory") + growth=float(np.max(q)/max(q[0],np.finfo(float).eps)); terminal=float(q[-1]/max(q[0],np.finfo(float).eps)); switched=bool(np.max(q)>=switch_ratio); decayed=bool(terminal<=decay_ratio); label="unstable" if switched or growth>growth_limit else ("stable" if decayed else "bounded") + rows.append({"amplitude":a,"finite_time_growth":growth,"terminal_ratio":terminal,"asymptotic_decay":decayed,"branch_switching":switched,"classification":label}); labels.append(label) + report[family]=rows + overall="unresolved" if not labels else ("unstable" if "unstable" in labels else ("stable" if all(x=="stable" for x in labels) else "bounded")) + return {"schema":"steady-pinball-nonlinear-return/v1","families":report,"classification":overall,"claim_boundary":"finite-amplitude nonlinear return only; not global linear stability"} + + +def matrix_free_arnoldi(operator, dimension, *, epsilons=(1e-3,1e-4,1e-5), krylov_dimensions=(4,6,8), eigen_tolerance=1e-5): + """Generic feasibility Arnoldi for callable Jv(v,epsilon) or propagator(v).""" + n=int(dimension); eps=tuple(float(x) for x in epsilons); dims=tuple(int(x) for x in krylov_dimensions) + if n<2 or not callable(operator): raise ValueError("operator must be callable and dimension >=2") + if any(x<=0 or not np.isfinite(x) for x in eps) or any(m<2 or m>n for m in dims): raise ValueError("invalid epsilon or Krylov dimensions") + def apply(v,e): + try: y=operator(v,e) + except TypeError: y=operator(v) + y=np.asarray(y,dtype=float) + if y.shape!=(n,) or not np.isfinite(y).all(): raise ValueError("operator returned invalid vector") + return y + rows=[] + for e in eps: + for m in dims: + Q=np.zeros((n,m+1)); H=np.zeros((m+1,m)); Q[:,0]=np.arange(1,n+1); Q[:,0]/=np.linalg.norm(Q[:,0]); used=m + for j in range(m): + w=apply(Q[:,j],e) + for i in range(j+1): H[i,j]=np.dot(Q[:,i],w); w-=H[i,j]*Q[:,i] + H[j+1,j]=np.linalg.norm(w) + if H[j+1,j]<=100*np.finfo(float).eps: used=j+1; break + Q[:,j+1]=w/H[j+1,j] + vals=np.linalg.eigvals(H[:used,:used]); lead=vals[np.argmax(np.abs(vals))]; rows.append({"epsilon":e,"krylov_dimension":m,"used_dimension":used,"leading_eigenvalue":[float(lead.real),float(lead.imag)],"spectral_radius":float(abs(lead))}) + radii=np.array([r["spectral_radius"] for r in rows]).reshape(len(eps),len(dims)); ec=float(np.max(np.abs(np.diff(radii[:,-1])))) if len(eps)>1 else float("inf"); mc=float(np.max(np.abs(radii[:,-1]-radii[:,-2]))) if len(dims)>1 else float("inf"); passed=bool(ec<=eigen_tolerance and mc<=eigen_tolerance) + return {"schema":"steady-pinball-matrix-free-arnoldi/v1","runs":rows,"convergence":{"epsilon_max_change":ec,"krylov_max_change":mc,"tolerance":float(eigen_tolerance),"passed":passed},"global_stability":"AVAILABLE_FEASIBILITY_ONLY" if passed else "UNAVAILABLE_CONVERGENCE_GATES_FAILED","claim_boundary":"generic time-stepper/Jv feasibility only"} + + +# Stage-3 authenticated transient v2. The v1 format remains readable only through +# the explicitly bounded diagnostic loader below and is never promoted. +TRANSIENT_SCHEMA="steady-pinball-transient/v2" +TRANSIENT_CAMPAIGN_SCHEMA="steady-pinball-transient-campaign/v2" +LEGACY_TRANSIENT_SCHEMAS=("steady-pinball-branch-acquisition/v1",) +TRANSIENT_ARRAY_FILE="transient.npz" +TRANSIENT_BODY_ORDER=("front","rear_y_plus","rear_y_minus") +TRANSIENT_GAP_ORDER=("front_to_rear_y_plus","front_to_rear_y_minus","rear_y_plus_to_rear_y_minus") +TRANSIENT_STATION_ORDER=(2.0,4.0,6.0,10.0) +TRANSIENT_ARRAY_SCHEMAS={ + "clock":{"tail":[2],"columns":["post_parent_lattice_step","t_star"]}, + "action_omega":{"tail":[3],"columns":list(TRANSIENT_BODY_ORDER)}, + "torque_body":{"tail":[3],"columns":list(TRANSIENT_BODY_ORDER)}, + "power_body":{"tail":[3],"columns":list(TRANSIENT_BODY_ORDER)}, + "gap_Q":{"tail":[3],"columns":list(TRANSIENT_GAP_ORDER)}, + "gap_mass":{"tail":[3],"columns":list(TRANSIENT_GAP_ORDER)}, + "gap_J":{"tail":[3],"columns":list(TRANSIENT_GAP_ORDER)}, + "rear_wall_mean":{"tail":[2],"columns":["rear_y_plus","rear_y_minus"]}, + "rear_wall_rms":{"tail":[2],"columns":["rear_y_plus","rear_y_minus"]}, + "recirculation":{"tail":[1],"columns":["area_star"]}, + "station_deficits":{"tail":[4],"columns":["x_over_D=2","x_over_D=4","x_over_D=6","x_over_D=10"]}, + "field_L2_star":{"tail":[1],"columns":["synchronized_role_minus_continuation"]}, + "field_Linf_star":{"tail":[1],"columns":["synchronized_role_minus_continuation"]}, + "distance_accepted_L2_star":{"tail":[1],"columns":["authenticated_accepted_endpoint"]}, + "distance_reverse_L2_star":{"tail":[1],"columns":["authenticated_reverse_endpoint"]}, +} + + +def transient_contract(*, campaign_kind, campaign_id, roles, parent, references, diameter, u_inf=.01, + rho_ref=1., sample_dt=.1, torque_ownership="actuator_on_fluid", action_schedule=None): + """Create the complete immutable v2 acquisition/analysis contract.""" + if campaign_kind not in ("causal-switch","nonlinear-return"): raise ValueError("invalid transient campaign kind") + if not isinstance(campaign_id,str) or not campaign_id: raise ValueError("campaign_id is required") + parent=Path(parent).resolve(strict=True); role_list=list(roles) + if not role_list or len(set(role_list))!=len(role_list): raise ValueError("roles must be unique and nonempty") + refs={} + for name in ("accepted_endpoint","reverse_endpoint"): + value=references.get(name) + if not isinstance(value,dict) or not value.get("path") or not value.get("manifest_payload_sha256"): + raise ValueError(f"reference {name} requires endpoint path and manifest payload hash") + refs[name]={"path":str(Path(value["path"]).resolve()),"manifest_payload_sha256":str(value["manifest_payload_sha256"])} + nd=NondimensionalContract(float(diameter),float(u_inf),float(rho_ref)) + schedules={} if action_schedule is None else action_schedule + schedule_semantics={ + "pulse_end_index":"sample reached after the final pulsed evolution interval; the release action is installed before this sample is captured; null when no pulse is applied", + "release_index":"first sample under the release action and the pulse-end normalization index; equals pulse_end_index for pulsed roles and is zero for unpulsed roles", + "field_distance":"field_L2_star and field_Linf_star are synchronized role-minus-continuation distances on the common fluid mask, never distances from the role's own release state", + } + return {"schema":TRANSIENT_CAMPAIGN_SCHEMA,"immutable":True,"campaign_kind":campaign_kind,"campaign_id":campaign_id, + "roles":role_list,"parent":{"path":str(parent),"sha256":_sha256(parent),"bytes":parent.stat().st_size}, + "references":refs,"body_order":list(TRANSIENT_BODY_ORDER),"gap_order":list(TRANSIENT_GAP_ORDER), + "gap_orientation":"center_a to center_b; normal=left(tangent); frozen by gap_order", + "station_order_x_over_D":list(TRANSIENT_STATION_ORDER),"action_schedule":schedules, + "action_schedule_semantics":schedule_semantics, + "clock":{"columns":["post_parent_lattice_step","t_star"],"includes_t_star_zero":True,"sample_dt_star":float(sample_dt)}, + "torque":{"ownership":torque_ownership,"sign":"omega>0 geometric CCW; power>0 actuator-to-fluid"}, + "nondimensional_contract":nd.convert()["metadata"],"array_schemas":TRANSIENT_ARRAY_SCHEMAS, + "branch_order":{"definition":"m=(dR^2-dA^2)/(dR^2+dA^2)","requires_authenticated_endpoint_fields":True, + "switch_rule":"margin plus hysteresis only; norm crossings prohibited"}} + + +class TransientReacquisitionRequired(ValueError): + """Authenticated transient lacks semantics/data required for strict analysis.""" + + +def _validate_transient_schedule(contract, n): + expected={ + "pulse_end_index":"sample reached after the final pulsed evolution interval; the release action is installed before this sample is captured; null when no pulse is applied", + "release_index":"first sample under the release action and the pulse-end normalization index; equals pulse_end_index for pulsed roles and is zero for unpulsed roles", + "field_distance":"field_L2_star and field_Linf_star are synchronized role-minus-continuation distances on the common fluid mask, never distances from the role's own release state", + } + if contract.get("action_schedule_semantics")!=expected: + raise TransientReacquisitionRequired("missing or invalid pulse_end_index/release_index semantics") + schedules=contract.get("action_schedule") + if not isinstance(schedules,dict) or set(schedules)!=set(contract.get("roles",[])): + raise TransientReacquisitionRequired("action schedule must cover every transient role exactly") + for role,schedule in schedules.items(): + if not isinstance(schedule,dict): raise TransientReacquisitionRequired(f"invalid action schedule for {role}") + release=schedule.get("release_index"); pulse_end=schedule.get("pulse_end_index") + if isinstance(release,bool) or not isinstance(release,int) or not 0<=release=1.8)&(xx<=10)&(np.abs(yy)<=1.5),weights) + stations=[] + for xd in TRANSIENT_STATION_ORDER: + ix=int(round(c[0,0]+xd*D)) + if not 0<=ix=pulse_steps: action=np.asarray(record["action_omega"],float); _set_exact_action(sim,action); pulse_steps=None + row,field,mask,weights=_capture_transient_v2(sim,record,action,stop,D,accepted,reverse,reference_mask); rows.append(row); fields.append(field); masks.append(mask) + finally: sim.close() + common=np.logical_and.reduce(masks) + if continuation is None: + if role!="continue-accepted": raise RuntimeError("synchronized continuation fields are required before perturbation acquisition") + continuation_fields=fields; continuation_mask=common + else: + continuation_fields,continuation_mask=continuation + if len(continuation_fields)!=len(fields): raise RuntimeError("continuation and perturbation clocks differ") + common=common&continuation_mask + if not common.any(): raise RuntimeError("continuation-relative common mask is empty") + arrays={k:np.asarray([r[k] for r in rows],float) for k in rows[0]} + deltas=[f-c for f,c in zip(fields,continuation_fields)] + arrays["field_L2_star"]=np.asarray([[quadrature_l2(d/.01,common,weights)["L2"]/D] for d in deltas]) + arrays["field_Linf_star"]=np.asarray([[np.max(np.abs(d[common]/.01))] for d in deltas]) + manifest=write_transient_artifact(out,contract,role,arrays) + return manifest,(fields,common) + + +def _acquire_transient_v2(out,*,kind,parent,accepted_endpoint,reverse_endpoint,intended_celeris_root,campaign_id,amplitudes=(),horizon=10.,pulse_duration=.5,sample_dt=.1,simulation_factory=None): + _assert_cfd_environment(intended_celeris_root=intended_celeris_root); record,endpoint,parent_arrays,checkpoint=_load_accepted_parent(parent) + if record["source_environment"].get("celeris_intended_root")!=str(Path(intended_celeris_root).resolve()): raise RuntimeError("parent Celeris root differs from intended root") + refs,accepted,reverse,mask=_transient_references(record,endpoint,parent_arrays,accepted_endpoint,reverse_endpoint); D=float(endpoint["spec"]["D"]); U=.01; steps=int(round(horizon*D/U)); stride=int(round(sample_dt*D/U)); baseline=np.asarray(record["action_omega"],float) + if steps=steps: raise ValueError("pulse duration must be synchronized and before horizon") + roles=["continue-accepted"]+[f"{f}-a{a:.12g}" for f in STABILITY_FAMILIES for a in amps]; actions={roles[0]:baseline} + for role in roles[1:]: + family=role.split("-a",1)[0]; a=float(role.split("-a",1)[1]); actions[role]=baseline+(np.array([0.,-a,+a]) if family=="symmetric" else np.array([0.,+a,+a])) + schedule={r:{"initial_action_omega":actions[r].tolist(),"release_action_omega":baseline.tolist(),"pulse_end_index":None if r=="continue-accepted" or pulse is None else pulse//stride,"release_index":0 if r=="continue-accepted" or pulse is None else pulse//stride} for r in roles}; contract=transient_contract(campaign_kind=kind,campaign_id=campaign_id,roles=roles,parent=checkpoint,references=refs,diameter=D,sample_dt=sample_dt,action_schedule=schedule); factory=_production_factory(intended_celeris_root,simulation_factory); continuation={} + def run(stage,role): + enforce_launch_cooldown(); _,captured=_run_transient_v2_role(record,checkpoint,stage/role,role,contract,actions[role],steps,stride,D,factory,accepted,reverse,mask,None if role=="continue-accepted" or pulse is None else pulse,continuation.get("data")) + if role=="continue-accepted": continuation["data"]=captured + with exclusive_cfd_lease(role=kind+"-v2"): _atomic_campaign(out,roles,run) + return load_transient_campaign(out,campaign_kind=kind) + + +def acquire_causal_switch_v2(out,**kwargs): return _acquire_transient_v2(out,kind="causal-switch",**kwargs) +def acquire_nonlinear_return_v2(out,**kwargs): return _acquire_transient_v2(out,kind="nonlinear-return",**kwargs) + + +def write_transient_artifact(out, contract, role, arrays): + """Atomically write one hash-bound named-array transient role.""" + out=Path(out) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if role not in contract["roles"]: raise ValueError("role is not in campaign contract") + _validate_transient_arrays(arrays,contract) + tmp=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + np.savez_compressed(tmp/TRANSIENT_ARRAY_FILE,**arrays) + source_files=(Path(__file__),Path(__file__).with_name("metrics.py"),Path(__file__).with_name("contract.py")) + manifest={"schema":TRANSIENT_SCHEMA,"immutable":True,"role":role,"campaign_contract":contract, + "files":{TRANSIENT_ARRAY_FILE:{"sha256":_sha256(tmp/TRANSIENT_ARRAY_FILE),"bytes":(tmp/TRANSIENT_ARRAY_FILE).stat().st_size}}, + "source_hashes":{str(f.relative_to(Path(__file__).resolve().parents[2])):_sha256(f) for f in source_files}, + "reproduce_command":f'PYTHONPATH="$PWD/src" conda run -n pinball_math python -m steady_pinball_theory.runner inspect-transient {out}'} + manifest["payload_sha256"]=hashlib.sha256(_canonical_json(manifest)).hexdigest() + (tmp/MANIFEST_FILE).write_text(json.dumps(manifest,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(tmp,out) + finally: + if tmp.exists(): + import shutil; shutil.rmtree(tmp) + return manifest + + +def _validate_endpoint_reference(binding): + path=Path(binding["path"]) + manifest,_=load_validate_artifact(path) + if manifest["manifest_payload_sha256"]!=binding["manifest_payload_sha256"]: raise ValueError("reference endpoint identity mismatch") + return manifest + + +def load_validate_transient(path, *, expected_role=None, validate_references=True, allow_superseded_power_sign=False): + """Authenticate transient v2; reject superseded raw-Celeris power signs by default.""" + path=Path(path); raw=json.loads((path/MANIFEST_FILE).read_text()); payload=raw.pop("payload_sha256",None) + if raw.get("schema")!=TRANSIENT_SCHEMA or not raw.get("immutable") or payload!=hashlib.sha256(_canonical_json(raw)).hexdigest(): raise ValueError("transient manifest payload authentication failed") + raw["payload_sha256"]=payload; role=raw.get("role"); contract=raw.get("campaign_contract",{}) + if expected_role is not None and role!=expected_role: raise ValueError("transient role mismatch") + if contract.get("schema")!=TRANSIENT_CAMPAIGN_SCHEMA or role not in contract.get("roles",[]): raise ValueError("transient campaign/role binding mismatch") + convention=contract.get("torque",{}).get("ownership") + if convention!="actuator_on_fluid" and not allow_superseded_power_sign: + raise TransientReacquisitionRequired("superseded transient power sign: raw Celeris torque requires actuator_on_fluid and power_body=tau_read*action_omega; use migrate-transient-ownership") + if allow_superseded_power_sign and convention not in ("fluid_on_body","actuator_on_fluid"): + raise ValueError("unknown transient torque convention") + parent=Path(contract["parent"]["path"]) + if not parent.is_file() or parent.stat().st_size!=contract["parent"]["bytes"] or _sha256(parent)!=contract["parent"]["sha256"]: raise ValueError("transient parent identity mismatch") + entry=raw["files"].get(TRANSIENT_ARRAY_FILE,{}) + payload_path=path/TRANSIENT_ARRAY_FILE + if not payload_path.is_file() or payload_path.stat().st_size!=entry.get("bytes") or _sha256(payload_path)!=entry.get("sha256"): raise ValueError("transient NPZ hash/bytes mismatch") + with np.load(payload_path,allow_pickle=False) as z: arrays={name:z[name].copy() for name in z.files} + _validate_transient_arrays(arrays,contract) + if validate_references: + for binding in contract["references"].values(): _validate_endpoint_reference(binding) + migration=contract.get("ownership_migration") + if migration is not None: + oracle_binding,_=load_qualify_torque_oracle(migration["oracle"]["path"]) + for key in ("sha256","bytes","payload_sha256"): + if oracle_binding[key]!=migration["oracle"].get(key): raise ValueError("migrated transient oracle binding mismatch") + source_binding=migration.get("source_roles",{}).get(role,{}) + source_manifest,source_arrays=load_validate_transient(source_binding.get("path",""),expected_role=role,allow_superseded_power_sign=True) + if source_manifest["payload_sha256"]!=source_binding.get("manifest_payload_sha256") or source_manifest["files"][TRANSIENT_ARRAY_FILE]["sha256"]!=source_binding.get("array_sha256"): + raise ValueError("migrated transient source binding mismatch") + for name,value in arrays.items(): + if name!="power_body" and not np.array_equal(value,source_arrays[name]): raise ValueError("migration changed a non-power array") + return raw,arrays + + +def load_legacy_transient_diagnostic(path): + """Read legacy v1 only under a fixed, non-upgradable scientific ceiling.""" + path=Path(path); raw=json.loads((path/MANIFEST_FILE).read_text()) + if raw.get("schema") not in LEGACY_TRANSIENT_SCHEMAS: raise ValueError("not a supported legacy transient") + file=path/"telemetry.npz"; entry=raw.get("files",{}).get("telemetry.npz",{}) + if not file.is_file() or _sha256(file)!=entry.get("sha256") or file.stat().st_size!=entry.get("bytes"): raise ValueError("legacy transient hash/bytes mismatch") + with np.load(file,allow_pickle=False) as z: arrays={k:z[k].copy() for k in z.files} + return {"classification":"BOUNDED_DIAGNOSTIC","ceiling":"fixed; cannot establish causality, branch switching, return, or uncertainty","manifest":raw},arrays + + +def load_transient_campaign(root, *, campaign_kind=None, allow_superseded_power_sign=False): + root=Path(root); roles={} + for child in sorted(root.iterdir() if root.is_dir() else []): + if child.is_dir() and (child/MANIFEST_FILE).is_file(): + manifest,arrays=load_validate_transient(child,allow_superseded_power_sign=allow_superseded_power_sign); roles[manifest["role"]]=(manifest,arrays) + if not roles: raise FileNotFoundError("no authenticated transient v2 roles") + contracts=[m[0]["campaign_contract"] for m in roles.values()]; identity=hashlib.sha256(_canonical_json(contracts[0])).hexdigest() + if any(hashlib.sha256(_canonical_json(c)).hexdigest()!=identity for c in contracts): raise ValueError("campaign contracts differ between roles") + contract=contracts[0] + if set(roles)!=set(contract["roles"]): raise ValueError("campaign is missing or has extra roles") + if campaign_kind is not None and contract["campaign_kind"]!=campaign_kind: raise ValueError("wrong transient campaign kind") + return contract,roles + + + +def migrate_transient_ownership(source, oracle, out): + """CPU-only no-clobber derivation of corrected actuator-on-fluid transient v2.""" + source,out=Path(source),Path(out) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"campaign parent does not exist: {out.parent}") + contract,roles=load_transient_campaign(source,allow_superseded_power_sign=True); oracle_binding,_=load_qualify_torque_oracle(oracle) + if contract.get("torque",{}).get("ownership")!="fluid_on_body": + raise ValueError("migration source must use the superseded fluid_on_body raw-Celeris power sign") + corrected=json.loads(json.dumps(contract)); corrected["campaign_id"]=contract["campaign_id"]+"-actuator-on-fluid" + corrected["torque"]={"ownership":"actuator_on_fluid","sign":"omega>0 geometric CCW; power_body=tau_read*omega; power>0 actuator-to-fluid", + "qualification":"runtime manufactured oracle overrides falsified cut-link source-sign inference"} + source_bindings={} + for role,(manifest,_) in roles.items(): + source_bindings[role]={"path":str((source/role).resolve()),"manifest_payload_sha256":manifest["payload_sha256"], + "array_sha256":manifest["files"][TRANSIENT_ARRAY_FILE]["sha256"]} + corrected["ownership_migration"]={"schema":"steady-pinball-transient-ownership-migration/v1","source_campaign":str(source.resolve()), + "source_roles":source_bindings,"oracle":oracle_binding,"derivation":"all arrays value-exact from authenticated source except power_body=tau_read*action_omega", + "provenance_only_effect_on_analysis":"return labels unchanged; analysis provenance/source hashes may differ"} + def build(stage,role): + _,arrays=roles[role]; migrated={name:value.copy() for name,value in arrays.items()}; migrated["power_body"]=migrated["torque_body"]*migrated["action_omega"] + write_transient_artifact(stage/role,corrected,role,migrated) + _atomic_campaign(out,corrected["roles"],build) + return load_transient_campaign(out,campaign_kind=corrected["campaign_kind"]) + + +def onset_interval(clock, signal, baseline, *, noise_window=3, threshold_multiplier=5., explicit_floor=None, consecutive=3): + """Strict first sustained onset interval; equality is not a crossing.""" + t=np.asarray(clock,float); y=np.asarray(signal,float); b=np.asarray(baseline,float) + if t.ndim!=1 or y.shape!=t.shape or b.shape!=t.shape or len(t)=len(t): raise ValueError("invalid onset noise window") + noise=float(np.std((y-b)[:noise_window],ddof=0)); threshold=max(float(explicit_floor or 0.),float(threshold_multiplier)*noise) + exceed=np.abs(y-b)>threshold + for i in range(1,len(t)-consecutive+1): + if exceed[i:i+consecutive].all(): return {"interval":[float(t[i-1]),float(t[i])],"threshold":threshold,"status":"RESOLVED_STRICT"} + return {"interval":None,"threshold":threshold,"status":"UNRESOLVED_NO_SUSTAINED_CROSSING"} + + +def _interval_order(first, second): + if first["interval"] is None or second["interval"] is None: return "UNRESOLVED" + a,b=first["interval"],second["interval"] + if a[1]growth_ratio else ("PARTIAL" if terminal<1 else "AMBIGUOUS"))) + rows[role]={"label":label,"pulse_end_index":pulse_end,"release_index":release,"terminal_release_ratio":terminal,"finite_horizon_growth":growth,"branch_order":order["m"].tolist()} + result={"schema":"steady-pinball-nonlinear-return-analysis/v2","classification":"BOUNDED","availability":"AVAILABLE_FINITE_HORIZON","labels":["RETURN","PARTIAL","GROWTH","BRANCH_SWITCH","AMBIGUOUS"],"runs":rows,"claim_boundary":"finite-horizon labels only; no stable or asymptotic interpretation"} + return _write_analysis(out,result,command) + + +def inspect_transient(path): + manifest,arrays=load_validate_transient(path) + return {"schema":manifest["schema"],"role":manifest["role"],"campaign_id":manifest["campaign_contract"]["campaign_id"],"payload_sha256":manifest["payload_sha256"],"arrays":{k:{"shape":list(v.shape),"dtype":str(v.dtype)} for k,v in arrays.items()}} + + + +TORQUE_ORACLE_SCHEMA="steady-pinball-torque-oracle/v1" +TORQUE_ORACLE_ROLES=("plus_omega","minus_omega","zero") +TORQUE_ORACLE_KERNEL_SOURCES=( + "src/CelerisLab/lbm/kernels/boundary/curved_boundary.cuh", + "src/CelerisLab/lbm/kernels/core/obs.cuh", +) + + +def _torque_oracle_config(D, U, rho): + """Small isolated-circle domain retaining the production LBM method.""" + D=float(D); U=float(U); rho=float(rho) + if not np.isfinite([D,U,rho]).all() or D<8 or U<=0 or rho<=0: + raise ValueError("torque oracle requires finite D>=8, U>0, and rho>0") + nx=int(round(8*D)); ny=int(round(6*D)) + cfg={"grid":{"lattice_model":"D2Q9","nx":nx,"ny":ny,"nz":1}, + "physics":{"data_type":"FP32","viscosity":U*D/50.0,"velocity":U,"rho":rho}, + "method":{"collision":"MRT","streaming":"double_buffer","store_precision":"FP32","ddf_shifting":False, + "les":{"enabled":False,"cs":0.16,"closed_form":True},"trt":{"magic_param":0.1875}, + "inlet":{"profile":"uniform","scheme":"regularized","trt_neq_damp":0.5,"regularized_neq_damp":0.5}, + "outlet":{"mode":"neq_extrap","backflow_clamp":True,"blend_alpha":0.7,"srt_neq_damp":0.5}, + "y_wall_bc":"free_slip","omega_guard":{"min":0.01,"max":1.99}}, + "cuda":{"threads_per_block":256,"compute_capability":"auto"}} + return cfg,[2.0*D,3.0*D],0.5*D + + +def _torque_oracle_source_record(root, *, celeris_module=None, source_environment=None): + if source_environment is None: + if celeris_module is None: raise ValueError("Celeris module is required for production source identity") + source_environment=_source_identity(celeris_module=celeris_module,intended_celeris_root=root) + root=Path(root).resolve() + hashes={} + for relative in TORQUE_ORACLE_KERNEL_SOURCES: + path=root/relative + if not path.is_file(): raise FileNotFoundError(f"required torque kernel source missing: {path}") + hashes[relative]=_sha256(path) + return {"celeris":source_environment,"force_torque_kernel_source_hashes":hashes} + + +def _evaluate_torque_oracle(role_rows, *, D, U, rho, omega, parity_tolerance, zero_tolerance): + """Qualify the raw Celeris torque channel's empirical actuator-to-fluid work sign.""" + if parity_tolerance<0 or zero_tolerance<0: raise ValueError("diagnostic tolerances must be nonnegative") + means={role:float(np.mean(np.asarray(role_rows[role],float)[:,2])) for role in TORQUE_ORACLE_ROLES} + driven=max(abs(means["plus_omega"]),abs(means["minus_omega"])); scale=max(driven,np.finfo(float).tiny) + sign={"plus_omega":bool(means["plus_omega"]*omega>0),"minus_omega":bool(means["minus_omega"]*(-omega)>0)} + parity=float(abs(means["plus_omega"]+means["minus_omega"])/scale); zero_ratio=float(abs(means["zero"])/scale) + powers={"plus_omega":float(omega*means["plus_omega"]),"minus_omega":float((-omega)*means["minus_omega"])} + gates={"same_sign_torque_and_rotation_both_directions":bool(all(sign.values())), + "odd_torque_parity":bool(parity<=parity_tolerance),"zero_role_bounded":bool(zero_ratio<=zero_tolerance), + "positive_omega_tau_actuator_power_both_directions":bool(all(value>0 for value in powers.values()))} + denom_tau=.5*rho*U*U*D*D; denom_power=.5*rho*U**3*D; roles={}; actions={"plus_omega":omega,"minus_omega":-omega,"zero":0.0} + for role in TORQUE_ORACLE_ROLES: + tau=means[role]; action=actions[role]; power=action*tau + roles[role]={"action_omega":float(action),"clock_columns":["lattice_step","tU_over_D"], + "raw_normalize_true_torque":[list(map(float,row)) for row in role_rows[role]], + "mean_raw_torque":tau,"C_tau":float(tau/denom_tau), + "actuator_power_omega_tau":float(power),"C_P":float(power/denom_power)} + passed=bool(all(gates.values())) + return {"qualification":"PASS" if passed else "BOUNDED","strict_pass":passed, + "celeris_torque_channel_work_sign":"actuator_on_fluid" if passed else "not_established", + "force_ownership":"not_established","newton_pair_force_ownership_inference":"prohibited_from_torque_oracle", + "ownership_established":"not_established","gates":gates, + "diagnostics":{"sign_products_tau_omega":{"plus_omega":means["plus_omega"]*omega,"minus_omega":means["minus_omega"]*(-omega)}, + "odd_parity_relative_defect":parity,"odd_parity_tolerance":float(parity_tolerance), + "zero_to_driven_torque_ratio":zero_ratio,"zero_role_tolerance":float(zero_tolerance)},"roles":roles} + + +def load_qualify_torque_oracle(path): + """Authenticate an oracle and apply the corrected runtime interpretation.""" + path=Path(path); file=path/"oracle.json" if path.is_dir() else path + raw=json.loads(file.read_text()); payload=raw.pop("payload_sha256",None) + if raw.get("schema")!=TORQUE_ORACLE_SCHEMA or payload!=hashlib.sha256(_canonical_json(raw)).hexdigest(): + raise ValueError("torque oracle payload authentication failed") + setup=raw.get("setup",{}); rows={role:raw.get("roles",{}).get(role,{}).get("raw_normalize_true_torque") for role in TORQUE_ORACLE_ROLES} + if any(value is None for value in rows.values()): raise ValueError("torque oracle lacks raw role telemetry") + actions=setup.get("exact_actions_by_role",{}); omega=float(actions.get("plus_omega",0.)) + if omega<=0 or actions.get("minus_omega")!=-omega or actions.get("zero")!=0.: raise ValueError("torque oracle exact actions invalid") + evaluated=_evaluate_torque_oracle(rows,D=setup["D"],U=setup["U"],rho=setup["rho"],omega=omega, + parity_tolerance=raw.get("diagnostics",{}).get("odd_parity_tolerance",.1), + zero_tolerance=raw.get("diagnostics",{}).get("zero_role_tolerance",.1)) + if not evaluated["strict_pass"]: raise ValueError("torque oracle fails corrected actuator-on-fluid gates") + return {"path":str(file.resolve()),"sha256":_sha256(file),"bytes":file.stat().st_size,"payload_sha256":payload, + "runtime_interpretation":evaluated},raw + + +def qualify_torque_oracle(out, *, intended_celeris_root, D=20.0, U=.01, rho=1.0, omega=.002, + t_end=2.0, sample_dt=.25, parity_tolerance=.1, zero_tolerance=.1, + simulation_factory=None, source_environment=None, cooldown=True): + """Run fresh +omega, -omega, and zero one-circle simulations and publish once.""" + out=Path(out) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(f"artifact parent does not exist: {out.parent}") + if not np.isfinite([omega,t_end,sample_dt]).all() or omega<=0 or t_end<=0 or sample_dt<=0: + raise ValueError("omega, t_end, and sample_dt must be finite and positive") + root=Path(intended_celeris_root).expanduser().resolve(strict=True) + celeris_module=None; production=simulation_factory is None + if production: + _assert_cfd_environment(intended_celeris_root=root) + import CelerisLab + celeris_module=CelerisLab; simulation_factory=CelerisLab.Simulation + cfg,center,radius=_torque_oracle_config(D,U,rho) + steps=int(round(t_end*D/U)); stride=int(round(sample_dt*D/U)) + if steps<2*stride or steps%stride: raise ValueError("t_end/sample_dt must form at least two exact sample intervals") + sources=_torque_oracle_source_record(root,celeris_module=celeris_module,source_environment=source_environment) + actions={"plus_omega":float(omega),"minus_omega":-float(omega),"zero":0.0}; rows={} + def run_role(stage, role): + if cooldown: enforce_launch_cooldown() + body={"objects":[{"type":"cylinder","center":center,"radius":radius,"omega":actions[role]}]} + lp=stage/f"{role}-lbm.json"; bp=stage/f"{role}-body.json" + lp.write_text(json.dumps(cfg)); bp.write_text(json.dumps(body)) + sim=simulation_factory(lbm_config_path=str(lp),body_config_path=str(bp)); role_rows=[] + try: + if sim.bodies.count!=1 or [obj.obj_id for obj in sim.bodies.objects]!=[0]: raise RuntimeError("oracle requires exactly body registry ID 0") + sim.initialize() + for stop in range(stride,steps+1,stride): + sim.run(stride,zero_obs=True) + body_tau=np.asarray(sim.read_body(0,normalize=True).torque,float).reshape(-1) + direct=np.asarray(sim.read_torque(0,normalize=True),float).reshape(-1) + if body_tau.shape!=(1,) or not np.isfinite(body_tau).all() or not np.array_equal(body_tau,direct): + raise RuntimeError("Celeris returned invalid or inconsistent one-body torque") + role_rows.append([stop,stop*U/D,float(body_tau[0])]) + finally: sim.close() + rows[role]=role_rows + @contextmanager + def no_lease(): yield + with (exclusive_cfd_lease(role="torque-oracle") if production else no_lease()): + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.roles-",dir=out.parent)) + try: + for role in TORQUE_ORACLE_ROLES: run_role(temporary,role) + finally: + import shutil; shutil.rmtree(temporary) + result=_evaluate_torque_oracle(rows,D=D,U=U,rho=rho,omega=omega,parity_tolerance=parity_tolerance,zero_tolerance=zero_tolerance) + artifact={"schema":TORQUE_ORACLE_SCHEMA,"immutable":True, + "setup":{"justification":"single isolated rotating circle is the smallest canonical cut-link setup that isolates torque-channel work sign and odd rotational response without assigning force ownership", + "D":float(D),"U":float(U),"rho":float(rho),"Re_D":50.0,"two_dimensional_per_unit_span":True, + "center_xy":center,"radius":radius,"config_lbm":cfg,"fresh_simulation_per_role":True, + "read_semantics":{"normalize":True,"meaning":"cut-link lattice torque averaged once per accumulated LBM step; no coefficient, density, dynamic-pressure, body, or span normalization"}, + "t_end_U_over_D":float(t_end),"sample_dt_U_over_D":float(sample_dt),"final_lattice_step":steps,"sample_stride_lattice_steps":stride, + "exact_actions_by_role":actions}, + "source_identity":sources,**result} + artifact["payload_sha256"]=hashlib.sha256(_canonical_json(artifact)).hexdigest() + temporary=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)) + try: + (temporary/"oracle.json").write_text(json.dumps(artifact,indent=2,sort_keys=True,allow_nan=False)+"\n") + _publish_directory_no_replace(temporary,out) + finally: + if temporary.exists(): + import shutil; shutil.rmtree(temporary) + return artifact + +def _load_hashed_json(path, label): + path=Path(path).resolve(strict=True); value=json.loads(path.read_text()); claimed=value.pop("payload_sha256",None) + if not claimed or claimed!=hashlib.sha256(_canonical_json(value)).hexdigest(): raise ValueError(label+" payload authentication failed") + value["payload_sha256"]=claimed; return value + + +def _load_ccd_publication(root): + root=Path(root).resolve(strict=True); mp=root/"manifest.json" + if not mp.is_file(): raise ValueError("CCD manifest missing") + manifest=json.loads(mp.read_text()); files=manifest.get("files") + if manifest.get("complete") is not True or manifest.get("schema_id")!="ccd-karman-corrected-publication/v3" or not isinstance(files,dict) or "RESULTS.json" not in files: raise ValueError("CCD manifest schema/files invalid") + for name,digest in files.items(): + candidate=(root/name).resolve() + try: candidate.relative_to(root) + except ValueError as exc: raise ValueError("CCD manifest path escapes root") from exc + if not isinstance(digest,str) or len(digest)!=64 or not candidate.is_file() or _sha256(candidate)!=digest: raise ValueError("CCD manifest authentication failed: "+name) + result=json.loads((root/"RESULTS.json").read_text()) + if result.get("schema_id")!=manifest["schema_id"]: raise ValueError("CCD schema mismatch") + return result,{"path":str(root),"manifest_sha256":_sha256(mp),"files":dict(sorted(files.items()))} + + +def _load_sr_constant(path): + import re + path=Path(path).resolve(strict=True); catalog=path if path.suffix==".json" else path.parent/"catalog.json" + if not catalog.is_file(): raise ValueError("structured SR source unavailable") + data=json.loads(catalog.read_text()) + if data.get("schema_version")!="sr-results-catalog-v1": raise ValueError("SR catalog schema mismatch") + text=json.dumps(data,sort_keys=True); hits=re.findall(r"alpha_U = 1\.307782 Cl_rear,s - (3\.431209)",text) + if len(hits)!=1: raise ValueError("SR structured extraction is not unique") + return -float(hits[0]),catalog,{"path":str(catalog),"sha256":_sha256(catalog),"schema":data["schema_version"],"extraction_matches":1} + + +def _publication_metric(qin,qctl,*,center_x,D,U): + if not np.array_equal(qctl["x"],qin["x"]) or not np.array_equal(qctl["y"],qin["y"]): raise ValueError("qin/qctl grids differ") + xd=(qctl["x"]-center_x)/D; j=int(np.argmin(abs(xd-10))); common=qctl["fluid_mask"][:,j]&qin["fluid_mask"][:,j]; common[:2]=False; common[-2:]=False + direct=profile_errors(U+qctl["ux"][common,j]-qin["ux"][common,j],qctl["uy"][common,j]-qin["uy"][common,j],u_inf=U) + ideal=profile_errors(qctl["ux"][common,j],qctl["uy"][common,j],u_inf=U) + return direct,ideal,j,common + + +def _configure_publication_rendering(): + import locale + os.environ["TZ"]="UTC" + if hasattr(time,"tzset"): time.tzset() + selected=None + for candidate in ("C.UTF-8","C"): + try: selected=locale.setlocale(locale.LC_ALL,candidate); break + except locale.Error: pass + if selected is None: raise RuntimeError("unable to set C locale") + import matplotlib; matplotlib.use("Agg",force=True) + matplotlib.rcParams.update({"font.family":"DejaVu Sans","font.sans-serif":["DejaVu Sans"],"axes.unicode_minus":False,"savefig.dpi":180,"pdf.fonttype":42,"path.simplify":False,"svg.hashsalt":"steady-publication-v3"}) + return matplotlib,selected + + +def publish_article(*,steady,ledger,causal_analysis,causal_campaign,return_analysis,return_campaign,strip,ccd,sr,out): + matplotlib,selected_locale=_configure_publication_rendering() + import matplotlib.pyplot as plt + from matplotlib.patches import Circle + out=Path(out); steady=Path(steady).resolve(strict=True) + paths={"ledger":Path(ledger).resolve(strict=True),"causal_analysis":Path(causal_analysis).resolve(strict=True),"causal_campaign":Path(causal_campaign).resolve(strict=True),"return_analysis":Path(return_analysis).resolve(strict=True),"return_campaign":Path(return_campaign).resolve(strict=True),"strip":Path(strip).resolve(strict=True),"ccd":Path(ccd).resolve(strict=True),"sr":Path(sr).resolve(strict=True)} + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + names=("stationary","accepted-s3.55","reverse-s5.2"); ep={n:load_validate_artifact(steady/n) for n in ("qin",)+names} + L,C,R,S=(_load_hashed_json(paths[k],k) for k in ("ledger","causal_analysis","return_analysis","strip")) + if Path(L["campaign"]).resolve()!=steady or C["classification"]!="BOUNDED" or R["classification"]!="BOUNDED" or S["classification"]["confinement_mechanism"]!="FAIL": raise ValueError("input contract mismatch") + _,cr=load_transient_campaign(paths["causal_campaign"],campaign_kind="causal-switch"); _,rr=load_transient_campaign(paths["return_campaign"],campaign_kind="nonlinear-return") + ccdj,ccd_binding=_load_ccd_publication(paths["ccd"]); sr_constant,sr_catalog,sr_binding=_load_sr_constant(paths["sr"]) + tmp=Path(tempfile.mkdtemp(prefix=".article-",dir=out.parent)); figs=[] + pdf_meta={"Creator":"DynamisLab steady publisher v3","Producer":"Matplotlib","CreationDate":None,"ModDate":None}; png_meta={"Software":"DynamisLab steady publisher v3"} + def save(fig,n): + fig.savefig(tmp/f"{n}.png",dpi=180,bbox_inches="tight",metadata=png_meta); figs.append(f"{n}.png") + fig.savefig(tmp/f"{n}.pdf",dpi=180,bbox_inches="tight",metadata=pdf_meta); figs.append(f"{n}.pdf") + plt.close(fig) + try: + fig,ax=plt.subplots(2,2,figsize=(9,6)) + for a,t in zip(ax.flat,("endpoint performance\nEinf=0.02317","potential sign\nFAIL","NS partial ledger\nno residual","transient / return\nBOUNDED")): a.axis("off"); a.text(.5,.5,t,ha="center",va="center",fontsize=14) + save(fig,"01_evidence_overview") + g=S["finite_re_reconciliation"]; fig,a=plt.subplots(); a.bar(("potential g_opt","finite-Re g"),(g["theoretical_rear_opposite_g_opt_layer40"],g["actual_wls_g"])); a.axhline(0,color="k"); save(fig,"02_potential_sign_counterexample") + labels=("stationary","accepted","reverse"); spec=ep[names[1]][0]["spec"]; D=spec["D"]; U=spec["config_lbm"]["physics"]["velocity"]; center=spec["centers_xy"][0]; fig,ax=plt.subplots(3,3,figsize=(12,9)) + for i,n in enumerate(names): + a=ep[n][1]; x=(a["x"]-center[0])/D; y=(a["y"]-center[1])/D; X=(x>=-1)&(x<=10); Y=(y>=-3)&(y<=3); ux=a["ux"]/U-1 + omega,usable=conservative_masked_vorticity(a["x"],a["y"],a["ux"],a["uy"],a["fluid_mask"]); om=np.ma.masked_where(~usable,omega*D/U); extent=(x[X][0],x[X][-1],y[Y][0],y[Y][-1]) + ax[i,0].imshow(ux[np.ix_(Y,X)],extent=extent,origin="lower",aspect="auto",vmin=-1,vmax=1,cmap="coolwarm"); ax[i,1].imshow(om[np.ix_(Y,X)],extent=extent,origin="lower",aspect="auto",vmin=-5,vmax=5,cmap="RdBu_r") + for xd in (2,4,6,10): j=int(np.argmin(abs(x-xd))); m=a["fluid_mask"][:,j]; ax[i,2].plot(a["ux"][m,j]/U,y[m],label=f"x/D={xd}") + for field in ax[i,:2]: + field.set_xlabel("x/D"); field.set_ylabel("y/D"); field.axvline(10,color="k",ls="--",lw=.5); field.text(-.8,2.5,"U∞ →",fontsize=7) + for cx,cy in spec["centers_xy"]: field.add_patch(Circle(((cx-center[0])/D,(cy-center[1])/D),.5,fill=False,color="black",lw=.8)) + ax[i,2].set_ylabel("y/D"); ax[i,2].set_xlabel("u_x/U∞"); ax[i,0].set_title(labels[i]) + ax[0,0].set_title("u_x/U∞−1; x/D,y/D"); ax[0,1].set_title("ωD/U∞; conservative fluid stencil"); ax[0,2].set_title("profile stations"); ax[0,2].legend(fontsize=7); save(fig,"03_steady_fields_profiles") + cases=L["cases"]; fig,ax=plt.subplots(2,2,figsize=(9,7)) + ax[0,0].bar(labels,[cases[n]["gap_fluxes_separate_orientations"]["rear_rear"]["dimensionless"]["Q_star"] for n in names]); ax[0,0].set_title("rear-gap Q*") + ax[0,1].bar(labels,[cases[n]["gap_fluxes_separate_orientations"]["rear_rear"]["dimensionless"]["J_star"] for n in names]); ax[0,1].set_title("rear-gap J*") + ax[1,0].bar(labels,[cases[n]["torque_and_actuator_power"]["C_P"] for n in names]); ax[1,0].set_title("corrected CP") + ax[1,1].text(.5,.5,"spatial flux + dissipation + power\nstorage/time/body terms unavailable",ha="center"); ax[1,1].set_title("partial terms; no residual"); save(fig,"04_ns_corrected_partial_ledger") + fig,ax=plt.subplots(2,2,figsize=(9,7)); base=cr["continue-accepted"][1] + for role in ("zero","equal-amplitude-reverse"): + a=cr[role][1]; t=a["clock"][:,1]; ys=(a["gap_Q"][:,2]-base["gap_Q"][:,2],a["recirculation"][:,0]-base["recirculation"][:,0],a["station_deficits"][:,0]-base["station_deficits"][:,0],a["station_deficits"][:,3]-base["station_deficits"][:,3]) + for z,yv in zip(ax.flat,ys): z.plot(t,yv) + save(fig,"05_transient_selected_channels") + fig,ax=plt.subplots(1,2,figsize=(10,4)) + for role,(m,a) in rr.items(): + if role=="continue-accepted": continue + t=a["clock"][:,1]; k=m["campaign_contract"]["action_schedule"][role]["release_index"]; q=a["field_L2_star"][:,0]; ax[0].plot(t,q/q[k],label=role); ax[1].plot(t,R["runs"][role]["branch_order"]) + ax[0].legend(fontsize=6); save(fig,"06_return_curves_branch_order") + q=ep["qin"][1]; a=ep[names[1]][1]; direct,ideal,j,common=_publication_metric(q,a,center_x=center[0],D=D,U=U) + if direct["E_inf_vector"]!=0.0231672176752314: raise ValueError("primary metric identity mismatch") + nums={"primary_E_inf_vector_qctl_vs_qin_x_over_D_10":direct["E_inf_vector"],"ideal_uniform_reference_diagnostic_E_inf_vector":ideal["E_inf_vector"],"accepted_settling":ep[names[1]][0]["result"]["settling"]["value"],"g_opt":g["theoretical_rear_opposite_g_opt_layer40"],"g_finite_re":g["actual_wls_g"],"C_P":{n:cases[n]["torque_and_actuator_power"]["C_P"] for n in names},"return_labels":{k:v["label"] for k,v in R["runs"].items()},"causal_realizations":C["realizations"],"ccd_roi_errors":ccdj["roi_mean_target_errors"],"sr_constant":sr_constant} + inputs={"steady":{"path":str(steady),"files":{str(f.relative_to(steady)):_sha256(f) for f in sorted(steady.rglob("*")) if f.is_file()}},"ccd":ccd_binding,"sr":sr_binding} + for k,v in paths.items(): + if k in ("ccd","sr"): continue + inputs[k]={"path":str(v),"sha256":_sha256(v) if v.is_file() else hashlib.sha256(_canonical_json({str(f.relative_to(v)):_sha256(f) for f in sorted(v.rglob("*")) if f.is_file()})).hexdigest()} + command=f'PYTHONPATH="$PWD/src" TZ=UTC LC_ALL=C.UTF-8 conda run -n pinball_math python -m steady_pinball_theory.runner publish-article --steady "{steady}" --ledger "{paths["ledger"]}" --causal-analysis "{paths["causal_analysis"]}" --causal-campaign "{paths["causal_campaign"]}" --return-analysis "{paths["return_analysis"]}" --return-campaign "{paths["return_campaign"]}" --strip "{paths["strip"]}" --ccd "{paths["ccd"]}" --sr "{sr_catalog}" --out "$ARTICLE_OUT"' + res={"schema":"steady-pinball-article/v3","source_identity":{ "git_commit":_git_value(Path(__file__).resolve().parents[2],"rev-parse","HEAD"),"git_status_porcelain_steady_package":_git_value(Path(__file__).resolve().parents[2],"status","--porcelain","--","src/steady_pinball_theory"),"runner_sha256":_sha256(__file__),"metrics_sha256":_sha256(Path(__file__).with_name("metrics.py")),"contract_sha256":_sha256(Path(__file__).with_name("contract.py")),"python":sys.version,"numpy":np.__version__,"matplotlib":matplotlib.__version__,"backend":matplotlib.get_backend(),"locale":selected_locale,"timezone":"UTC","render":{"dpi":180,"font_family":"DejaVu Sans","pdf_metadata":pdf_meta,"png_metadata":png_meta}},"immutable":True,"classification":"BOUNDED","numbers":nums,"inputs":inputs,"figures":figs,"exact_reproduction_command":command}; res["payload_sha256"]=hashlib.sha256(_canonical_json(res)).hexdigest(); (tmp/"RESULTS.json").write_text(json.dumps(res,indent=2,sort_keys=True,allow_nan=False)+"\n") + report=["# 稳态流体弹球论文发布报告（v3）","",f"接受态 x/D=10 直接 q_ctl 对 q_in 全剖面 E∞={nums['primary_E_inf_vector_qctl_vs_qin_x_over_D_10']:.8f}；理想均匀参考诊断={nums['ideal_uniform_reference_diagnostic_E_inf_vector']:.9f}。证据支持端点性能和有限时域诊断，不支持完整机制、因果性或稳定性证明。","","## 第一部分：摘要","证据支持端点性能与有限时域诊断，分类为 BOUNDED。","","## 第二部分：方法与恰好四组主公式","### 主公式组 1：壁面定律与符号","(Uw,Vw)=(-omega*ry,omega*rx)，x 向右、y 向上，接受动作 [0,+Omega,-Omega]。","### 主公式组 2：格子到无量纲与功约定","x*=x/D，t*=tU∞/D，Q*=Q/(U∞D)，J*=J/(rho U∞²D)，C_P=sum(omega*tau_read)/(0.5 rho U∞³D)。normalize=True 只按累计 LBM 步平均格子切链和；不做系数、密度、动压、物体或跨度归一化；均为二维单位跨度。","### 主公式组 3：同一控制体动量/能量示意","同一包体 CV 上报告四面动量/机械能空间通量、CV 耗散与 P_act；存储/时间项和物体邻近梯度不可用，因此没有闭合残差。压力为 p'=cs²(rho-rho_ref) 弱可压代理。","### 主公式组 4：权威主指标","E_inf_vector(q_ctl,q_in)=max_y ||q_ctl-q_in||/U∞，x/D=10 完整共同流体剖面，精确值 0.0231672176752314。","","势流 g 与返回 r/m 仅作次级行内解释；g_opt 与有限 Re g 异号，故 FAIL。","","## 第三部分：结果","六幅独立图含定义、方向、单位、事件与图注；场图含圆柱、流向及 x/D=10。","","## 第四部分：讨论","扭矩原始工况经运行时重新解释满足 actuator-on-fluid PASS；不建立力通道所有权。CCD/SR 仅作语境。","","## 第五部分：局限","单次因果实现、有限时域返回、缺失存储/物体梯度均禁止因果、闭合残差与稳定性结论。","","## 第六部分：复现","```bash",command,"```","","## 贡献","统一色标端点场与剖面；修正 CP、间隙、尾迹部分项；瞬态及返回/分支序；全输出哈希绑定且不可覆盖。CCD/SR 仅作交叉参照。","","## 局限","单次因果实现为 BOUNDED；NS 不闭合；返回仅 tU/D=10；势流符号失败；CCD/SR 不证明稳态后体机制。"] + (tmp/"REPORT.md").write_text("\n".join(report)+"\n") + files={f.name:{"sha256":_sha256(f),"bytes":f.stat().st_size} for f in tmp.iterdir() if f.is_file()}; man={"schema":"steady-pinball-article-manifest/v2","immutable":True,"files":files}; man["payload_sha256"]=hashlib.sha256(_canonical_json(man)).hexdigest(); (tmp/"manifest.json").write_text(json.dumps(man,indent=2,sort_keys=True,allow_nan=False)+"\n"); _publish_directory_no_replace(tmp,out); return res + finally: + if tmp.exists(): + import shutil; shutil.rmtree(tmp) + + + +def _display_solid_mask(x,y,centers,radius): + x=np.asarray(x,float); y=np.asarray(y,float); centers=np.asarray(centers,float) + if x.ndim!=1 or y.ndim!=1 or centers.shape!=(3,2) or radius<=0: raise ValueError("invalid display geometry") + xx,yy=np.meshgrid(x,y,indexing="xy"); solid=np.zeros(xx.shape,bool) + for cx,cy in centers: solid|=(xx-cx)**2+(yy-cy)**2<=radius**2 + return solid + + +def _display_fields(a,qin,spec): + if not np.array_equal(a["x"],qin["x"]) or not np.array_equal(a["y"],qin["y"]): raise ValueError("display endpoint grids differ") + D=float(spec["D"]); U=float(spec["config_lbm"]["physics"]["velocity"]); common=a["fluid_mask"]&qin["fluid_mask"] + omega,usable=conservative_masked_vorticity(a["x"],a["y"],a["ux"],a["uy"],a["fluid_mask"]) + disturbance=np.where(common,np.hypot(a["ux"]/U-1,a["uy"]/U),np.nan) + error=np.where(common,np.hypot(a["ux"]-qin["ux"],a["uy"]-qin["uy"])/U,np.nan) + return {"common":common,"vorticity_mask":usable,"disturbance":disturbance,"velocity_error":error,"vorticity_star":np.where(usable,omega*D/U,np.nan)} + + +def _write_display_profiles(path,cases,stations=(2.,4.,6.,10.)): + columns=("case","s","x_over_D","y_over_D","ux_over_U","uy_over_U","velocity_error","vorticity_star","fluid_mask","source_artifact_sha256") + with Path(path).open("w",newline="",encoding="utf-8") as stream: + w=csv.DictWriter(stream,fieldnames=columns,lineterminator="\n"); w.writeheader() + for c in cases: + a=c["arrays"]; f=c["fields"] + for station in stations: + j=int(np.argmin(abs(c["x_D"]-station))) + for i,y in enumerate(c["y_D"]): + fluid=bool(f["common"][i,j]); vort=bool(f["vorticity_mask"][i,j]) + w.writerow({"case":c["name"],"s":"" if c["s"] is None else c["s"],"x_over_D":format(c["x_D"][j],".12g"),"y_over_D":format(y,".12g"),"ux_over_U":format(a["ux"][i,j]/c["U"],".12g") if fluid else "","uy_over_U":format(a["uy"][i,j]/c["U"],".12g") if fluid else "","velocity_error":format(f["velocity_error"][i,j],".12g") if fluid else "","vorticity_star":format(f["vorticity_star"][i,j],".12g") if vort else "","fluid_mask":int(fluid),"source_artifact_sha256":c["source_sha256"]}) + return columns + + + +def _display_qualification(manifest): + result=manifest["result"]; settling=result["settling"] + if not result["qualification_required"]: + if result["qualification_role"]!="unsteady_reference" or settling["qualified"]: + raise ValueError("invalid unsteady-reference qualification semantics") + return "unsteady_reference_not_required_to_settle" + if not result["qualification_passed"] or not settling["qualified"]: + raise ValueError("required display endpoint is not settling-qualified") + return "settling_qualified_steady_endpoint" + + +def _display_diagnostics(cases,qin,ledger_cases): + from .metrics import (absolute_vorticity_moments, near_wall_tangential_speed, + recirculation_observables, tensor_trapezoid_weights, + wake_deficit_observables) + case_rows=[]; gap_rows=[]; station_rows=[] + for c in cases: + name=c["name"]; a=c["arrays"]; f=c["fields"]; m=c["manifest"]; U=c["U"]; D=float(m["spec"]["D"]); led=ledger_cases[name] + weights=tensor_trapezoid_weights(c["x_D"],c["y_D"]); xx,yy=np.meshgrid(c["x_D"],c["y_D"]) + rec_mask=f["common"]&(xx>=1.8)&(xx<=10)&(abs(yy)<=1.5) + rec=recirculation_observables(c["x_D"],a["ux"]/U,rec_mask,weights) + vort_mask=f["vorticity_mask"]&(xx>=1.8)&(xx<4)&(abs(yy)<=3) + vort=absolute_vorticity_moments(c["y_D"],f["vorticity_star"],vort_mask,weights) + centers=np.asarray(m["spec"]["centers_xy"],float); wall=near_wall_tangential_speed(a["x"],a["y"],a["ux"],a["uy"],a["fluid_mask"],a["body_id"],centers,m["spec"]["radius"],body_ids=(1,2),body_labels=("rear_y_plus","rear_y_minus"))["bodies"] + force=np.asarray(a["force_history"][-10:,2:],float).reshape((-1,3,2)).mean(axis=0).sum(axis=0); scale=.5*float(m["spec"]["config_lbm"]["physics"]["rho"])*U*U*D + case_rows.append({"case":name,"s":"" if c["s"] is None else c["s"],"label":c["label"],"status":_display_qualification(m),"settling_value":m["result"]["settling"]["value"],"oracle_bound_C_P":led["torque_and_actuator_power"]["C_P"],"partial_ledger_status":led["same_cv_partial_ledger"]["balance_status"],"residual":"","recirculation_area_D2":rec["area"],"recirculation_x_min_D":"" if rec["x_min"] is None else rec["x_min"],"recirculation_x_max_D":"" if rec["x_max"] is None else rec["x_max"],"recirculation_extent_D":rec["streamwise_extent"],"total_force_x_lattice":force[0],"total_force_y_lattice":force[1],"reported_C_D":force[0]/scale,"reported_C_L":force[1]/scale,"force_ownership":"Celeris reported cut-link force; ownership not established by torque oracle","immediate_wake_abs_vorticity_integral":vort["absolute_vorticity_integral"],"immediate_wake_vorticity_y_width_D":vort["y_width"],"rear_y_plus_rms_tangential_speed_over_U":wall["rear_y_plus"]["rms_tangential_speed"]/U,"rear_y_minus_rms_tangential_speed_over_U":wall["rear_y_minus"]["rms_tangential_speed"]/U,"source_artifact_sha256":c["source_sha256"]}) + for gap,gdata in led["gap_fluxes_separate_orientations"].items(): + gap_rows.append({"case":name,"s":"" if c["s"] is None else c["s"],"gap":gap,"Q_star":gdata["dimensionless"]["Q_star"],"J_star":gdata["dimensionless"]["J_star"],"normal_x":gdata["normal"][0],"normal_y":gdata["normal"][1],"orientation":gdata["orientation"],"endpoint_exclusion_radius_over_D":gdata["endpoint_exclusion_radius_over_D"],"source_artifact_sha256":c["source_sha256"]}) + for station in (2.,4.,6.,10.): + j=int(np.argmin(abs(c["x_D"]-station))); common=f["common"][:,j]; direct=profile_errors(U+a["ux"][common,j]-qin["ux"][common,j],a["uy"][common,j]-qin["uy"][common,j],u_inf=U); wake=wake_deficit_observables(c["y_D"],a["ux"][:,j]/U,common) + station_rows.append({"case":name,"s":"" if c["s"] is None else c["s"],"x_over_D":c["x_D"][j],"E_inf_x":direct["E_inf_x"],"E_inf_y":direct["E_inf_y"],"E_inf_vector":direct["E_inf_vector"],"E_L2_vector":direct["E_L2_vector"],"momentum_deficit_proxy":wake["momentum_deficit_proxy"],"positive_deficit_measure":wake["positive_deficit_measure"],"signed_deficit_integral":wake["signed_deficit_integral"],"common_fluid_points":int(common.sum()),"source_artifact_sha256":c["source_sha256"]}) + return case_rows,gap_rows,station_rows + + +def _write_dict_csv(path,rows): + if not rows: raise ValueError("diagnostic CSV requires rows") + columns=tuple(rows[0]); + if any(tuple(row)!=columns for row in rows): raise ValueError("diagnostic CSV row schema mismatch") + with Path(path).open("w",newline="",encoding="utf-8") as stream: + writer=csv.DictWriter(stream,fieldnames=columns,lineterminator="\n"); writer.writeheader(); writer.writerows(rows) + return columns + +def publish_results_display(*,steady,strip,ledger,out): + """CPU-only immutable publication of steady displays and quantitative CSVs.""" + matplotlib,locale_name=_configure_publication_rendering(); import matplotlib.pyplot as plt + from matplotlib.patches import Circle + from .theory import affine_velocity,strip_basis_affine + steady=Path(steady).resolve(strict=True); strip=Path(strip).resolve(strict=True); ledger=Path(ledger).resolve(strict=True); out=Path(out) + if out.exists(): raise FileExistsError(f"refusing to clobber {out}") + if not out.parent.is_dir(): raise FileNotFoundError(out.parent) + strip_json=strip/"analysis.json" if strip.is_dir() else strip; strip_root=strip_json.parent + S=_load_hashed_json(strip_json,"strip"); L=_load_hashed_json(ledger,"ledger") + strip_npz=strip_root/"strip_arrays.npz"; entry=S["files"]["strip_arrays.npz"] + if _sha256(strip_npz)!=entry["sha256"] or strip_npz.stat().st_size!=entry["bytes"]: raise ValueError("strip arrays authentication failed") + if Path(L["campaign"]).resolve()!=steady: raise ValueError("ledger does not bind steady root") + names=("stationary","accepted-s3.55","reverse-s5.2"); loaded={n:load_validate_artifact(steady/n) for n in ("qin",)+names}; qin=loaded["qin"][1] + spec=loaded["accepted-s3.55"][0]["spec"]; D=float(spec["D"]); U=float(spec["config_lbm"]["physics"]["velocity"]); origin=np.asarray(spec["centers_xy"][0]) + labels={"stationary":"stationary unsteady reference","accepted-s3.55":"accepted s=3.55 (qualified)","reverse-s5.2":"stable reverse s=5.2 (qualified)"}; cases=[] + for name in names: + m,a=loaded[name]; cases.append({"name":name,"label":labels[name],"s":m["spec"].get("s"),"manifest":m,"arrays":a,"fields":_display_fields(a,qin,m["spec"]),"U":U,"x_D":(a["x"]-origin[0])/D,"y_D":(a["y"]-origin[1])/D,"source_sha256":m["files"][ARRAY_FILE]["sha256"]}) + tmp=Path(tempfile.mkdtemp(prefix=f".{out.name}.tmp-",dir=out.parent)); made=[] + def save(fig,name): + for ext,meta in (("png",{"Software":"DynamisLab steady display v1"}),("pdf",{"Creator":"DynamisLab steady display v1","Producer":"Matplotlib","CreationDate":None,"ModDate":None})): + fig.savefig(tmp/f"{name}.{ext}",dpi=240,bbox_inches="tight",metadata=meta); made.append(f"{name}.{ext}") + plt.close(fig) + centers=np.asarray(S["preregistration"]["centers_D"],float); radius=float(S["preregistration"]["radius_D"]) + def cylinders(ax): + for cx,cy in centers: ax.add_patch(Circle((cx,cy),radius,fc="white",ec="black",lw=.9,zorder=10)) + try: + x=np.linspace(-2,10,481); y=np.linspace(-3,3,241); xx,yy=np.meshgrid(x,y); solid=_display_solid_mask(x,y,centers,radius); exterior=~solid + affine=strip_basis_affine(centers,radius,"rear_opposite",H=S["preregistration"]["H_D"],u_inf=1,n_boundary=S["preregistration"]["n_boundary"],source_ratio=S["preregistration"]["source_ratio"],image_layers=40) + g=S["finite_re_reconciliation"]; panels=[] + for label,value in (("MFS zero circulation",0.),("MFS g_opt=+6.147944",g["theoretical_rear_opposite_g_opt_layer40"]),("MFS fitted g=-12.200554",g["actual_wls_g"])): + v=np.zeros(xx.shape+(2,)); v[exterior]=affine_velocity(affine,value,np.column_stack((xx[exterior],yy[exterior]))); panels.append((label,x,y,np.ma.array(v[...,0],mask=solid),np.ma.array(v[...,1],mask=solid))) + for c in cases[1:]: + X=(c["x_D"]>=-2)&(c["x_D"]<=10); Y=(c["y_D"]>=-3)&(c["y_D"]<=3); ix=np.ix_(Y,X); mask=~c["arrays"]["fluid_mask"][ix] + panels.append((c["label"]+" CFD",c["x_D"][X],c["y_D"][Y],np.ma.array(c["arrays"]["ux"][ix]/U,mask=mask),np.ma.array(c["arrays"]["uy"][ix]/U,mask=mask))) + speed_lim=max(float(np.nanpercentile(np.ma.filled(np.hypot(u,v),np.nan),99.5)) for _,_,_,u,v in panels) + fig,axs=plt.subplots(5,1,figsize=(11,13),sharex=True,sharey=True,constrained_layout=True) + for ax,(label,xp,yp,up,vp) in zip(axs,panels): + im=ax.pcolormesh(xp,yp,np.hypot(up,vp),cmap="viridis",vmin=0,vmax=speed_lim,shading="auto",rasterized=True); ax.streamplot(xp,yp,up,vp,color="white",density=1.3,linewidth=.45,arrowsize=.7); cylinders(ax); ax.set_ylabel("y/D"); ax.set_title(label,loc="left",fontsize=10); ax.annotate("flow",(9.5,2.55),(8,2.55),arrowprops={"arrowstyle":"->"}) + axs[-1].set_xlabel("x/D"); fig.colorbar(im,ax=axs,label="total speed |u|/U∞",shrink=.7); save(fig,"01_total_velocity_streamlines") + dlim=max(float(np.nanpercentile(c["fields"]["disturbance"],99.5)) for c in cases); olim=max(float(np.nanpercentile(abs(c["fields"]["vorticity_star"]),99.5)) for c in cases) + fig,axs=plt.subplots(3,3,figsize=(14,8.5),sharex=True,sharey=True,constrained_layout=True) + for row,c in enumerate(cases): + X=(c["x_D"]>=-2)&(c["x_D"]<=10); Y=(c["y_D"]>=-3)&(c["y_D"]<=3); ix=np.ix_(Y,X); a=c["arrays"]; f=c["fields"] + d_im=axs[row,0].pcolormesh(c["x_D"][X],c["y_D"][Y],np.ma.masked_invalid(f["disturbance"][ix]),cmap="magma",vmin=0,vmax=dlim,shading="auto",rasterized=True); o_im=axs[row,1].pcolormesh(c["x_D"][X],c["y_D"][Y],np.ma.masked_invalid(f["vorticity_star"][ix]),cmap="RdBu_r",vmin=-olim,vmax=olim,shading="auto",rasterized=True) + mask=~a["fluid_mask"][ix]; axs[row,2].streamplot(c["x_D"][X],c["y_D"][Y],np.ma.array(a["ux"][ix]/U,mask=mask),np.ma.array(a["uy"][ix]/U,mask=mask),color="black",density=1.3,linewidth=.45,arrowsize=.7) + for ax in axs[row]: cylinders(ax); ax.set_ylabel("y/D") + axs[row,0].text(.02,.94,c["label"],transform=axs[row,0].transAxes,va="top",color="white",bbox={"facecolor":"black","alpha":.45,"edgecolor":"none"}) + for ax,title in zip(axs[0],("velocity disturbance |u/U∞−eₓ|","conservative masked ωD/U∞","total-velocity streamlines")): ax.set_title(title) + for ax in axs[-1]: ax.set_xlabel("x/D") + fig.colorbar(d_im,ax=axs[:,0],label="|u/U∞−eₓ|",shrink=.7); fig.colorbar(o_im,ax=axs[:,1],label="ωD/U∞",shrink=.7); save(fig,"02_cfd_disturbance_vorticity_streamlines") + profile_cols=_write_display_profiles(tmp/"profiles_long.csv",cases); made.append("profiles_long.csv") + summary_cols=("case","s","label","status","qualification_required","settling_qualified","settling_value","max_velocity_error","max_abs_vorticity_star","fluid_points","source_artifact_sha256") + with (tmp/"summary.csv").open("w",newline="",encoding="utf-8") as stream: + w=csv.DictWriter(stream,fieldnames=summary_cols,lineterminator="\n"); w.writeheader() + for c in cases: w.writerow({"case":c["name"],"s":"" if c["s"] is None else c["s"],"label":c["label"],"status":_display_qualification(c["manifest"]),"qualification_required":c["manifest"]["result"]["qualification_required"],"settling_qualified":c["manifest"]["result"]["settling"]["qualified"],"settling_value":c["manifest"]["result"]["settling"]["value"],"max_velocity_error":np.nanmax(c["fields"]["velocity_error"]),"max_abs_vorticity_star":np.nanmax(abs(c["fields"]["vorticity_star"])),"fluid_points":c["fields"]["common"].sum(),"source_artifact_sha256":c["source_sha256"]}) + made.append("summary.csv") + diagnostic_rows,gap_rows,station_rows=_display_diagnostics(cases,qin,L["cases"]) + diagnostic_csv={} + for filename,rows in (("ns_case_summary.csv",diagnostic_rows),("ns_gap_fluxes.csv",gap_rows),("ns_station_diagnostics.csv",station_rows)): + diagnostic_csv[filename]=list(_write_dict_csv(tmp/filename,rows)); made.append(filename) + # Compact diagnostic comparison; it is explicitly not a closed NS balance. + fig,axs=plt.subplots(2,2,figsize=(11,8),constrained_layout=True); display_rows=diagnostic_rows[1:]; names2=[r["label"] for r in display_rows] + axs[0,0].bar(names2,[r["oracle_bound_C_P"] for r in display_rows]); axs[0,0].set_title("Oracle-bound actuator C_P") + gaps=("front_upper_rear","front_lower_rear","rear_rear"); width=.35; pos=np.arange(3) + for k,c in enumerate(cases[1:]): + rows=[r for r in gap_rows if r["case"]==c["name"]]; by={r["gap"]:r for r in rows}; axs[0,1].bar(pos+(k-.5)*width,[by[g]["Q_star"] for g in gaps],width,label=c["label"]) + axs[0,1].axhline(0,color="black",lw=.6); axs[0,1].set_xticks(pos,gaps,rotation=18); axs[0,1].set_title("Signed gap Q* (frozen normals)"); axs[0,1].legend(fontsize=7) + for c in cases[1:]: + rows=[r for r in station_rows if r["case"]==c["name"]]; axs[1,0].plot([r["x_over_D"] for r in rows],[r["E_inf_vector"] for r in rows],marker="o",label=c["label"]) + axs[1,0].set_xlabel("x/D"); axs[1,0].set_ylabel("E∞ vector vs q_in"); axs[1,0].set_title("Wake profile error"); axs[1,0].legend(fontsize=7) + xbars=np.arange(2); axs[1,1].bar(xbars-width/2,[r["recirculation_area_D2"] for r in display_rows],width,label="recirculation area/D²"); axs[1,1].bar(xbars+width/2,[r["immediate_wake_abs_vorticity_integral"] for r in display_rows],width,label="∫|ω*|dA*"); axs[1,1].set_xticks(xbars,names2); axs[1,1].set_title("Selected near-wake diagnostics"); axs[1,1].legend(fontsize=7) + fig.suptitle("Partial endpoint NS diagnostics — no residual closure\naccepted s=3.55 and stable reverse s=5.2 have mismatched amplitudes",fontsize=13); save(fig,"03_ns_diagnostics_partial_no_residual") + readme="""# Steady results display v2 + +This immutable CPU-only artifact renders existing authenticated endpoint fields; it did not execute CFD. + +## Figures + +- `01_total_velocity_streamlines`: total velocity, not disturbance velocity. The three MFS panels are inviscid finite-image strip references at zero circulation, favorable `g_opt`, and the finite-Re fitted `g`. The final panels are accepted `s=3.55` and stable reverse `s=5.2` CFD. Shared speed normalization, arrows, and solid masks support visual comparison, but streamlines do not establish mechanism, stability, or equivalence between potential and viscous flow. +- `02_cfd_disturbance_vorticity_streamlines`: rows are the stationary unsteady reference, accepted qualified endpoint, and stable reverse qualified endpoint. Columns show velocity disturbance from uniform inflow, conservative masked `omega D/U_inf`, and total-velocity streamlines. Blank vorticity cells lack a fully fluid centered stencil. Endpoint fields show spatial structure, not causality or asymptotic stability. +- `03_ns_diagnostics_partial_no_residual`: oracle-bound actuator power, signed gap fluxes using the exact frozen normals in `ns_gap_fluxes.csv`, wake-profile errors, recirculation, and vorticity diagnostics. This is an endpoint spatial partial ledger: storage/time-consistent and some body-adjacent terms are unavailable, so no residual is computed. Accepted `s=3.55` and stable reverse `s=5.2` differ in actuation amplitude and are not a same-amplitude controlled comparison. + +## CSVs + +`profiles_long.csv` retains every row on each selected station; `fluid_mask=1` identifies common case/q_in fluid points, and vorticity is blank only where its conservative stencil is unavailable. `summary.csv` distinguishes an unsteady reference not required to settle from settling-qualified steady endpoints. The three `ns_*.csv` files preserve diagnostics, exact orientations, provenance hashes, and partial-ledger limitations. +""" + (tmp/"README.md").write_text(readme); made.append("README.md") + command=f'PYTHONPATH="$PWD/src" TZ=UTC LC_ALL=C.UTF-8 conda run -n pinball_math python -m steady_pinball_theory.runner publish-results-display --steady "{steady}" --strip "{strip_json}" --ledger "{ledger}" --out "{out}"' + sources={"steady_root":{"path":str(steady),"files":{str(f.relative_to(steady)):_sha256(f) for f in sorted(steady.rglob("*")) if f.is_file()}},"strip_analysis":{"path":str(strip_json),"sha256":_sha256(strip_json)},"strip_arrays":{"path":str(strip_npz),"sha256":_sha256(strip_npz)},"oracle_bound_ledger":{"path":str(ledger),"sha256":_sha256(ledger)}} + manifest={"schema":"steady-pinball-results-display/v2","immutable":True,"scientific_scope":"CPU-only rendering and CSV export; no CFD executed","labels":labels,"orientation":{"array_axes":"yx","coordinates":"x-right_y-up","axes":"x/D horizontal, y/D vertical","origin":"front cylinder center"},"units":{"x_over_D":"1","y_over_D":"1","ux_over_U":"1","uy_over_U":"1","velocity_error":"|q_case-q_in|/U_inf","vorticity_star":"omega D/U_inf","fluid_mask":"boolean 0/1"},"color_limits":{"total_speed_over_U":[0,speed_lim],"velocity_disturbance":[0,dlim],"vorticity_star":[-olim,olim]},"masks":{"cfd":"solver FLUID-bit mask; vorticity additionally requires an all-fluid conservative centered stencil","potential":"analytic closed cylinder interiors masked before MFS evaluation and streamplot"},"csv":{"profiles_long":{"path":"profiles_long.csv","columns":list(profile_cols),"stations_x_over_D":[2,4,6,10]},"summary":{"path":"summary.csv","columns":list(summary_cols)},"diagnostics":diagnostic_csv},"potential":{"model":"finite-image free-slip-strip MFS rear_opposite affine circulation basis","image_layers":40,"g_values":[0,g["theoretical_rear_opposite_g_opt_layer40"],g["actual_wls_g"]],"total_velocity":True},"render":{"matplotlib":matplotlib.__version__,"backend":matplotlib.get_backend(),"locale":locale_name,"timezone":"UTC","dpi":240,"shared_normalization":True,"streamline_arrowheads":True},"interpretation":{"partial_ledger":"endpoint spatial partial; no residual closure","amplitude_mismatch":"accepted s=3.55 versus stable reverse s=5.2","panel_guide":"README.md"},"sources":sources,"exact_reproduction_command":command} + manifest["files"]={name:{"sha256":_sha256(tmp/name),"bytes":(tmp/name).stat().st_size} for name in made}; manifest["payload_sha256"]=hashlib.sha256(_canonical_json(manifest)).hexdigest(); (tmp/"manifest.json").write_text(json.dumps(manifest,indent=2,sort_keys=True,allow_nan=False)+"\n"); _publish_directory_no_replace(tmp,out); return manifest + finally: + if tmp.exists(): + import shutil; shutil.rmtree(tmp) + def main(argv=None): - p=argparse.ArgumentParser(); p.add_argument('command',choices=['oracle','diagnostic']); p.add_argument('--out',type=Path) - p.add_argument('--D',type=float,default=10.0); p.add_argument('--s',type=float,default=5.0); p.add_argument('--t-end',type=float,default=40.0); p.add_argument('--sample-dt',type=float,default=2.0) - a=p.parse_args(argv); c=CanonicalContract(diameter=a.D) - if a.command=='oracle': print(json.dumps(c.oracle(a.s),indent=2)); return 0 - if a.out is None: p.error('--out required') - a.out.mkdir(parents=True,exist_ok=False) - rows=[] - for b in ('qin','plus-minus','minus-plus'): - rows.append(run_case(a.out/b,branch=b,s=a.s,D=a.D,t_end=a.t_end,sample_dt=a.sample_dt)) - - q=np.load(a.out/'qin'/'endpoint.npz'); ix=int(round(c.centers[0][0]+c.primary_station_d*a.D)); refux=q['ux'][2:-2,ix]; refuy=q['uy'][2:-2,ix] - for row in rows: - e=np.load(a.out/row['branch']/'endpoint.npz'); du=(e['ux'][2:-2,ix]-refux)/c.u_inf; dv=(e['uy'][2:-2,ix]-refuy)/c.u_inf; vec=np.hypot(du,dv) - row['direct_qin']={"E_inf_x":float(np.max(np.abs(du))),"E_inf_y":float(np.max(np.abs(dv))),"E_inf_vector":float(np.max(vec)),"E_L2_vector":float(np.sqrt(np.mean(vec*vec)))} - (a.out/'summary.json').write_text(json.dumps(rows,indent=2)); return 0 - -if __name__=='__main__': raise SystemExit(main()) + p=argparse.ArgumentParser(); sub=p.add_subparsers(dest="command",required=True) + val=sub.add_parser("validate"); val.add_argument("artifact",type=Path) + article=sub.add_parser("publish-article") + display=sub.add_parser("publish-results-display") + for flag in ("steady","strip","ledger","out"): display.add_argument("--"+flag,type=Path,required=True) + for flag in ("steady","ledger","causal-analysis","causal-campaign","return-analysis","return-campaign","strip","ccd","sr","out"): article.add_argument("--"+flag,type=Path,required=True) + transient_val=sub.add_parser("validate-transient"); transient_val.add_argument("artifact",type=Path) + transient_inspect=sub.add_parser("inspect-transient"); transient_inspect.add_argument("artifact",type=Path) + transient_migrate=sub.add_parser("migrate-transient-ownership"); transient_migrate.add_argument("source",type=Path); transient_migrate.add_argument("--oracle",type=Path,required=True); transient_migrate.add_argument("--out",type=Path,required=True) + causal_v2=sub.add_parser("analyze-causal-switch"); causal_v2.add_argument("campaign",type=Path); causal_v2.add_argument("--out",type=Path,required=True); causal_v2.add_argument("--explicit-floor",type=float,default=1e-6) + return_v2=sub.add_parser("analyze-nonlinear-return"); return_v2.add_argument("campaign",type=Path); return_v2.add_argument("--out",type=Path,required=True) + analyze=sub.add_parser("analyze"); analyze.add_argument("campaign",type=Path); analyze.add_argument("--out",type=Path,required=True) + steady_analyze=sub.add_parser("analyze-steady"); steady_analyze.add_argument("campaign",type=Path); steady_analyze.add_argument("--out",type=Path,required=True) + ns_analyze=sub.add_parser("analyze-ns-ledger"); ns_analyze.add_argument("campaign",type=Path); ns_analyze.add_argument("--out",type=Path,required=True) + cred=sub.add_parser("analyze-credibility"); cred.add_argument("--out",type=Path,required=True); cred.add_argument("--evidence-root",type=Path); cred.add_argument("--agreement-tol",type=float,default=0.05) + promote=sub.add_parser("promote-evidence"); promote.add_argument("source",type=Path); promote.add_argument("dest",type=Path); promote.add_argument("--question",required=True); promote.add_argument("--notes",default="") + strip=sub.add_parser("analyze-strip"); strip.add_argument("--out",type=Path,required=True); strip.add_argument("--finite-analysis",type=Path) + karman=sub.add_parser("karman-baseline"); karman.add_argument("--out",type=Path,default=Path("/tmp/karman-baseline-20260806")) + semi=sub.add_parser("analyze-semi-analytic"); semi.add_argument("--out",type=Path,required=True); semi.add_argument("--evidence-root",type=Path) + oracle=sub.add_parser("oracle"); oracle.add_argument("--D",type=float,default=20.0); oracle.add_argument("--s",type=float,default=3.55) + reinterpret_oracle=sub.add_parser("reinterpret-torque-oracle"); reinterpret_oracle.add_argument("oracle",type=Path) + torque_oracle=sub.add_parser("qualify-torque-oracle"); torque_oracle.add_argument("--celeris-root",type=Path,required=True); torque_oracle.add_argument("--out",type=Path,required=True); torque_oracle.add_argument("--D",type=float,default=20.0); torque_oracle.add_argument("--U",type=float,default=.01); torque_oracle.add_argument("--rho",type=float,default=1.0); torque_oracle.add_argument("--omega",type=float,default=.002); torque_oracle.add_argument("--t-end",type=float,default=2.0); torque_oracle.add_argument("--sample-dt",type=float,default=.25); torque_oracle.add_argument("--parity-tol",type=float,default=.1); torque_oracle.add_argument("--zero-tol",type=float,default=.1) + acquire=sub.add_parser("acquire"); acquire.add_argument("--celeris-root",type=Path,required=True); acquire.add_argument("--role",choices=STEADY_ROLES,required=True); acquire.add_argument("--out",type=Path,required=True); acquire.add_argument("--D",type=float,default=20.0); acquire.add_argument("--s",type=float) + steady=sub.add_parser("steady-contract"); steady.add_argument("--celeris-root",type=Path,required=True); steady.add_argument("--out",type=Path,required=True); steady.add_argument("--D",type=float,default=20.0) + campaign=sub.add_parser("campaign"); campaign.add_argument("--celeris-root",type=Path,required=True); campaign.add_argument("--out",type=Path,required=True); campaign.add_argument("--D",type=float,default=20.0); campaign.add_argument("--s",type=float); campaign.add_argument("--t-end",type=float,default=250.0); campaign.add_argument("--sample-dt",type=float,default=2.0) + parent_cmd=sub.add_parser("acquire-parent"); parent_cmd.add_argument("--celeris-root",type=Path,required=True); parent_cmd.add_argument("--out",type=Path,required=True); parent_cmd.add_argument("--D",type=float,default=20.0); parent_cmd.add_argument("--s",type=float,default=3.55) + switch_cmd=sub.add_parser("acquire-causal-switch"); switch_cmd.add_argument("--celeris-root",type=Path,required=True); switch_cmd.add_argument("--parent",type=Path,required=True); switch_cmd.add_argument("--accepted-endpoint",type=Path,required=True); switch_cmd.add_argument("--reverse-endpoint",type=Path,required=True); switch_cmd.add_argument("--campaign-id",required=True); switch_cmd.add_argument("--out",type=Path,required=True); switch_cmd.add_argument("--horizon",type=float,default=10.0); switch_cmd.add_argument("--sample-dt",type=float,default=.1) + stability_cmd=sub.add_parser("acquire-stability"); stability_cmd.add_argument("--celeris-root",type=Path,required=True); stability_cmd.add_argument("--parent",type=Path,required=True); stability_cmd.add_argument("--accepted-endpoint",type=Path,required=True); stability_cmd.add_argument("--reverse-endpoint",type=Path,required=True); stability_cmd.add_argument("--campaign-id",required=True); stability_cmd.add_argument("--out",type=Path,required=True); stability_cmd.add_argument("--amplitude",type=float,action="append",required=True); stability_cmd.add_argument("--horizon",type=float,default=10.0); stability_cmd.add_argument("--pulse-duration",type=float,default=.5); stability_cmd.add_argument("--sample-dt",type=float,default=.1) + diagnostic=sub.add_parser("diagnostic"); diagnostic.add_argument("--celeris-root",type=Path,required=True); diagnostic.add_argument("--out",type=Path,required=True); diagnostic.add_argument("--D",type=float,default=20.0); diagnostic.add_argument("--s",type=float,default=3.55); diagnostic.add_argument("--branch",choices=("plus-minus","minus-plus"),default="plus-minus"); diagnostic.add_argument("--t-end",type=float,default=250.0); diagnostic.add_argument("--sample-dt",type=float,default=2.0) + a=p.parse_args(argv) + if a.command=="publish-results-display": + r=publish_results_display(steady=a.steady,strip=a.strip,ledger=a.ledger,out=a.out); print(json.dumps({"schema":r["schema"],"payload_sha256":r["payload_sha256"]},indent=2)); return 0 + if a.command=="publish-article": + r=publish_article(steady=a.steady,ledger=a.ledger,causal_analysis=a.causal_analysis,causal_campaign=a.causal_campaign,return_analysis=a.return_analysis,return_campaign=a.return_campaign,strip=a.strip,ccd=a.ccd,sr=a.sr,out=a.out); print(json.dumps({"schema":r["schema"],"payload_sha256":r["payload_sha256"]},indent=2)); return 0 + if a.command=="validate": print(json.dumps(load_validate_artifact(a.artifact)[0],indent=2)); return 0 + if a.command=="validate-transient": print(json.dumps(inspect_transient(a.artifact),indent=2,sort_keys=True,allow_nan=False)); return 0 + if a.command=="inspect-transient": print(json.dumps(inspect_transient(a.artifact),indent=2,sort_keys=True,allow_nan=False)); return 0 + if a.command=="migrate-transient-ownership": + contract,roles=migrate_transient_ownership(a.source,a.oracle,a.out); print(json.dumps({"schema":contract["schema"],"campaign_id":contract["campaign_id"],"roles":sorted(roles)},indent=2)); return 0 + if a.command=="analyze-causal-switch": print(json.dumps(analyze_causal_switch_v2(a.campaign,a.out,explicit_floor=a.explicit_floor),indent=2,sort_keys=True,allow_nan=False)); return 0 + if a.command=="analyze-nonlinear-return": print(json.dumps(analyze_nonlinear_return_v2(a.campaign,a.out),indent=2,sort_keys=True,allow_nan=False)); return 0 + if a.command=="analyze": print(json.dumps(analyze_campaign(a.campaign,a.out)["classification"],indent=2)); return 0 + if a.command=="analyze-steady": + result=analyze_steady_contract(a.campaign,a.out) + print(json.dumps({"schema":result["schema"],"classification":result["classification"]},indent=2)); return 0 + if a.command=="analyze-ns-ledger": + result=analyze_ns_ledger(a.campaign,a.out) + print(json.dumps({"schema":result["schema"],"claim_classification":result["claim_classification"]},indent=2)); return 0 + if a.command=="analyze-credibility": print(json.dumps(analyze_credibility(out=a.out,evidence_root=a.evidence_root,agreement_tol=a.agreement_tol)["classification"],indent=2)); return 0 + if a.command=="promote-evidence": print(json.dumps(promote_evidence(a.source,a.dest,scientific_question=a.question,notes=a.notes),indent=2)); return 0 + if a.command=="analyze-strip": print(json.dumps(analyze_strip(a.out,finite_analysis=a.finite_analysis)["classification"],indent=2)); return 0 + if a.command=="karman-baseline": print(json.dumps(write_karman_baseline(a.out)["classification"],indent=2)); return 0 + if a.command=="analyze-semi-analytic": print(json.dumps(analyze_semi_analytic(out=a.out,evidence_root=a.evidence_root)["classification"],indent=2)); return 0 + if a.command=="oracle": print(json.dumps(CanonicalContract(diameter=a.D).oracle(a.s),indent=2)); return 0 + if a.command=="reinterpret-torque-oracle": + binding,stored=load_qualify_torque_oracle(a.oracle); result=binding["runtime_interpretation"] + print(json.dumps({"schema":stored["schema"],"stored_qualification":stored.get("qualification"),"immutable_source":binding,"reinterpreted":result},indent=2,sort_keys=True,allow_nan=False)); return 0 + if a.command=="qualify-torque-oracle": + result=qualify_torque_oracle(a.out,intended_celeris_root=a.celeris_root,D=a.D,U=a.U,rho=a.rho,omega=a.omega,t_end=a.t_end,sample_dt=a.sample_dt,parity_tolerance=a.parity_tol,zero_tolerance=a.zero_tol) + print(json.dumps({"schema":result["schema"],"qualification":result["qualification"],"celeris_torque_channel_work_sign":result["celeris_torque_channel_work_sign"],"force_ownership":result["force_ownership"]},indent=2)); return 0 + if a.command=="acquire-parent": acquire_accepted_parent(a.out,intended_celeris_root=a.celeris_root,s=a.s,D=a.D); return 0 + if a.command=="acquire-causal-switch": acquire_causal_switch_v2(a.out,parent=a.parent,accepted_endpoint=a.accepted_endpoint,reverse_endpoint=a.reverse_endpoint,intended_celeris_root=a.celeris_root,campaign_id=a.campaign_id,horizon=a.horizon,sample_dt=a.sample_dt); return 0 + if a.command=="acquire-stability": acquire_nonlinear_return_v2(a.out,parent=a.parent,accepted_endpoint=a.accepted_endpoint,reverse_endpoint=a.reverse_endpoint,intended_celeris_root=a.celeris_root,campaign_id=a.campaign_id,amplitudes=a.amplitude,horizon=a.horizon,pulse_duration=a.pulse_duration,sample_dt=a.sample_dt); return 0 + if a.command=="diagnostic": run_case(a.out,kind="diagnostic",s=a.s,branch=a.branch,D=a.D,t_end=a.t_end,sample_dt=a.sample_dt,intended_celeris_root=a.celeris_root); return 0 + if a.command=="acquire": + required_s=3.55 if a.role=="accepted" else (5.2 if a.role=="reverse" else None) + if a.role in ("qin","stationary") and a.s is not None: p.error(f"{a.role} rejects --s") + run_case(a.out,kind=a.role,s=required_s if a.s is None else a.s,D=a.D,intended_celeris_root=a.celeris_root); return 0 + if a.command=="steady-contract": + roles=(("qin","qin",None),("stationary","stationary",None),("accepted-s3.55","accepted",3.55),("reverse-s3.55","reverse",3.55),("reverse-s5.2","reverse",5.2)); _assert_cfd_environment(intended_celeris_root=a.celeris_root) + def build(stage,item): + name,kind,svalue=item; enforce_launch_cooldown(); _run_case_unlocked(stage/name,kind=kind,s=svalue,D=a.D,intended_celeris_root=a.celeris_root) + with exclusive_cfd_lease(role="steady-contract"): _atomic_campaign(a.out,roles,build) + return 0 + if a.s is not None: p.error("campaign has frozen s values and rejects --s") + roles=(("qin",None),)+tuple((f"accepted-s{svalue:.2f}",svalue) for svalue in ACCEPTED_S); _assert_cfd_environment(intended_celeris_root=a.celeris_root) + def build(stage,item): + name,svalue=item; enforce_launch_cooldown(); _run_case_unlocked(stage/name,kind="qin" if svalue is None else "accepted",s=svalue,D=a.D,t_end=a.t_end,sample_dt=a.sample_dt,intended_celeris_root=a.celeris_root) + with exclusive_cfd_lease(role="campaign"): _atomic_campaign(a.out,roles,build) + return 0 +if __name__=="__main__": raise SystemExit(main()) diff --git a/src/steady_pinball_theory/tests/test_core.py b/src/steady_pinball_theory/tests/test_core.py index 4918506..8fe941d 100644 --- a/src/steady_pinball_theory/tests/test_core.py +++ b/src/steady_pinball_theory/tests/test_core.py @@ -1,52 +1,1972 @@ import numpy as np -from steady_pinball_theory.contract import CanonicalContract,wall_velocity -from steady_pinball_theory.metrics import profile_errors -from steady_pinball_theory.theory import solve_mfs +import pytest +from pathlib import Path +from steady_pinball_theory.contract import CanonicalContract, NondimensionalContract, wall_velocity +from steady_pinball_theory.metrics import ( + affine_profile_sensitivity, common_exterior_error, gap_flux, + one_sided_profile_error_slopes, profile_errors, reflection_parity_defect, + aligned_position_l2, karman_observer_mask, karman_propagation_metrics, + normalized_invariant_drift, + bilinear_sample_velocity, ccw_contour_circulation, outer_wls_effective_circulation, + outer_wls_total_model, + fit_two_point_affine_closure, predict_affine_closure, strip_modal_projection, + propagate_strip_modes, strip_mode_parity_sector, tensor_trapezoid_weights, + quadrature_l2, conservative_masked_vorticity, absolute_vorticity_moments, + recirculation_observables, wake_deficit_observables, + near_wall_tangential_speed, wall_vorticity_production_proxy, + separation_reattachment_estimator, control_volume_streamwise_momentum_ledger, + torque_power_availability, torque_to_actuator_power, station_flux_metrics, + volume_viscous_dissipation, gap_mass_momentum_flux, + control_volume_mechanical_energy_ledger, fit_conservation_model, + predict_conservation_model, rectangular_control_volume_fluxes, + weak_compressible_pressure_proxy, +) +from steady_pinball_theory.theory import ( + affine_velocity, basis_affine, circulation_basis, cylinder_velocity, + classify_stagnation_root, continue_stagnation_points, dense_diagnostics, + far_field_coefficients, find_interior_stagnation_points, + finite_vortex_rhs, mutual_vortex_velocity, prepare_unbounded_body_response, + rear_opposite_affine, reconstruct_multipoles, singular_velocity, + solve_laurent, solve_mfs, source_multipole_coefficients, velocity_jacobian, + strip_basis_affine, strip_mode_field, exact_circle_vortex_response, + integrate_point_vortices_rk4, karman_self_advection, karman_stable_aspect, + point_vortex_hamiltonian, point_vortex_rhs, staggered_karman_train, + vas_critical_hamiltonian, vas_foppl_equilibrium, vas_foppl_hamiltonian, + vas_foppl_rhs, +) + +CENTERS = np.array([[0.0, 0.0], [1.3, 0.75], [1.3, -0.75]]) + + +def circle_points(radius, n=4096, factor=1.0): + theta = (np.arange(n) + 0.371) * 2 * np.pi / n + normal = np.column_stack((np.cos(theta), np.sin(theta))) + return theta, factor * radius * normal, normal def test_canonical_geometry_and_reynolds(): - c=CanonicalContract(); assert c.centers==((1000.0,299.5),(1026.0,314.5),(1026.0,284.5)); assert c.viscosity==0.004 + c = CanonicalContract() + assert c.centers == ((1000.0, 299.5), (1026.0, 314.5), (1026.0, 284.5)) + assert c.viscosity == 0.004 + def test_source_level_wall_oracle(): - c=CanonicalContract(); o=c.oracle(5.0) - assert o['plus-minus']['action']==[0.0,0.005,-0.005] - assert o['plus-minus']['rear_y_plus_outer_top'][0] < 0 - assert o['plus-minus']['rear_y_plus_gap_bottom'][0] > 0 - assert o['minus-plus']['rear_y_plus_outer_top'][0] > 0 - assert wall_velocity(2,3,4)==(-8.0,6.0) + c = CanonicalContract(); oracle = c.oracle(5.0) + assert oracle["plus-minus"]["action"] == [0.0, 0.005, -0.005] + assert oracle["plus-minus"]["rear_y_plus_outer_top"][0] < 0 + assert oracle["plus-minus"]["rear_y_plus_gap_bottom"][0] > 0 + assert oracle["minus-plus"]["rear_y_plus_outer_top"][0] > 0 + assert wall_velocity(2, 3, 4) == (-8.0, 6.0) + def test_primary_metric_is_pointwise_vector_norm(): - r=profile_errors(np.array([1.,.8]),np.array([0.,.1]),u_inf=1.) - assert np.isclose(r['E_inf_vector'],np.sqrt(.05)) - -def test_unbounded_mfs_impermeability_and_zero_source(): - centers=np.array([[0.,0.],[1.3,.75],[1.3,-.75]]) - sol,diag=solve_mfs(centers,.5,[0.,2.,-2.],n_boundary=48) - assert diag['boundary_Linf'] < 2e-5 - for q in sol.strengths.reshape(3,-1): assert abs(q.sum()) < 1e-10 - -def test_strip_images_reduce_wall_normal_velocity(): - centers=np.array([[0.,0.],[1.3,.75],[1.3,-.75]]) - sol,diag=solve_mfs(centers,.5,[0.,2.,-2.],n_boundary=48,H=15.,image_layers=20) - x=np.linspace(-5,8,300); p=np.r_[np.c_[x,np.full_like(x,15.)],np.c_[x,np.full_like(x,-15.)]] - assert np.max(np.abs(sol.velocity(p)[:,1])) < 2e-3 - assert diag['boundary_Linf'] < 3e-5 + result = profile_errors(np.array([1.0, 0.8]), np.array([0.0, 0.1]), u_inf=1.0) + assert np.isclose(result["E_inf_vector"], np.sqrt(0.05)) -def test_mfs_resolution_and_source_radius_sensitivity(): - centers=np.array([[0.,0.],[1.3,.75],[1.3,-.75]]) - rows=[] - for n in (32,48,64): - for ratio in (.55,.65,.75): - _,d=solve_mfs(centers,.5,[0.,2.,-2.],n_boundary=n,source_ratio=ratio) - rows.append(d['boundary_Linf']) - assert max(rows) < 2e-4 +@pytest.mark.parametrize("kwargs,match", [ + ({"centers": [[0, 0], [0.9, 0]], "radius": 0.5, "circulations": [0, 0]}, "non-overlapping"), + ({"centers": [[0, np.nan]], "radius": 0.5, "circulations": [0]}, "finite"), + ({"centers": [[0, 0]], "radius": 0, "circulations": [0]}, "positive"), + ({"centers": [[0, 0]], "radius": 0.5, "circulations": [0], "u_inf": np.inf}, "finite"), + ({"centers": [[0, 0]], "radius": 0.5, "circulations": [0], "n_boundary": 7}, ">= 8"), + ({"centers": [[0, 0]], "radius": 0.5, "circulations": [0], "n_boundary": 8.0}, "integer"), + ({"centers": [[0, 0]], "radius": 0.5, "circulations": [0], "source_ratio": 1}, "source_ratio"), + ({"centers": [[0, 0.6]], "radius": 0.5, "circulations": [0], "H": 1}, "inside"), + ({"centers": [[0, 0]], "radius": 0.5, "circulations": [0], "image_layers": -1}, ">= 0"), +]) +def test_mfs_rejects_invalid_inputs(kwargs, match): + with pytest.raises(ValueError, match=match): + solve_mfs(**kwargs) -def test_strip_image_layer_sensitivity(): - centers=np.array([[0.,0.],[1.3,.75],[1.3,-.75]]) - vals=[] - for layers in (10,20,40): - sol,d=solve_mfs(centers,.5,[0.,2.,-2.],n_boundary=48,H=15.,image_layers=layers) - vals.append(sol.velocity(np.array([[10.,0.]]))[0]) - assert d['boundary_Linf'] < 4e-5 - assert np.max(np.linalg.norm(np.diff(vals,axis=0),axis=1)) < 2e-4 + + + +def test_vas_exact_foppl_equilibrium_hamiltonian_and_rhs(): + position, kappa = vas_foppl_equilibrium(2.0) + exact = np.array([np.sqrt(55.0) / 4.0, 3.0 / 4.0]) + assert np.allclose(position, exact, atol=2e-15) + assert kappa == 45.0 / 32.0 + assert np.linalg.norm(vas_foppl_rhs(position, kappa)) < 2e-15 + hc = 0.5 * kappa * (1.0 - np.log(0.5 * kappa)) + assert vas_critical_hamiltonian(kappa) == hc + assert vas_foppl_hamiltonian(position, kappa) < hc + + +def test_vas_hamiltonian_gradient_rhs_and_short_conservation(): + kappa = 45.0 / 32.0 + position = np.array([2.1, 0.9]) + step = 2e-6 + gradient = np.array([ + (vas_foppl_hamiltonian(position + [step, 0], kappa) + - vas_foppl_hamiltonian(position - [step, 0], kappa)) / (2 * step), + (vas_foppl_hamiltonian(position + [0, step], kappa) + - vas_foppl_hamiltonian(position - [0, step], kappa)) / (2 * step), + ]) + assert np.allclose(vas_foppl_rhs(position, kappa), + [gradient[1], -gradient[0]], atol=2e-10) + + from scipy.integrate import solve_ivp + initial_h = vas_foppl_hamiltonian(position, kappa) + result = solve_ivp(lambda _, state: vas_foppl_rhs(state, kappa), (0.0, 1.0), + position, rtol=2e-12, atol=2e-14, method="DOP853") + assert result.success + drift = max(abs(vas_foppl_hamiltonian(state, kappa) - initial_h) + for state in result.y.T) + assert drift < 2e-11 + + +def test_exact_circle_routh_response_and_mfs_regular_self_convergence(): + center = np.array([0.2, -0.1]) + radius = 0.7 + position = np.array([[1.45, 0.43]]) + gamma = np.array([1.8]) + exact = exact_circle_vortex_response( + position[0], gamma[0], center=center, radius=radius) + relative = position[0] - center + assert np.allclose(exact["image_position"], + center + radius**2 * relative / np.dot(relative, relative)) + step = 2e-6 + gradient = [] + for axis in range(2): + delta = np.zeros(2); delta[axis] = step + hp = exact_circle_vortex_response( + position[0] + delta, gamma[0], center=center, radius=radius)["hamiltonian"] + hm = exact_circle_vortex_response( + position[0] - delta, gamma[0], center=center, radius=radius)["hamiltonian"] + gradient.append((hp - hm) / (2 * step)) + expected_from_h = np.array([gradient[1], -gradient[0]]) / gamma[0] + assert np.allclose(expected_from_h, exact["regular_self_velocity"], atol=2e-11) + errors = [] + for n_boundary in (16, 24, 40): + solver = prepare_unbounded_body_response( + [center], radius, n_boundary=n_boundary) + numerical = solver.response(position, gamma).velocity(position)[0] + errors.append(np.linalg.norm(numerical - exact["regular_self_velocity"])) + assert errors[1] < errors[0] / 5 + assert errors[2] < errors[1] / 20 + assert errors[2] < 2e-8 + + +def test_karman_finite_train_center_velocity_converges_to_infinite_street(): + spacing, separation, gamma = 1.7, 0.43, 2.2 + expected = karman_self_advection(spacing, separation, gamma) + errors = [] + for half_window in (10, 30, 90): + positions, strengths = staggered_karman_train( + half_window, spacing=spacing, separation=separation, + circulation=gamma) + center_index = half_window + velocity = mutual_vortex_velocity(positions, strengths)[center_index] + errors.append(abs(velocity[0] - expected)) + assert abs(velocity[1]) < 3e-15 + assert errors[1] < errors[0] / 2.5 + assert errors[2] < errors[1] / 2.5 + assert errors[2] < 1.2e-3 + + +def test_karman_exact_temporal_neutral_aspect_identity(): + p0 = karman_stable_aspect() + assert np.isclose(np.sinh(np.pi * p0), 1.0, atol=2e-15) + assert np.isclose(p0, 0.28054992616959007, atol=2e-16) + + + +def test_point_vortex_hamiltonian_gradient_matches_rhs_and_conserves(): + positions=np.array([[-1.1,-.4],[.2,.6],[1.4,-.2]]) + strengths=np.array([-1.2,.8,1.1]); rhs=point_vortex_rhs(positions,strengths) + step=2e-6; gradient=np.empty_like(positions) + for i in range(len(positions)): + for axis in range(2): + delta=np.zeros_like(positions); delta[i,axis]=step + gradient[i,axis]=(point_vortex_hamiltonian(positions+delta,strengths)-point_vortex_hamiltonian(positions-delta,strengths))/(2*step) + canonical=np.column_stack((gradient[:,1]/strengths,-gradient[:,0]/strengths)) + assert np.allclose(rhs,canonical,atol=3e-11) + run=integrate_point_vortices_rk4(positions,strengths,horizon=.1,time_step=.0025) + assert normalized_invariant_drift(run["hamiltonian"],scale=abs(run["hamiltonian"][0]))<2e-12 + + +def test_karman_central_window_and_integrator_convergence(): + h=karman_stable_aspect(); states={}; errors=[]; uniform=[] + for M in (12,24,48): + x,k=staggered_karman_train(M,separation=h); mask=karman_observer_mask(x,1.) + rhs=point_vortex_rhs(x,k); mean=np.mean(rhs[mask],axis=0); errors.append(abs(mean[0]-karman_self_advection(1,h,1))) + uniform.append(np.sqrt(np.mean(np.sum((rhs[mask]-mean)**2,axis=1)))) + states[M]=(integrate_point_vortices_rk4(x,k,horizon=.25,time_step=.0025)["states"][-1],mask,x,k) + assert errors[2].2*h and np.isfinite(list(v for key,v in metrics.items() if isinstance(v,float))).all() + + +def test_karman_collision_masks_sensitivity_and_artifact_no_clobber(tmp_path): + with pytest.raises(ValueError,match="collision"): + point_vortex_rhs([[0,0],[1e-8,0]],[1,-1],collision_distance=1e-6) + with pytest.raises(ValueError,match="observer"): + karman_observer_mask([[0,0],[1,0]],1,half_width=.1) + x,k=staggered_karman_train(12,separation=karman_stable_aspect()); mask=karman_observer_mask(x,1) + perturbed=x.copy(); perturbed[np.flatnonzero((k<0)&np.isclose(x[:,0],0))[0],1]+=.01*karman_stable_aspect() + assert aligned_position_l2(x,perturbed,mask)["L2"]>0 + from steady_pinball_theory.runner import write_karman_baseline + out=tmp_path/"k1"; first=write_karman_baseline(out) + assert first["classification"]["K1"]=="FAIL" and not first["classification"]["K2_authorized"] + assert not first["checks"]["translation_window_convergence"] + with pytest.raises(FileExistsError): write_karman_baseline(out) + import json,hashlib + manifest=json.loads((out/"manifest.json").read_text()) + for name in ("config.json","result.json"): + assert hashlib.sha256((out/name).read_bytes()).hexdigest()==manifest["files"][name]["sha256"] + + +def test_free_vortex_response_enforces_dense_offgrid_impermeability(): + response_solver = prepare_unbounded_body_response(CENTERS, 0.5, n_boundary=64) + position = np.array([[-1.1, 0.37]]) + strength = np.array([1.8]) + response = response_solver.response(position, strength) + theta = (np.arange(3073) + 0.271828) * 2 * np.pi / 3073 + normals0 = np.column_stack((np.cos(theta), np.sin(theta))) + points = np.concatenate([center + 0.5 * normals0 for center in CENTERS]) + normals = np.tile(normals0, (len(CENTERS), 1)) + incident = strength[0] * singular_velocity(points, position[0], vortex=True) + residual = np.einsum("ij,ij->i", incident + response.velocity(points), normals) + assert np.max(np.abs(residual)) < 3e-7 + + +def test_free_vortex_response_decays_without_body_circulation(): + solver = prepare_unbounded_body_response(CENTERS, 0.5, n_boundary=48) + response = solver.response([[-1.2, 0.3]], [2.1]) + assert np.array_equal(response.circulations, np.zeros(3)) + assert np.max(np.abs(response.strengths.reshape(3, -1).sum(axis=1))) < 2e-14 + near = np.linalg.norm(response.velocity([[8.0, 3.0]])[0]) + far = np.linalg.norm(response.velocity([[80.0, 30.0]])[0]) + assert far < near / 50 + theta, offsets, tangent_normal = circle_points(0.5, n=4096, factor=1.08) + tangent = np.column_stack((-tangent_normal[:, 1], tangent_normal[:, 0])) + for center in CENTERS: + velocity = response.velocity(center + offsets) + circulation = 1.08 * 0.5 * 2 * np.pi * np.mean( + np.einsum("ij,ij->i", velocity, tangent)) + assert abs(circulation) < 2e-10 + + +def test_two_vortex_rhs_excludes_self_and_retains_mutual_induction(): + positions = np.array([[-2.0, -0.4], [-2.0, 0.6]]) + strengths = np.array([1.3, -0.8]) + mutual = mutual_vortex_velocity(positions, strengths) + expected = np.array([[-0.8 / (2 * np.pi), 0.0], + [-1.3 / (2 * np.pi), 0.0]]) + assert np.allclose(mutual, expected, atol=2e-15) + base, _ = solve_mfs(CENTERS, 0.5, [0.0, 1.4, -1.4], n_boundary=48) + response_solver = prepare_unbounded_body_response(CENTERS, 0.5, n_boundary=48) + rhs = finite_vortex_rhs( + base, positions, strengths, body_response=response_solver) + response = response_solver.response(positions, strengths) + assert np.isfinite(rhs).all() + assert np.allclose( + rhs, base.velocity(positions) + mutual + response.velocity(positions), + atol=2e-14) + + +@pytest.mark.parametrize("positions,strengths,match", [ + ([[np.nan, 0.0]], [1.0], "finite"), + ([[-2.0, 0.0], [-2.0, 0.0]], [1.0, -1.0], "distinct"), + ([[0.0, 0.0]], [1.0], "outside"), + ([[-2.0, 0.0]], [1.0, 2.0], "one finite value"), +]) +def test_free_vortex_invalid_and_colliding_inputs_fail(positions, strengths, match): + base, _ = solve_mfs(CENTERS, 0.5, [0.0, 0.0, 0.0], n_boundary=24) + with pytest.raises(ValueError, match=match): + finite_vortex_rhs(base, positions, strengths) + + +def test_exact_one_cylinder_field_wall_circulation_and_gamma_trace(): + radius, u_inf, gamma = 0.7, 1.3, 2.1 + theta, points, normal = circle_points(radius, factor=1.8) + tangent = np.column_stack((-np.sin(theta), np.cos(theta))) + velocity = cylinder_velocity(points, [0, 0], radius, u_inf=u_inf, circulation=gamma) + radial = np.einsum("ij,ij->i", velocity, normal) + tangential = np.einsum("ij,ij->i", velocity, tangent) + r = 1.8 * radius + assert np.max(np.abs(radial - u_inf * (1 - radius**2 / r**2) * np.cos(theta))) < 2e-15 + expected_t = -u_inf * (1 + radius**2 / r**2) * np.sin(theta) + gamma / (2*np.pi*r) + assert np.max(np.abs(tangential - expected_t)) < 2e-15 + _, wall, normal = circle_points(radius) + tangent = np.column_stack((-normal[:, 1], normal[:, 0])) + v0 = cylinder_velocity(wall, [0, 0], radius, u_inf=u_inf, circulation=0) + vg = cylinder_velocity(wall, [0, 0], radius, u_inf=u_inf, circulation=gamma) + assert np.max(np.abs(np.einsum("ij,ij->i", vg, normal))) < 2e-15 + assert np.max(np.abs(np.einsum("ij,ij->i", vg-v0, normal))) < 2e-15 + assert np.max(np.abs(np.einsum("ij,ij->i", vg-v0, tangent)-gamma/(2*np.pi*radius))) < 2e-15 + contour_velocity = cylinder_velocity(points, [0, 0], radius, u_inf=u_inf, circulation=gamma) + circulation = 2*np.pi*r*np.mean(np.einsum("ij,ij->i", contour_velocity, tangent)) + assert abs(circulation-gamma) < 2e-14 + + +def test_zero_inflow_tangential_counterexample(): + radius, omega = 0.7, -1.2 + gamma = 2*np.pi*radius**2*omega + _, wall, normal = circle_points(radius) + tangent = np.column_stack((-normal[:, 1], normal[:, 0])) + velocity = cylinder_velocity(wall, [0, 0], radius, u_inf=0, circulation=gamma) + assert np.max(np.abs(np.einsum("ij,ij->i", velocity, normal))) < 1e-15 + assert np.max(np.abs(np.einsum("ij,ij->i", velocity, tangent)-radius*omega)) < 1e-15 + + +def test_dense_unbounded_diagnostics_and_circulation(): + sol, algebra = solve_mfs(CENTERS, 0.5, [0, 2, -2], n_boundary=48) + dense = dense_diagnostics(sol, n_angle=1536, contour_factor=1.06, far_radius=100) + assert algebra["rank"] == algebra["unknowns"] + assert max(algebra["zero_source_error"]) < 1e-13 + assert algebra["collocation_Linf"] < 1e-11 + assert max(x["Linf"] for x in dense["off_collocation_bodies"]) < 2e-7 + assert max(abs(x) for x in dense["circulation_errors"]) < 2e-7 + assert dense["far_field_Linf"] < 3e-4 + + +def test_strip_finite_image_field_consistency_on_declared_exterior(): + fields = {} + walls = {} + for layers in (20, 40, 80): + sol, _ = solve_mfs(CENTERS, 0.5, [0, 2, -2], n_boundary=48, H=15, + image_layers=layers) + dense = dense_diagnostics(sol, n_angle=1024, wall_interval=(-5, 8), n_wall=1201) + assert max(x["Linf"] for x in dense["off_collocation_bodies"]) < 2e-7 + # Regression guard with >10x safety over the measured layer-20 value; + # it was set post hoc and is not scientific acceptance evidence. + assert dense["strip_wall"]["Linf"] < 1e-7 + fields[layers] = sol + walls[layers] = dense["strip_wall"]["Linf"] + successive = [] + for coarse, fine in ((20, 40), (40, 80)): + result = common_exterior_error( + fields[fine].velocity, fields[coarse].velocity, CENTERS, 0.5, + bounds=(-3, 6, -3, 3), shape=(121, 81), exclusion_factor=1.1) + successive.append(result["weighted_RMS"]) + assert walls[40] < walls[20] and walls[80] < walls[40] + assert successive[1] < 0.6 * successive[0] + assert successive[1] < 1e-5 + + +def test_mfs_order_and_source_radius_scientific_checks(): + offgrid = [] + for n in (24, 32, 48): + sol, _ = solve_mfs(CENTERS, 0.5, [0, 0, 0], n_boundary=n) + offgrid.append(max(x["Linf"] for x in dense_diagnostics( + sol, n_angle=1024)["off_collocation_bodies"])) + assert offgrid[1] < offgrid[0] / 20 and offgrid[2] < offgrid[1] / 100 + + for circulation in ([0, 0, 0], [0, 2, -2]): + solutions = {} + for ratio in (0.55, 0.65, 0.75): + solution, _ = solve_mfs( + CENTERS, 0.5, circulation, n_boundary=64, source_ratio=ratio) + solutions[ratio] = solution + dense = dense_diagnostics(solution, n_angle=2048) + assert max(x["Linf"] for x in dense["off_collocation_bodies"]) < 2e-7 + for ratio in (0.55, 0.75): + comparison = common_exterior_error( + solutions[0.65].velocity, solutions[ratio].velocity, CENTERS, 0.5, + bounds=(-3, 6, -3, 3), shape=(181, 121), exclusion_factor=1.1) + assert comparison["relative_to_uniform_speed"] < 1e-8 + + +def test_independently_discretized_laurent_agreement_and_metric_sensitivity(): + mfs, _ = solve_mfs(CENTERS, 0.5, [0, 0, 0], n_boundary=64) + errors = [] + for order in (6, 8, 12): + laurent, diag = solve_laurent(CENTERS, 0.5, order=order) + assert diag["rank"] == diag["unknowns"] + assert diag["off_collocation_angles_per_body"] > 3 * (4 * order) + result = common_exterior_error( + laurent.velocity, mfs.velocity, CENTERS, 0.5, + bounds=(-3, 6, -3, 3), shape=(181, 121), exclusion_factor=1.1) + assert result["retained_points"] > 19000 + errors.append(result["relative_to_reference_disturbance"]) + assert errors[1] < errors[0] / 5 + assert errors[2] < errors[1] / 30 + assert errors[2] < 5e-7 + + laurent, diag = solve_laurent(CENTERS, 0.5, order=12) + assert diag["off_collocation_Linf"] < 1e-5 + grid_results = [common_exterior_error( + laurent.velocity, mfs.velocity, CENTERS, 0.5, + bounds=(-3, 6, -3, 3), shape=shape, exclusion_factor=1.1) + for shape in ((121, 81), (181, 121), (241, 161))] + grid_values = np.array([x["relative_to_reference_disturbance"] for x in grid_results]) + assert np.max(np.abs(grid_values / grid_values[1] - 1.0)) < 0.15 + mask_values = [] + for exclusion in (1.05, 1.10, 1.15): + result = common_exterior_error( + laurent.velocity, mfs.velocity, CENTERS, 0.5, + bounds=(-3, 6, -3, 3), shape=(241, 161), exclusion_factor=exclusion) + mask_values.append(result["relative_to_reference_disturbance"]) + assert max(mask_values) < 8e-7 + assert mask_values[0] > mask_values[1] > mask_values[2] + + +def test_exact_rear_pair_far_field_coefficient_and_zero_log(): + xr, b, gamma = 1.3, 0.75, 2.4 + centers = np.array([[xr, b], [xr, -b]]) + points = np.array([[800.0, 110.0], [-700.0, 190.0]]) + direct = (gamma * singular_velocity(points, centers[0], vortex=True) + - gamma * singular_velocity(points, centers[1], vortex=True)) + z = points[:, 0] + 1j * points[:, 1] + coefficient = -gamma * b / np.pi + leading_q = -coefficient / z**2 + leading = np.column_stack((leading_q.real, -leading_q.imag)) + assert np.max(np.linalg.norm(direct - leading, axis=1)) < 5e-9 + assert coefficient < 0 + assert np.isclose(coefficient, -gamma*b/np.pi) + + +def test_source_multipole_reconstruction_converges_on_valid_exterior_points(): + full, _ = solve_mfs(CENTERS, 0.5, [0, 1.7, -1.7], n_boundary=64) + probes = np.array([[-2.0, 1.7], [3.0, 0.0], [2.6, 2.2], [10.0, -1.3]]) + errors = [] + for order in (1, 2, 4, 8): + reduced = reconstruct_multipoles(full, order) + errors.append(np.max(np.linalg.norm(reduced.velocity(probes)-full.velocity(probes), axis=1))) + assert errors[-1] < errors[1] / 100 + assert errors[-1] < 2e-8 + with pytest.raises(ValueError, match="outside source rings"): + reconstruct_multipoles(full, 2).velocity(CENTERS[:1]) + + +def test_source_coefficients_match_direct_source_velocity(): + full, _ = solve_mfs(CENTERS, 0.5, [0, 0, 0], n_boundary=48) + coefficients, radii = source_multipole_coefficients(full, 16) + assert np.allclose(radii, 0.325) + source_only = type(full)(full.centers, full.radius, full.strengths, full.source_points, + np.zeros(3), 0.0, None, full.image_layers) + reduced = reconstruct_multipoles(source_only, 16) + points = np.array([[-2.0, 2.0], [3.0, 0.0], [2.8, -2.1]]) + assert coefficients.shape == (3, 16) + assert np.max(np.linalg.norm(reduced.velocity(points)-source_only.velocity(points), axis=1)) < 2e-12 + + +def test_zero_net_circulation_reflection_parity_and_affine_coefficient(): + gamma = 2.3 + sol, _ = solve_mfs(CENTERS, 0.5, [0, gamma, -gamma], n_boundary=64) + coeff = far_field_coefficients(sol) + assert abs(coeff["log"]) < 1e-14 + grid = np.column_stack((np.linspace(-2, 8, 301), np.linspace(0.03, 2.8, 301))) + assert reflection_parity_defect(sol.velocity, grid)["Linf"] < 1e-10 + affine = rear_opposite_affine(CENTERS, 0.5, n_boundary=64) + predicted = affine["C0"] + gamma*affine["dC"] + assert abs(coeff["dipole"]-predicted) < 2e-12 + assert affine["dC"].real < 0 + assert abs(affine["dC"].imag) < 2e-12 + + +def test_cancellation_root_and_held_out_gamma_region_convergence(): + affine = rear_opposite_affine(CENTERS, 0.5, n_boundary=64) + assert affine["gamma_opt"] > 0 + assert affine["exact"] + assert abs(affine["residual"]) < 2e-12 + y = np.linspace(-3, 3, 1201) + profile_points = np.column_stack((np.full_like(y, 10.0), y)) + zero, _ = solve_mfs(CENTERS, 0.5, [0, 0, 0], n_boundary=64) + optimum, _ = solve_mfs( + CENTERS, 0.5, [0, affine["gamma_opt"], -affine["gamma_opt"]], n_boundary=64) + zero_profile = zero.velocity(profile_points) + optimum_profile = optimum.velocity(profile_points) + assert profile_errors(optimum_profile[:, 0], optimum_profile[:, 1], u_inf=1)["E_inf_vector"] \ + < profile_errors(zero_profile[:, 0], zero_profile[:, 1], u_inf=1)["E_inf_vector"] / 8 + for gamma in (affine["gamma_opt"], 1.37): + full, _ = solve_mfs(CENTERS, 0.5, [0, gamma, -gamma], n_boundary=64) + full_profile = full.velocity(profile_points) + region_errors, profile_reconstruction_errors = [], [] + for order in (1, 2, 4, 8): + reduced = reconstruct_multipoles(full, order) + result = common_exterior_error( + full.velocity, reduced.velocity, CENTERS, 0.5, + bounds=(-3, 6, -3, 3), shape=(181, 121), exclusion_factor=1.1) + region_errors.append(result["relative_to_reference_disturbance"]) + reduced_profile = reduced.velocity(profile_points) + delta = reduced_profile - full_profile + profile_reconstruction_errors.append(profile_errors( + 1.0 + delta[:, 0], delta[:, 1], u_inf=1.0)["E_inf_vector"]) + assert region_errors[-1] < region_errors[1] / 50 + assert region_errors[-1] < 5e-5 + assert profile_reconstruction_errors[-1] < profile_reconstruction_errors[1] / 1e6 + assert profile_reconstruction_errors[-1] < 5e-15 + + +@pytest.mark.parametrize("name,expected", [ + ("rear_opposite", [0, 1/np.sqrt(2), -1/np.sqrt(2)]), + ("common_rear", [0, 1/np.sqrt(2), 1/np.sqrt(2)]), + ("front_only", [1, 0, 0]), +]) +def test_stage4_bases_have_frozen_equal_norm(name, expected): + basis = circulation_basis(name) + assert np.allclose(basis, expected) + assert np.isclose(np.linalg.norm(basis), 1.0) + + +def test_stage4_counterfactual_sensitivity_parity_and_ablation(): + y = np.linspace(-3, 3, 1201) + points = np.column_stack((np.full_like(y, 10.0), y)) + sample = np.column_stack((np.linspace(-2, 8, 301), np.linspace(0.03, 2.8, 301))) + rows = {} + for name in ("rear_opposite", "common_rear", "front_only"): + affine = basis_affine(CENTERS, 0.5, name, n_boundary=64) + base = affine["zero"].velocity(points) + direction = affine["unit"].velocity(points)-base + smooth = affine_profile_sensitivity(base, direction) + slopes = one_sided_profile_error_slopes(base, direction, [0.2, 0.1, 0.05, 0.025]) + optimum = affine_velocity(affine, smooth["g_opt"], points) + rows[name] = (affine, smooth, slopes, profile_errors( + optimum[:, 0], optimum[:, 1], u_inf=1)["E_inf_vector"]) + rear, common, front = rows["rear_opposite"], rows["common_rear"], rows["front_only"] + assert abs(rear[0]["dlog"]) < 1e-13 + assert abs(common[0]["dlog"]) > 0.1 and abs(front[0]["dlog"]) > 0.1 + assert rear[0]["dC"].real < 0 and abs(rear[0]["dC"].imag) < 1e-12 + assert rear[1]["dJ_dg_at_zero"] < 0 + assert rear[1]["J_opt"] < min(common[1]["J_opt"], front[1]["J_opt"])/5 + assert rear[3] < min(common[3], front[3])/5 + assert rear[2]["last_change"] < 2e-4 + assert reflection_parity_defect( + lambda p: affine_velocity(rear[0], 1.0, p), sample)["Linf"] < 3e-10 + # Common-rear and front-only are deliberately not symmetric rear-opposite fields. + assert reflection_parity_defect( + lambda p: affine_velocity(common[0], 1.0, p), sample)["Linf"] > 1e-3 + + +def test_stage4_gap_flux_is_oriented_and_converged(): + affine = basis_affine(CENTERS, 0.5, "rear_opposite", n_boundary=64) + velocity = lambda p: affine_velocity(affine, 1.0, p) + upper = gap_flux(velocity, CENTERS[0], CENTERS[1], 0.5, samples=1001) + lower = gap_flux(velocity, CENTERS[0], CENTERS[2], 0.5, samples=1001) + upper_fine = gap_flux(velocity, CENTERS[0], CENTERS[1], 0.5, samples=2001) + assert abs(upper["flux"]-upper_fine["flux"]) < 1e-7 + assert np.isclose(upper["flux"], -lower["flux"], atol=1e-10) + + + +def test_stage5_root_accuracy_jacobian_convergence_and_classification(): + affine = lambda p: np.column_stack((2*p[:, 0] + p[:, 1] - 0.3, + p[:, 0] - 3*p[:, 1] + 0.2)) + exact_jacobian = np.array([[2.0, 1.0], [1.0, -3.0]]) + exact_root = np.linalg.solve(exact_jacobian, np.array([0.3, -0.2])) + errors = [np.linalg.norm(velocity_jacobian(affine, exact_root, step=h)-exact_jacobian) + for h in (1e-3, 3e-4, 1e-4)] + assert max(errors) < 2e-12 + audit = find_interior_stagnation_points( + affine, [[10.0, 10.0]], 0.5, bounds=(-1, 1, -1, 1), seed_shape=(9, 9), + exclusion_margin=0.08, root_tolerance=1e-11) + assert audit["kind"] == "sampled root audit" and len(audit["roots"]) == 1 + root = audit["roots"][0] + assert np.linalg.norm(root["point"]-exact_root) < 2e-11 + assert root["residual"] < 1e-11 and root["nondegenerate"] + assert root["singular_values"][-1] > 1.7 + + +def test_stage5_continuation_and_deliberate_failure_controls(): + base = lambda p: p + shifted = lambda p: p-np.array([0.03, -0.04]) + kwargs = dict(centers=[[10.0, 10.0]], radius=0.5, bounds=(-1, 1, -1, 1), + seed_shape=(9, 9), root_tolerance=1e-11) + a0 = find_interior_stagnation_points(base, **kwargs) + a1 = find_interior_stagnation_points(shifted, **kwargs) + continuation = continue_stagnation_points(a0, a1, maximum_displacement=0.2) + assert not continuation["flagged"] + assert abs(continuation["pairs"][0]["displacement"]-0.05) < 1e-10 + degenerate = lambda p: np.column_stack((p[:, 0], np.zeros(len(p)))) + info = classify_stagnation_root(degenerate, [0.0, 0.0]) + assert info["residual"] == 0 and not info["nondegenerate"] + assert info["singular_values"][-1] == 0 + constant = lambda p: np.column_stack((np.ones(len(p)), np.zeros(len(p)))) + assert not find_interior_stagnation_points(constant, **kwargs)["roots"] + failed = continue_stagnation_points(a0, {"roots": []}) + assert failed["flagged"] and failed["candidate_count"] == 0 + + +def test_stage5_exact_circle_boundary_roots_are_excluded(): + velocity = lambda p: cylinder_velocity(p, [0, 0], 0.5, circulation=0.0) + audit = find_interior_stagnation_points( + velocity, [[0, 0]], 0.5, bounds=(-2, 2, -2, 2), seed_shape=(13, 13), + exclusion_margin=0.08, root_tolerance=1e-10) + assert audit["roots"] == [] + + +def test_stage5_canonical_sampled_audit_and_affine_continuity(): + gamma = rear_opposite_affine(CENTERS, 0.5, n_boundary=64)["gamma_opt"] + solutions = [] + for factor in (0.98, 1.0, 1.02): + solution, diag = solve_mfs( + CENTERS, 0.5, [0, factor*gamma, -factor*gamma], n_boundary=64) + # Broad fail-fast sanity bounds; measured conditioning belongs in diagnostics, + # not in a nearly exact scientific-acceptance envelope. + assert diag["singular_value_min"] > 1e-8 and diag["condition"] < 1e8 + solutions.append(solution) + audit = find_interior_stagnation_points(solution.velocity, CENTERS, 0.5) + assert audit["roots"] == [] + probes = np.array([[-1.5, 1.5], [2.5, 0.0], [4.0, -1.0]]) + vm, v0, vp = [solution.velocity(probes) for solution in solutions] + assert np.max(np.abs((vm+vp)/2-v0)) < 3e-13 + for dx, db in ((-0.02, 0), (0.02, 0), (0, -0.02), (0, 0.02)): + centers = np.array([[0.0, 0.0], [1.3+dx, 0.75+db], + [1.3+dx, -0.75-db]]) + perturbed, _ = solve_mfs( + centers, 0.5, [0, gamma, -gamma], n_boundary=64) + assert find_interior_stagnation_points( + perturbed.velocity, centers, 0.5)["roots"] == [] + + + +def test_bilinear_ccw_vortex_sign_and_mask_gate(): + x=np.linspace(-2,2,401); y=np.linspace(-2,2,401); xx,yy=np.meshgrid(x,y,indexing="xy") + gamma=1.7; r2=xx*xx+yy*yy; r2[200,200]=1.0 + ux=-gamma*yy/(2*np.pi*r2); uy=gamma*xx/(2*np.pi*r2) + ux[200,200]=uy[200,200]=0 + result=ccw_contour_circulation(x,y,ux,uy,[0,0],[0.6,0.9,1.2],samples=1024) + assert np.allclose(result["circulation"],gamma,rtol=3e-4) + negative=ccw_contour_circulation(x,y,-ux,-uy,[0,0],[0.9],samples=512) + assert negative["circulation"][0] < 0 + valid=np.ones_like(ux,dtype=bool); valid[200,290]=False + with pytest.raises(ValueError,match="invalid"): + ccw_contour_circulation(x,y,ux,uy,[0,0],[0.9],samples=512,valid_mask=valid) + + +def test_outer_wls_and_two_point_held_out_closure_recovery(): + yy,xx=np.mgrid[:31,:41]; model=np.stack((np.sin(xx/8)*np.cos(yy/9),np.cos(xx/7)*np.sin(yy/8)),axis=-1) + mask=np.ones(model.shape[:2],dtype=bool); weights=1/(1+xx) + fit=outer_wls_effective_circulation(2.75*model,model,mask,weights=weights) + assert abs(fit["gamma_eff"]-2.75)<1e-13 and fit["weighted_RMS"]<1e-13 + closure=fit_two_point_affine_closure([3.45,3.65],[2.0,3.0]) + assert np.isclose(predict_affine_closure(closure,3.55),2.5) + + +def test_total_model_wls_cannot_omit_blockage_base(): + yy,xx=np.mgrid[:17,:23] + direction=np.stack((np.sin(xx/5),np.cos(yy/4)),axis=-1) + base=np.stack((0.3+0.02*xx,-0.1+0.01*yy),axis=-1) + observed=base-2.4*direction; mask=np.ones(observed.shape[:2],dtype=bool) + corrected=outer_wls_total_model(observed,base,direction,mask) + omitted=outer_wls_effective_circulation(observed,direction,mask) + assert np.isclose(corrected["gamma_eff"],-2.4,atol=1e-13) + assert np.max(np.abs(corrected["prediction"]-observed))<1e-13 + assert abs(omitted["gamma_eff"]+2.4)>1e-3 + + +def test_strip_exact_mode_projection_and_propagation(): + H=3.; y=np.linspace(-H,H,4001); x0=np.zeros_like(y) + v0=strip_mode_field(y,x0,H,[0.7,-0.2],through_flow=0.3) + p0=strip_modal_projection(y,v0,H,modes=4) + assert np.allclose(p0["modes"][:2,2],[0.7,-0.2],atol=2e-7) + assert np.allclose(p0["modes"][:2,3],[0.7,-0.2],atol=2e-7) + dx=1.4; v1=strip_mode_field(y,np.full_like(y,dx),H,[0.7,-0.2],through_flow=0.3) + p1=strip_modal_projection(y,v1,H,modes=4); predicted=propagate_strip_modes(p0,dx) + assert np.allclose(p1["modes"][:2,2:4],predicted["modes"][:2,2:4],atol=3e-7) + assert abs(p1["through_flow_zero_mode"]-0.3)<2e-7 + + +def test_strip_affine_layers_and_ablation_are_strip_native(): + probes=np.array([[7.,-2.],[7.,0.],[7.,2.]]) + fields={} + for layers in (10,20,40): + fields[layers]=strip_basis_affine(CENTERS,0.5,"rear_opposite",H=8,n_boundary=32,image_layers=layers) + assert fields[layers]["zero"].H==8 and fields[layers]["unit"].H==8 + d10=fields[10]["unit"].velocity(probes)-fields[20]["unit"].velocity(probes) + d20=fields[20]["unit"].velocity(probes)-fields[40]["unit"].velocity(probes) + assert np.linalg.norm(d20)={"Q_g","J_g","mass_flux"} + assert case["same_cv_partial_ledger"]["balance_status"]=="endpoint_spatial_partial_not_closed" + assert case["same_cv_partial_ledger"]["residual"] is None + text=(out/"analysis.json").read_text(); json.loads(text) + assert "NaN" not in text and "Infinity" not in text + with pytest.raises(FileExistsError,match="clobber"): analyze_ns_ledger(root,out) + cli_out=tmp_path/"ns-cli" + assert main(["analyze-ns-ledger",str(root),"--out",str(cli_out)])==0 + assert (cli_out/"analysis.json").is_file() + + +def test_ns_ledger_fails_clearly_without_v5_roles_or_with_v4(tmp_path): + import hashlib,json + from steady_pinball_theory.runner import ARRAY_FILE,_canonical_json,_sha256,analyze_ns_ledger + root=tmp_path/"missing"; root.mkdir() + with pytest.raises(FileNotFoundError,match="v5.*v4 torque-free"): + analyze_ns_ledger(root,tmp_path/"out") + _write_synthetic_steady_roles(root) + legacy=root/"accepted-s3.55"; manifest=json.loads((legacy/"manifest.json").read_text()) + manifest["schema"]=manifest["spec"]["schema"]="steady-pinball-endpoint/v4" + manifest["spec"]["history_schema"].pop("torque"); manifest["manifest_payload_sha256"]=hashlib.sha256(_canonical_json({k:v for k,v in manifest.items() if k!="manifest_payload_sha256"})).hexdigest() + (legacy/"manifest.json").write_text(json.dumps(manifest,indent=2,sort_keys=True)+"\n") + with pytest.raises(ValueError,match="torque-capable endpoint schema v5"): + analyze_ns_ledger(root,tmp_path/"out") + + +def test_mechanism_analysis_rejects_unqualified_reverse_s5_2(tmp_path): + from steady_pinball_theory.runner import analyze_steady_contract + root=tmp_path/"campaign"; root.mkdir() + _write_synthetic_steady_roles(root,reverse_5_2_qualified=False) + with pytest.raises(ValueError,match="reverse-s5.2 is not a qualified steady endpoint"): + analyze_steady_contract(root,tmp_path/"analysis") + + +def test_mechanism_analysis_allows_absent_reverse_s3_55_control(tmp_path): + from steady_pinball_theory.runner import analyze_steady_contract + root=tmp_path/"campaign"; root.mkdir() + _write_synthetic_steady_roles(root) + import shutil; shutil.rmtree(root/"reverse-s3.55") + result=analyze_steady_contract(root,tmp_path/"analysis") + assert not result["reverse_s3.55_negative_control"]["present"] + + +def test_residual_quadrature_regions_are_explicit_l2_not_rms(): + x=np.array([0.,1.,2.]); y=np.array([-1.,0.,1.]); weights=tensor_trapezoid_weights(x,y) + field=np.zeros((3,3,2)); field[...,0]=2.; mask=np.ones((3,3),dtype=bool) + result=quadrature_l2(field,mask,weights,normalizer=2*field) + assert np.isclose(result["retained_measure"],4.) + assert np.isclose(result["L2"],4.) and np.isclose(result["normalized_L2"],.5) + with pytest.raises(ValueError,match="retains no"): quadrature_l2(field,np.zeros_like(mask),weights) + with pytest.raises(ValueError,match="zero"): quadrature_l2(field,mask,weights,normalizer=np.zeros_like(field)) + + +def test_conservative_masked_vorticity_and_moments(): + x=np.linspace(-1,1,9); y=np.linspace(-2,2,13); xx,yy=np.meshgrid(x,y,indexing="xy") + ux=-3*yy; uy=2*xx; valid=np.ones_like(xx,dtype=bool); valid[6,4]=False + omega,use=conservative_masked_vorticity(x,y,ux,uy,valid) + assert np.allclose(omega[use],5.) and not use[6,4] + assert not use[6,3] and not use[6,5] and not use[5,4] and not use[7,4] + moments=absolute_vorticity_moments(y,omega,use,tensor_trapezoid_weights(x,y)) + assert abs(moments["y_centroid"])<1e-14 and moments["y_width"]>0 + + +def test_recirculation_and_wake_moment_synthetic_fields(): + x=np.arange(5.); y=np.linspace(-1,1,5); weights=tensor_trapezoid_weights(x,y) + ux=np.ones((5,5)); ux[1:4,1:4]=-1; mask=np.ones_like(ux,dtype=bool) + rec=recirculation_observables(x,ux,mask,weights) + assert rec["x_min"]==1 and rec["x_max"]==3 and rec["streamwise_extent"]==2 and rec["area"]>0 + empty=recirculation_observables(x,np.ones_like(ux),mask,weights) + assert empty["area"]==0 and empty["x_min"] is None + wake=wake_deficit_observables(y,np.array([1,.5,0,.5,1.]),np.ones(5,dtype=bool)) + assert np.isclose(wake["momentum_deficit_proxy"],1.) + assert wake["positive_deficit_measure"]>0 and np.isclose(wake["signed_deficit_integral"],1.) + + +def test_gap_flux_grid_mask_fail_fast_and_parity_sign(): + x=np.linspace(-2,2,81); y=np.linspace(-2,2,81); xx,yy=np.meshgrid(x,y,indexing="xy") + ux=-yy; uy=xx; valid=np.ones_like(ux,dtype=bool) + velocity=lambda p: bilinear_sample_velocity(x,y,ux,uy,p,valid_mask=valid) + upper=gap_flux(velocity,[-1,0],[1,0],.25,samples=401) + assert upper["normal"]==[-0.,1.] and upper["flux"]==pytest.approx(0,abs=1e-14) + valid[40,40]=False + with pytest.raises(ValueError,match="invalid"): + gap_flux(lambda p: bilinear_sample_velocity(x,y,ux,uy,p,valid_mask=valid),[-1,0],[1,0],.25,samples=401) + + +def test_near_wall_helpers_masks_and_fail_closed(): + x=np.arange(0.,21.); y=np.arange(0.,21.) + xx,yy=np.meshgrid(x,y,indexing="xy"); cx,cy,radius=10.,10.,4. + solid=(xx-cx)**2+(yy-cy)**20 + empty=near_wall_tangential_speed(x,y,ux,uy,fluid,body,centers,radius,body_ids=(2,),body_labels=("other",)) + assert empty["bodies"]["other"]["availability"]=="unavailable_no_adjacent_fluid" + proxy=wall_vorticity_production_proxy(x,y,ux,uy,fluid,body,centers,radius,body_ids=(1,),body_labels=("rear",),min_pairs=1000) + assert proxy["bodies"]["rear"]["availability"]=="unavailable_insufficient_radial_stencil" + sep=separation_reattachment_estimator(x,y,np.ones_like(ux),fluid,body,centers,radius,body_ids=(1,),body_labels=("rear",),min_samples=16) + assert sep["bodies"]["rear"]["availability"].startswith("unavailable_") + torque=torque_power_availability(force_history=np.zeros((4,8))) + assert torque["availability"]=="unavailable_no_torque_history" + ledger=control_volume_streamwise_momentum_ledger( + x,y,np.ones_like(ux),np.zeros_like(uy),np.ones_like(ux),fluid,x_left=5.,x_right=15., + force_history=np.column_stack((np.arange(4),np.arange(4),np.ones((4,6))))) + assert ledger["balance_status"]=="incomplete_not_closed" + assert ledger["viscous_stress"]["availability"].startswith("unavailable_") + assert "NEVER" in ledger["claim_limit"] + with pytest.raises(ValueError,match="stations"): + control_volume_streamwise_momentum_ledger(x,y,ux,uy,np.ones_like(ux),fluid,x_left=15.,x_right=5.) + + +def test_analyze_credibility_no_clobber(tmp_path): + from steady_pinball_theory.runner import analyze_credibility, _evidence_root + evidence=_evidence_root() + if not (evidence/"authoritative"/"steady-convergence-20260802"/"grid_summary.json").exists(): + pytest.skip("promoted credibility evidence unavailable") + out=tmp_path/"cred" + result=analyze_credibility(out=out,evidence_root=evidence) + assert result["schema"]=="steady-pinball-credibility-analysis/v1" + assert result["classification"]["mechanism"]=="NOT_CLAIMED" + assert result["classification"]["numerical_observation"] in ("PASS","BOUNDED") + assert any(item["name"]=="outlet_boundary_sensitivity" and item["status"]=="BOUNDED" + for item in result["missing_or_bounded_tests"]) + with pytest.raises(FileExistsError): + analyze_credibility(out=out,evidence_root=evidence) + + +def test_near_wall_and_fail_closed_separation_proxy(): + x=np.arange(21.); y=np.arange(21.); xx,yy=np.meshgrid(x,y,indexing="xy") + centers=np.array([[0.,0.],[10.,10.]]); body=np.full((21,21),-1,dtype=np.int16) + solid=(xx-10)**2+(yy-10)**2<=4; body[solid]=1; fluid=~solid + ux=-(yy-10); uy=xx-10 # geometric CCW solid-body-like field + near=near_wall_tangential_speed(x,y,ux,uy,fluid,body,centers,2.0,body_ids=(1,),body_labels=("rear",)) + assert near["bodies"]["rear"]["availability"]=="available" + assert near["bodies"]["rear"]["points"]>0 + sep=separation_reattachment_estimator(x,y,np.ones_like(ux),fluid,body,centers,2.0,body_ids=(1,),body_labels=("rear",)) + assert sep["bodies"]["rear"]["availability"].startswith("unavailable") + vort=wall_vorticity_production_proxy(x,y,ux,uy,fluid,body,centers,2.0,body_ids=(1,),body_labels=("rear",),min_pairs=4) + assert vort["bodies"]["rear"]["availability"] in ("available","unavailable_insufficient_radial_stencil") + + +def test_control_volume_ledger_incomplete_and_torque_unavailable(): + x=np.linspace(0,10,21); y=np.linspace(-2,2,17) + xx,yy=np.meshgrid(x,y,indexing="xy"); ux=np.ones_like(xx); uy=np.zeros_like(xx); rho=np.ones_like(xx) + fluid=np.ones_like(xx,dtype=bool); forces=np.zeros((12,8)); forces[:,2]=0.1; forces[:,4]=0.2; forces[:,6]=0.3 + ledger=control_volume_streamwise_momentum_ledger(x,y,ux,uy,rho,fluid,x_left=1.0,x_right=9.0,force_history=forces,viscosity=0.01) + assert ledger["balance_status"]=="incomplete_not_closed" + assert ledger["viscous_stress"]["availability"].startswith("unavailable") + assert ledger["body_force"]["availability"].startswith("available") + torque=torque_power_availability(forces) + assert torque["availability"]=="unavailable_no_torque_history" + + +def test_transpiration_neumann_zero_mean_and_branch_sign(): + from steady_pinball_theory.theory import (composite_model_fields, + displacement_transpiration_rhs, gap_couette_poiseuille_section, + solve_mfs, solve_mfs_neumann) + centers = np.array([[0., 0.], [1.3, 0.75], [1.3, -0.75]]) + radius = 0.5 + zero, _ = solve_mfs(centers, radius, np.zeros(3), u_inf=1.0, H=15, n_boundary=32, image_layers=20) + rhs = displacement_transpiration_rhs( + centers, radius, np.array([0., 3.45, -3.45]), zero.velocity, + n_boundary=32, delta_star_scale=0.05) + for ib in range(3): + sl = rhs["body_index"] == ib + assert abs(float(np.mean(rhs["v_n"][sl]))) < 1e-12 + _, diag = solve_mfs_neumann( + centers, radius, rhs["v_n"], circulations=np.zeros(3), u_inf=1.0, + H=15, n_boundary=32, image_layers=20) + assert diag["collocation_Linf"] < 0.05 + cp = gap_couette_poiseuille_section(0.5, 1.0, -1.0) + assert cp["Q_g"] == 0.0 + assert cp["J_g"] > 0 + acc = composite_model_fields( + np.array([[2.0, 0.0], [4.0, 0.0]]), centers=centers, radius=radius, + omega=3.45, branch="plus-minus") + rev = composite_model_fields( + np.array([[2.0, 0.0], [4.0, 0.0]]), centers=centers, radius=radius, + omega=5.2, branch="minus-plus") + assert acc["gaps"]["rear_rear"]["Q_g"] * rev["gaps"]["rear_rear"]["Q_g"] < 0 + + +def test_composite_fit_and_zero_rotation_limit(): + from steady_pinball_theory.metrics import fit_linear_composite, held_out_improvement + from steady_pinball_theory.theory import composite_model_fields + centers = np.array([[0., 0.], [1.3, 0.75], [1.3, -0.75]]) + obs = np.zeros((5, 5, 2)) + base = np.ones_like(obs) * np.array([0.1, 0.0]) + comp = base + np.array([0.02, 0.01]) + m = np.ones(obs.shape[:2], dtype=bool) + fit = fit_linear_composite(comp, [("base", base), ("extra", comp - base)], m) + assert fit["coefficients"]["base"] == pytest.approx(1.0, abs=1e-10) + assert fit["coefficients"]["extra"] == pytest.approx(1.0, abs=1e-10) + zero = composite_model_fields( + np.array([[3.0, 0.0]]), centers=centers, radius=0.5, omega=0.0, + branch="plus-minus", coeffs={"alpha_vi": 1.0, "alpha_gap": 1.0, "wake_amplitude": 0.0}) + assert np.linalg.norm(zero["q_vi"]) < 1e-12 + assert np.linalg.norm(zero["q_gap"]) < 1e-12 + imp = held_out_improvement(base, np.zeros_like(base), m) + assert imp["relative_improvement"] > 0 + + +# NS-first CPU primitives: localized analytic/manufactured tests. +def test_ns_torque_power_sign_ownership_cp_and_zero_limit(): + omega=np.array([[2.,-3.],[2.,-3.]]) + fluid_tau=np.array([[-4.,6.],[-4.,6.]]) + result=torque_to_actuator_power(fluid_tau,omega,torque_ownership="fluid_on_body",rho_ref=2.,u_ref=2.,diameter=.5) + assert np.allclose(result["actuator_torque"],-fluid_tau) + assert np.allclose(result["total_power"],[26.,26.]) + assert result["C_P"]==pytest.approx(6.5) # scale=.5*rho*U^3*D=4 + direct=torque_to_actuator_power(-fluid_tau,omega,torque_ownership="actuator_on_fluid",rho_ref=2.,u_ref=2.,diameter=.5) + assert direct["C_P"]==result["C_P"] + zero=torque_to_actuator_power(fluid_tau,np.zeros_like(omega),torque_ownership="fluid_on_body",rho_ref=2.,u_ref=2.,diameter=.5) + assert zero["C_P"]==0 + with pytest.raises(ValueError,match="ownership"): torque_to_actuator_power([1.],[1.],torque_ownership="ambiguous",rho_ref=1,u_ref=1,diameter=1) + + +def test_ns_station_flux_dimensions_matched_qin_and_normal_sign(): + y=np.linspace(-1,1,101); mask=np.ones_like(y,dtype=bool); rho=np.full_like(y,2.); p=np.full_like(y,3.) + qin=station_flux_metrics(y,np.ones_like(y),np.zeros_like(y),rho,p,mask) + assert qin["mass_flux"]==pytest.approx(4.) + assert np.allclose(qin["momentum_flux"],[10.,0.]) + assert qin["kinetic_energy_flux"]==pytest.approx(2.) + assert qin["mechanical_energy_flux"]==pytest.approx(8.) + matched=station_flux_metrics(y,np.ones_like(y),np.zeros_like(y),rho,p,mask,q_in=qin) + assert np.allclose(matched["delta_from_q_in"]["momentum_flux"],0) + reversed_face=station_flux_metrics(y,np.ones_like(y),np.zeros_like(y),rho,p,mask,normal=(-1.,0.)) + assert reversed_face["mass_flux"]==-qin["mass_flux"] and reversed_face["mechanical_energy_flux"]==-qin["mechanical_energy_flux"] + with pytest.raises(ValueError,match="same frozen normal"): station_flux_metrics(y,np.ones_like(y),np.zeros_like(y),rho,p,mask,normal=(-1.,0.),q_in=qin) + + +def test_ns_masked_volume_dissipation_manufactured_strain_and_zero(): + x=np.linspace(-2,2,81); y=np.linspace(-1,1,61); xx,yy=np.meshgrid(x,y,indexing="xy"); mask=np.ones_like(xx,dtype=bool) + # u=(a*x,-a*y): div u=0, 2*S:S=4*a^2. + a=.7; result=volume_viscous_dissipation(x,y,a*xx,-a*yy,.3,mask) + expected=.3*4*a*a*result["retained_area"] + assert result["viscous_dissipation"]==pytest.approx(expected,rel=2e-14) + zero=volume_viscous_dissipation(x,y,np.ones_like(xx),np.zeros_like(xx),.3,mask) + assert zero["viscous_dissipation"]==pytest.approx(0.,abs=1e-15) + holed=mask.copy(); holed[30,40]=False + assert not volume_viscous_dissipation(x,y,a*xx,-a*yy,.3,holed)["usable_mask"][30,41] + + +def test_ns_gap_qg_jg_density_orientation_and_sign(): + velocity=lambda p: np.tile([0.,2.],(len(p),1)); density=lambda p: np.full(len(p),3.) + gap=gap_mass_momentum_flux(velocity,density,[0.,0.],[2.,0.],.5,samples=101) + assert gap["normal"]==[-0.,1.] and gap["Q_g"]==pytest.approx(2.) + assert gap["mass_flux"]==pytest.approx(6.) and gap["J_g"]==pytest.approx(12.) + reverse=gap_mass_momentum_flux(velocity,density,[2.,0.],[0.,0.],.5,samples=101) + assert reverse["Q_g"]==-gap["Q_g"] and reverse["mass_flux"]==-gap["mass_flux"] + assert reverse["J_g"]==gap["J_g"] + + +def test_ns_mechanical_energy_ledger_never_false_closes_and_manufactured_balance(): + left={"mechanical_energy_flux":10.}; right={"mechanical_energy_flux":7.} + incomplete=control_volume_mechanical_energy_ledger(left,right,viscous_dissipation=2.,actuator_power_to_fluid=1.) + assert not incomplete["closure_available"] and incomplete["residual"] is None + balanced=control_volume_mechanical_energy_ledger(left,right,viscous_dissipation=2.,actuator_power_to_fluid=1.,lateral_mechanical_energy_flux=2.,storage_rate=0.) + assert balanced["closure_available"] and balanced["residual"]==pytest.approx(0.) + unbalanced=control_volume_mechanical_energy_ledger(left,right,viscous_dissipation=2.,actuator_power_to_fluid=0.,lateral_mechanical_energy_flux=2.,storage_rate=0.) + assert unbalanced["residual"]==pytest.approx(1.) + + +def test_ns_low_dimensional_conservation_fit_dimensions_uncertainty_and_holdout(): + x=np.linspace(-2,2,12); X=np.column_stack((np.ones_like(x),x)); y=3.+2*x + fit=fit_conservation_model(X[:9],y[:9],feature_names=["source","flux"],feature_dimensions=["P","P"],target_dimension="P",feature_scales=[1.,2.],target_scale=4.,held_out=(X[9:],y[9:])) + assert np.allclose(fit["coefficients"],[3.,2.],atol=1e-13) + assert fit["rank"]==2 and np.isfinite(fit["condition_number"]) and fit["uncertainty_available"] + assert fit["held_out"]["RMS"]<1e-13 + assert np.allclose(predict_conservation_model(fit,X[9:],feature_names=["source","flux"],feature_dimensions=["P","P"]),y[9:]) + with pytest.raises(ValueError,match="dimensions do not match"): predict_conservation_model(fit,X[9:],feature_names=["source","flux"],feature_dimensions=["P","velocity"]) + with pytest.raises(ValueError,match="dimensions mismatch"): fit_conservation_model(X,y[:,None],feature_names=["a","b"],feature_dimensions=["P","P"],target_dimension="P",feature_scales=[1,1],target_scale=1) + + + +def test_stage45_causal_switch_contract_and_analysis(tmp_path): + from steady_pinball_theory.runner import (SWITCH_TELEMETRY_CHANNELS, + analyze_paired_causal_switch, causal_switch_contract) + parent=tmp_path/"accepted.chk"; parent.write_bytes(b"accepted-parent") + contract=causal_switch_contract(parent,bootstrap_samples=100,seed=4) + assert set(contract["branches"])=={"continue-accepted","zero","equal-amplitude-reverse"} + assert np.allclose(contract["branches"]["equal-amplitude-reverse"]["action_omega"],[0.,-.00355,.00355]) + assert np.allclose(contract["branches"]["continue-accepted"]["wall_oracle"]["action"],[0.,.00355,-.00355]) + nrep,nt,nc=4,7,len(SWITCH_TELEMETRY_CHANNELS); clock=np.zeros((nrep,nt,2)); clock[:,:,0]=np.arange(nt); clock[:,:,1]=np.arange(nt)*.1 + base=np.ones((nrep,nt,nc)); zero=base.copy(); reverse=base.copy(); zero[:,3:,:]+=.1; reverse[:,2:,:]+=.2 + telemetry={"continue-accepted":np.concatenate((clock,base),axis=2),"zero":np.concatenate((clock,zero),axis=2),"equal-amplitude-reverse":np.concatenate((clock,reverse),axis=2)} + out=tmp_path/"analysis"; result=analyze_paired_causal_switch(contract,telemetry,out=out) + assert result["classification"]=="PASS" and all(g["pass"] for g in result["gates"].values()) + assert result["onset"]["ordering"][0]["reverse_minus_zero_onset"]==pytest.approx(-.1) + assert result["gates"]["replication"]["pass"] and result["gates"]["local_before_downstream"]["pass"] + assert "cross-correlation alone" in result["claim_boundary"] + one={key:value[:1] for key,value in telemetry.items()} + bounded=analyze_paired_causal_switch(contract,one) + assert bounded["classification"]=="BOUNDED" and not bounded["gates"]["replication"]["pass"] + with pytest.raises(FileExistsError): analyze_paired_causal_switch(contract,telemetry,out=out) + telemetry["zero"]=telemetry["zero"].copy(); telemetry["zero"][0,2,1]+=.01 + with pytest.raises(ValueError,match="synchronized"): analyze_paired_causal_switch(contract,telemetry) + + +def test_stage45_nonlinear_return_classification(): + from steady_pinball_theory.runner import analyze_nonlinear_return + t=np.arange(5.); stable=np.array([.2,.12,.06,.03,.01]); bounded=np.array([.2,.25,.24,.22,.2]) + result=analyze_nonlinear_return(t,{"symmetric":{.01:stable,.02:stable*.8},"antisymmetric":{.01:bounded,.02:bounded*.8}}) + assert result["classification"]=="bounded" + assert all(x["classification"]=="stable" for x in result["families"]["symmetric"]) + unstable=analyze_nonlinear_return(t,{"symmetric":{.01:stable},"antisymmetric":{.01:[.2,.3,.6,1.1,1.3]}}) + assert unstable["classification"]=="unstable" and unstable["families"]["antisymmetric"][0]["branch_switching"] + + +def test_stage45_matrix_free_arnoldi_convergence_and_fail_closed(): + from steady_pinball_theory.runner import matrix_free_arnoldi + diagonal=np.diag([.9,.6,.3,.1]) + good=matrix_free_arnoldi(lambda v,eps:diagonal@v,4,epsilons=(1e-2,1e-4),krylov_dimensions=(3,4),eigen_tolerance=.1) + assert good["convergence"]["passed"] and good["global_stability"]=="AVAILABLE_FEASIBILITY_ONLY" + assert good["runs"][-1]["spectral_radius"]==pytest.approx(.9) + bad=matrix_free_arnoldi(lambda v,eps:(diagonal+eps*np.eye(4))@v,4,epsilons=(.2,.01),krylov_dimensions=(2,4),eigen_tolerance=1e-6) + assert not bad["convergence"]["passed"] + assert bad["global_stability"]=="UNAVAILABLE_CONVERGENCE_GATES_FAILED" + + +def test_legacy_force_only_requires_explicit_loader(tmp_path): + import hashlib,json + from steady_pinball_theory.runner import (ARRAY_FILE, SCHEMA, _canonical_json, _sha256, + load_legacy_force_artifact, load_validate_artifact) + spec,arrays=_synthetic_artifact_inputs("stationary") + spec=json.loads(json.dumps(spec)); spec["schema"]="steady-pinball-endpoint/v4"; spec["history_schema"].pop("torque") + arrays=dict(arrays); arrays.pop("torque_history"); out=tmp_path/"legacy"; out.mkdir() + np.savez_compressed(out/ARRAY_FILE,**arrays) + manifest={"schema":spec["schema"],"immutable":True,"spec":spec,"result":{}, + "files":{ARRAY_FILE:{"sha256":_sha256(out/ARRAY_FILE),"bytes":(out/ARRAY_FILE).stat().st_size}}} + manifest["manifest_payload_sha256"]=hashlib.sha256(_canonical_json(manifest)).hexdigest() + (out/"manifest.json").write_text(json.dumps(manifest,indent=2,sort_keys=True)+"\n") + with pytest.raises(ValueError,match="v5"): load_validate_artifact(out) + loaded,legacy=load_legacy_force_artifact(out) + assert loaded["schema"].endswith("/v4") and "torque_history" not in legacy and SCHEMA.endswith("/v5") + + +def test_production_guards_gpu_root_lease_cooldown_and_no_clobber(tmp_path): + import json + from steady_pinball_theory.runner import (_assert_cfd_environment, enforce_launch_cooldown, + exclusive_cfd_lease, run_case) + root=tmp_path/"CelerisLab"; root.mkdir() + env={"CONDA_DEFAULT_ENV":"pycuda_3_10","CUDA_VISIBLE_DEVICES":"3"} + assert _assert_cfd_environment(intended_celeris_root=root,env=env)==("3",root.resolve()) + for visible in (None,"","0,1"): + bad=dict(env) + if visible is None: bad.pop("CUDA_VISIBLE_DEVICES") + else: bad["CUDA_VISIBLE_DEVICES"]=visible + with pytest.raises(RuntimeError,match="exactly one GPU"): + _assert_cfd_environment(intended_celeris_root=root,env=bad) + with pytest.raises(RuntimeError,match="explicit intended"): + _assert_cfd_environment(intended_celeris_root=None,env=env) + lease=tmp_path/"lease" + with exclusive_cfd_lease(lease,role="test"): + with pytest.raises(RuntimeError,match="already exists"): + with exclusive_cfd_lease(lease,role="other"): pass + assert not lease.exists() + cooldown=tmp_path/"cooldown"; slept=[]; clock=iter([100.,110.,130.]) + assert enforce_launch_cooldown(cooldown,delay_seconds=30,monotonic=lambda:next(clock),sleep=slept.append)==0 + assert enforce_launch_cooldown(cooldown,delay_seconds=30,monotonic=lambda:next(clock),sleep=slept.append)==20 + assert slept[-1]==20 + with pytest.raises(ValueError,match="30"): enforce_launch_cooldown(cooldown,delay_seconds=29) + existing=tmp_path/"existing"; existing.mkdir() + with pytest.raises(FileExistsError,match="clobber"): + run_case(existing,kind="qin",intended_celeris_root=root) + + +def test_celeris_source_identity_is_root_bound_and_hashes_configs(tmp_path): + from types import SimpleNamespace + from steady_pinball_theory.runner import _source_identity + root=tmp_path/"CelerisLab"; package=root/"src/CelerisLab"; configs=package/"lbm/kernels/config" + configs.mkdir(parents=True); (package/"__init__.py").write_text('__version__="test"\n') + (package/"simulation.py").write_text("# simulation\n"); (configs/"config_obs.h").write_text("#define OBS 1\n") + identity=_source_identity(celeris_module=SimpleNamespace(__file__=str(package/"__init__.py"),__version__="test"),intended_celeris_root=root) + assert identity["celeris_import_file"]==str((package/"__init__.py").resolve()) + assert identity["celeris_import_root"]==str(root.resolve()) and identity["celeris_version"]=="test" + assert "src/CelerisLab/lbm/kernels/config/config_obs.h" in identity["celeris_source_hashes"] + outside=tmp_path/"outside.py"; outside.write_text("# outside\n") + with pytest.raises(RuntimeError,match="outside intended root"): + _source_identity(celeris_module=SimpleNamespace(__file__=str(outside),__version__="x"),intended_celeris_root=root) + + + +def test_atomic_campaign_hides_partial_roles_and_no_clobber(tmp_path): + from steady_pinball_theory.runner import _atomic_campaign + out=tmp_path/"campaign"; seen=[] + def fail(stage,role): + (stage/role).mkdir(); seen.append(role) + if role=="second": raise RuntimeError("role failed") + with pytest.raises(RuntimeError,match="role failed"): + _atomic_campaign(out,("first","second","third"),fail) + assert seen==["first","second"] and not out.exists() + assert not list(tmp_path.glob(".campaign.tmp-*")) + _atomic_campaign(out,("only",),lambda stage,role:(stage/role).mkdir()) + assert (out/"only").is_dir() + with pytest.raises(FileExistsError,match="clobber"): + _atomic_campaign(out,("again",),lambda stage,role:None) + + +def test_fake_parent_restore_precedes_actions_and_is_fresh(tmp_path): + from types import SimpleNamespace + from steady_pinball_theory.runner import _new_parent_simulation, _set_exact_action, _sha256 + checkpoint=tmp_path/"parent.chk"; checkpoint.write_bytes(b"exact-parent") + record={"checkpoint":{"sha256":_sha256(checkpoint)},"config_lbm":{"grid":{"nx":20,"ny":12}}, + "centers_xy":[[4.,6.],[7.,8.],[7.,4.]],"radius":1.,"action_omega":[0.,.2,-.2]} + instances=[] + class FakeSimulation: + def __init__(self,**kwargs): + self.events=[]; self.bodies=SimpleNamespace(count=3,objects=[SimpleNamespace(obj_id=i,center=[*c]) for i,c in enumerate(record["centers_xy"])]); instances.append(self) + def initialize(self): self.events.append("initialize") + def load_checkpoint(self,path): self.events.append(("restore",Path(path).read_bytes())) + def set_body(self,i,omega): self.events.append(("action",i,omega)) + def close(self): self.events.append("close") + actions=([0.,.2,-.2],[0.,0.,0.],[0.,-.2,.2]) + for action in actions: + sim=_new_parent_simulation(record,checkpoint,FakeSimulation); _set_exact_action(sim,action); sim.close() + assert len({id(x) for x in instances})==3 + for sim,action in zip(instances,actions): + assert sim.events[:2]==["initialize",("restore",b"exact-parent")] + assert sim.events[2:5]==[("action",i,float(w)) for i,w in enumerate(action)] + + +def test_parent_restore_and_spatial_capture_fail_closed(tmp_path): + from types import SimpleNamespace + from steady_pinball_theory.runner import _capture_branch_row, _new_parent_simulation, _sha256 + checkpoint=tmp_path/"parent.chk"; checkpoint.write_bytes(b"p") + record={"checkpoint":{"sha256":_sha256(checkpoint)},"config_lbm":{"grid":{"nx":20,"ny":12}}, + "centers_xy":[[4.,6.],[7.,8.],[7.,4.]],"radius":1.,"action_omega":[0.,.2,-.2]} + class NoRestore: + def __init__(self,**kwargs): self.bodies=SimpleNamespace(count=3,objects=[]) + def initialize(self): pass + def close(self): pass + with pytest.raises(RuntimeError,match="load_checkpoint"): + _new_parent_simulation(record,checkpoint,NoRestore) + class NoFields: + def get_macroscopic(self): return {"ux":np.zeros(1),"uy":np.zeros(1),"rho":np.ones(1)} + with pytest.raises(ValueError,match="ux size"): + _capture_branch_row(NoFields(),record,[0,.2,-.2],1,1.) + + +def test_stability_amplitude_gate_precedes_simulation(tmp_path,monkeypatch): + import steady_pinball_theory.runner as runner + root=tmp_path/"CelerisLab"; root.mkdir() + monkeypatch.setattr(runner,"_assert_cfd_environment",lambda **kwargs:("0",root)) + monkeypatch.setattr(runner,"_load_accepted_parent",lambda parent:({"source_environment":{"celeris_intended_root":str(root.resolve())}},None,None,None)) + with pytest.raises(ValueError,match="two distinct positive amplitudes"): + runner.acquire_stability(tmp_path/"out",parent=tmp_path/"parent",intended_celeris_root=root,amplitudes=[.01,.01],simulation_factory=lambda **kwargs:None) + + +def test_online_branch_capture_uses_validated_gap_exclusion_contract(): + import inspect + from steady_pinball_theory.runner import _capture_branch_row + source=inspect.getsource(_capture_branch_row) + assert "exclusion_radius=1.1*radius" in source + assert "samples=1001" in source + + +def test_single_clock_three_body_power_is_scalar_total(): + tau_fluid_on_body=np.array([0.,-.02,.02]); omega=np.array([0.,.0035,-.0035]) + record=torque_to_actuator_power(tau_fluid_on_body[None,:],omega[None,:],torque_ownership="fluid_on_body",rho_ref=1.,u_ref=.01,diameter=20.) + assert np.asarray(record["total_power"]).shape==(1,) + assert float(record["total_power"][0])==pytest.approx(.00014) + assert record["sampling_semantics"]["normalize_true"].endswith("exactly once") + + +# Stage-1 lattice/project nondimensionalization contract. +def test_stage1_all_nondimensional_scales_and_zero_limits(): + c=NondimensionalContract(diameter=4.,u_inf=2.,rho_ref=3.) + out=c.convert(x=8.,t=6.,nu=16.,omega=1.,Q=24.,J=144., + force=48.,torque=192.,power=96.) + assert out["x_star"]==2. and out["t_star"]==3. + assert out["nu_star"]==2. and out["omega_star"]==2. + assert out["Q_star"]==3. and out["J_star"]==3. + assert out["C_F"]==2. and out["C_tau"]==2. and out["C_P"]==2. + zero=c.convert(x=0.,t=0.,nu=0.,omega=0.,Q=0.,J=0.,force=0.,torque=0.,power=0.) + assert all(zero[key]==0. for key in ("x_star","t_star","nu_star","omega_star","Q_star","J_star","C_F","C_tau","C_P")) + assert out["metadata"]["scope"]=="two-dimensional per-unit-span" + + +def test_stage1_reference_rescaling_invariance(): + D,U,rho=3.,2.,5.; a=7. + physical=dict(x=1.2*D,t=.8*D/U,nu=.03*U*D,omega=.4*U/D,Q=.6*U*D, + J=.7*rho*U**2*D,force=.8*.5*rho*U**2*D, + torque=.9*.5*rho*U**2*D**2,power=1.1*.5*rho*U**3*D) + base=NondimensionalContract(D,U,rho).convert(**physical) + D2,U2,rho2=a*D,U/a,2*rho + scaled=dict(x=1.2*D2,t=.8*D2/U2,nu=.03*U2*D2,omega=.4*U2/D2,Q=.6*U2*D2, + J=.7*rho2*U2**2*D2,force=.8*.5*rho2*U2**2*D2, + torque=.9*.5*rho2*U2**2*D2**2,power=1.1*.5*rho2*U2**3*D2) + other=NondimensionalContract(D2,U2,rho2).convert(**scaled) + for key in ("x_star","t_star","nu_star","omega_star","Q_star","J_star","C_F","C_tau","C_P"): + assert other[key]==pytest.approx(base[key]) + + +@pytest.mark.parametrize("refs",[(0,1,1),(1,0,1),(1,1,0),(-1,1,1),(np.nan,1,1)]) +def test_stage1_invalid_references_fail(refs): + with pytest.raises(ValueError,match="finite positive"): + NondimensionalContract(*refs) + + +def test_stage1_one_cylinder_power_identity_and_raw_semantics(): + rho,U,D,s=3.,2.,4.,.7 + tau_scale=.5*rho*U**2*D**2 + fluid_tau=np.array([[1.25*tau_scale]]) + omega=np.array([[2*s*U/D]]) + result=torque_to_actuator_power(fluid_tau,omega,torque_ownership="fluid_on_body",rho_ref=rho,u_ref=U,diameter=D) + assert result["raw_C_tau"][0,0]==pytest.approx(1.25) + assert result["C_P"]==pytest.approx(-2*s*1.25) + assert result["raw_torque_interpretation"].startswith("fluid_on_body") + assert "dynamic pressure" in result["sampling_semantics"]["normalizations_not_applied"] + + +def test_stage1_schema_freezes_single_time_average_only(): + from steady_pinball_theory.runner import case_spec + spec=case_spec("accepted",3.55) + semantics=spec["celeris_read_semantics"] + assert semantics["normalize_true"]=="mean per accumulated LBM step only; do not divide by stride again" + assert spec["history_schema"]["torque"]["ownership"]=="actuator_on_fluid" + assert "dynamic-pressure normalization" in semantics["not_applied"] + + +def test_gap_pressure_gradient_requires_explicit_positive_nu(): + from steady_pinball_theory.theory import gap_couette_poiseuille_section + with pytest.raises(ValueError,match="nonzero dp_dx requires"): + gap_couette_poiseuille_section(.5,1.,-1.,dp_dx=.2) + with pytest.raises(ValueError,match="finite and positive"): + gap_couette_poiseuille_section(.5,1.,-1.,dp_dx=.2,nu=0.) + resolved=gap_couette_poiseuille_section(.5,1.,-1.,dp_dx=.2,nu=.1) + assert np.isfinite(list(resolved.values())).all() + + +# Stage-2 same-control-volume endpoint ledger primitives. +def _stage2_cv_fields(): + x=np.arange(-4.,14.1,.25); y=np.arange(-5.,5.1,.25); xx,yy=np.meshgrid(x,y,indexing="xy") + fluid=np.ones_like(xx,dtype=bool); rho=1.+.03*xx + return x,y,xx,yy,fluid,rho + + +def test_stage2_pressure_proxy_gauge_and_not_zero_unavailable_semantics(): + rho=np.array([.9,1.,1.2]); proxy=weak_compressible_pressure_proxy(rho,rho_ref=1.) + assert np.allclose(proxy["values"],[-.1/3,0.,.2/3]) + assert proxy["availability"]=="available_weak_compressible_proxy" + assert "never unavailable" in proxy["claim_limit"] + shifted=weak_compressible_pressure_proxy(rho+.4,rho_ref=1.4) + assert np.allclose(shifted["values"],proxy["values"]) + + +def test_stage2_body_enclosing_cv_uniform_flow_faces_and_actual_bounds(): + x,y,xx,yy,fluid,rho=_stage2_cv_fields(); ux=np.ones_like(xx)*2.; uy=np.zeros_like(xx) + result=rectangular_control_volume_fluxes(x,y,ux,uy,np.ones_like(rho),fluid,[0.,0.],1.,rho_ref=1.) + assert set(result["faces"])=={"left","right","bottom","top"} + assert result["faces"]["left"]["normal"]==[-1.,0.] and result["faces"]["top"]["normal"]==[0.,1.] + assert result["bounds"]["actual_front_center_relative"]["x_over_D"]==[-2.,10.] + assert result["bounds"]["actual_front_center_relative"]["y_over_D"]==[-3.,3.] + assert result["outward_totals"]["mass_flux"]==pytest.approx(0.,abs=1e-12) + assert result["pressure"]["availability"]=="available_weak_compressible_proxy" + + +def test_stage2_linear_flow_viscous_traction_work_and_invalid_face_fail_closed(): + x,y,xx,yy,fluid,rho=_stage2_cv_fields(); ux=.2*xx+.3*yy+1.; uy=-.2*yy+.1*xx + result=rectangular_control_volume_fluxes(x,y,ux,uy,np.ones_like(rho),fluid,[0.,0.],1.,rho_ref=1.,viscosity=.4) + assert result["viscous_terms"]["availability"]=="available_centered_fluid_stencils" + assert np.isfinite(result["outward_totals"]["viscous_work"]) + invalid=fluid.copy(); invalid[np.argmin(abs(y)),np.argmin(abs(x+2))]=False + with pytest.raises(ValueError,match="left face contains nonfluid"): + rectangular_control_volume_fluxes(x,y,ux,uy,rho,invalid,[0.,0.],1.,rho_ref=1.,viscosity=.4) + unsupported=fluid.copy(); unsupported[np.argmin(abs(y)),np.argmin(abs(x+1.75))]=False + with pytest.raises(ValueError,match="unsupported velocity gradients"): + rectangular_control_volume_fluxes(x,y,ux,uy,rho,unsupported,[0.,0.],1.,rho_ref=1.,viscosity=.4) + + +def test_stage2_cv_dissipation_reports_body_stencil_omission(): + x,y,xx,yy,fluid,_=_stage2_cv_fields(); cv=(xx>=-2)&(xx<=10)&(yy>=-3)&(yy<=3) + body=(xx-1.)**2+yy**2<.7**2; cv_fluid=cv&~body + result=volume_viscous_dissipation(x,y,.4*xx,-.4*yy,.2,cv_fluid) + assert 00 + assert result["near_body_omission"].startswith("partial") + assert result["balance_status"]=="partial_not_closed_energy" + + +def test_stage2_gap_dimensionless_contract_keeps_orientations_separate(): + c=NondimensionalContract(2.,4.,3.) + upper=c.convert(Q=8.,J=192.,mass_flux=48.) + lower=c.convert(Q=-8.,J=192.,mass_flux=-48.) + assert upper["Q_star"]==1. and lower["Q_star"]==-1. + assert upper["J_star"]==lower["J_star"]==2. + assert upper["mass_flux_star"]==2. and lower["mass_flux_star"]==-2. + + +# Stage-3 transient v2 manufactured and provenance tests. +def test_stage3_common_mask_norms_grid_independent_and_branch_order(): + from steady_pinball_theory.metrics import common_mask_field_norms, branch_order + values=[] + for n in (21,41,81): + x=np.linspace(0,2,n); y=np.linspace(-1,1,n); ref=np.zeros((n,n,2)); cand=np.zeros_like(ref); cand[...,0]=2.; mask=np.ones((n,n),bool) + values.append(common_mask_field_norms(x,y,ref,cand,mask,contract=NondimensionalContract(2.,2.,1.))) + assert np.allclose([v["L2_star"] for v in values],1.) + assert np.allclose([v["Linf_star"] for v in values],1.) + order=branch_order([3.,1.,1.01],[1.,1.,1.],margin=.05,hysteresis=.02) + assert order["state"].tolist()==[1,1,1] + with pytest.raises(ValueError,match="undefined"): branch_order([0.],[0.]) + + +def test_stage3_onset_spikes_equality_and_strict_intervals(): + from steady_pinball_theory.runner import onset_interval, _interval_order + t=np.arange(7.); baseline=np.zeros(7) + spike=onset_interval(t,[0,0,2,0,0,0,0],baseline,noise_window=2,explicit_floor=1.,consecutive=3) + assert spike["status"].startswith("UNRESOLVED") + equality=onset_interval(t,[0,0,1,1,1,1,1],baseline,noise_window=2,explicit_floor=1.,consecutive=3) + assert equality["interval"] is None + sustained=onset_interval(t,[0,0,2,2,2,2,2],baseline,noise_window=2,explicit_floor=1.,consecutive=3) + assert sustained["interval"]==[1.,2.] + assert _interval_order(sustained,{"interval":[2.,3.]})=="UNRESOLVED_EQUAL_OR_OVERLAP" + assert _interval_order(sustained,{"interval":[3.,4.]})=="FIRST_STRICTLY_BEFORE" + + +def _stage3_arrays(n=5): + from steady_pinball_theory.runner import TRANSIENT_ARRAY_SCHEMAS + arrays={name:np.zeros((n,schema["tail"][0]),float) for name,schema in TRANSIENT_ARRAY_SCHEMAS.items()} + arrays["clock"][:,0]=np.arange(n); arrays["clock"][:,1]=np.arange(n)*.1 + arrays["action_omega"][:,1]=.2; arrays["action_omega"][:,2]=-.2 + arrays["torque_body"][:,1]=.3; arrays["torque_body"][:,2]=-.3 + arrays["power_body"]=arrays["torque_body"]*arrays["action_omega"] + arrays["field_L2_star"][:,0]=np.linspace(1,.1,n); arrays["field_Linf_star"][:,0]=np.linspace(1,.2,n) + arrays["distance_accepted_L2_star"][:,0]=.2; arrays["distance_reverse_L2_star"][:,0]=1. + return arrays + + +def test_stage3_transient_exact_schema_clock_power_and_tamper(tmp_path): + import json + from steady_pinball_theory.runner import transient_contract, write_transient_artifact, load_validate_transient + parent=tmp_path/"parent.chk"; parent.write_bytes(b"parent") + references={name:{"path":str(tmp_path/name),"manifest_payload_sha256":"0"*64} for name in ("accepted_endpoint","reverse_endpoint")} + schedule={"continue-accepted":{"initial_action_omega":[0.,.2,-.2],"release_action_omega":[0.,.2,-.2],"pulse_end_index":None,"release_index":0}} + contract=transient_contract(campaign_kind="causal-switch",campaign_id="manufactured",roles=["continue-accepted"],parent=parent,references=references,diameter=2.,u_inf=1.,action_schedule=schedule) + arrays=_stage3_arrays(); out=tmp_path/"role"; write_transient_artifact(out,contract,"continue-accepted",arrays) + manifest,loaded=load_validate_transient(out,validate_references=False) + assert manifest["schema"].endswith("/v2") and loaded["clock"][0,1]==0 + bad=_stage3_arrays(); bad["power_body"][1,1]+=1 + with pytest.raises(ValueError,match="ownership"): write_transient_artifact(tmp_path/"bad",contract,"continue-accepted",bad) + data=bytearray((out/"transient.npz").read_bytes()); data[-9]^=1; (out/"transient.npz").write_bytes(data) + with pytest.raises(ValueError,match="hash/bytes"): load_validate_transient(out,validate_references=False) + + +def test_stage3_orientation_signs_and_no_aggregate_channels(): + from steady_pinball_theory.runner import TRANSIENT_ARRAY_SCHEMAS, TRANSIENT_GAP_ORDER + assert TRANSIENT_GAP_ORDER==("front_to_rear_y_plus","front_to_rear_y_minus","rear_y_plus_to_rear_y_minus") + assert {"clock","action_omega","torque_body","power_body","gap_Q","gap_mass","gap_J","rear_wall_mean","rear_wall_rms","recirculation","station_deficits"} <= set(TRANSIENT_ARRAY_SCHEMAS) + assert not ({"telemetry","gap_sum","mixed_norm"}&set(TRANSIENT_ARRAY_SCHEMAS)) + + +def test_stage3_legacy_transient_has_fixed_bounded_ceiling(tmp_path): + import hashlib,json + from steady_pinball_theory.runner import load_legacy_transient_diagnostic, _canonical_json, _sha256 + out=tmp_path/"legacy"; out.mkdir(); np.savez_compressed(out/"telemetry.npz",telemetry=np.zeros((2,4))) + manifest={"schema":"steady-pinball-branch-acquisition/v1","immutable":True,"files":{"telemetry.npz":{"sha256":_sha256(out/"telemetry.npz"),"bytes":(out/"telemetry.npz").stat().st_size}}} + manifest["payload_sha256"]=hashlib.sha256(_canonical_json(manifest)).hexdigest(); (out/"manifest.json").write_text(json.dumps(manifest)) + diagnostic,_=load_legacy_transient_diagnostic(out) + assert diagnostic["classification"]=="BOUNDED_DIAGNOSTIC" and "cannot establish" in diagnostic["ceiling"] + + +def test_stage3_continuation_drift_and_release_normalization_boundaries(): + from steady_pinball_theory.runner import onset_interval + t=np.arange(6.); continuation=np.array([0,.01,.02,.03,.04,.05]); branch=continuation.copy() + assert onset_interval(t,branch,continuation,noise_window=2,explicit_floor=.01)["interval"] is None + release=np.array([9.,4.,2.,1.]); release_index=1 + ratio=release/release[release_index] + assert ratio[release_index]==1. and ratio[-1]==.25 + + +def test_stage3_one_realization_is_deterministic_bounded_contract(): + from steady_pinball_theory.runner import analyze_causal_switch_v2 + source=__import__("inspect").getsource(analyze_causal_switch_v2) + assert '"realizations":1' in source and '"deterministic BOUNDED; bootstrap forbidden' in source + + + +def test_stage3_fake_factory_v2_role_includes_zero_and_synchronized_release(tmp_path,monkeypatch): + from types import SimpleNamespace + import steady_pinball_theory.runner as runner + checkpoint=tmp_path/"parent.chk"; checkpoint.write_bytes(b"parent") + record={"checkpoint":{"sha256":runner._sha256(checkpoint)},"config_lbm":{"grid":{"nx":4,"ny":3}},"centers_xy":[[0.,0.],[1.,1.],[1.,-1.]],"radius":.25,"action_omega":[0.,.2,-.2]} + events=[] + class FakeSimulation: + def __init__(self,**kwargs): self.bodies=SimpleNamespace(count=3,objects=[SimpleNamespace(obj_id=i,center=[*c]) for i,c in enumerate(record["centers_xy"])]) + def initialize(self): events.append("initialize") + def load_checkpoint(self,path): events.append("restore") + def set_body(self,i,omega): events.append(("action",i,float(omega))) + def run(self,steps,zero_obs=True): events.append(("run",steps,zero_obs)) + def close(self): events.append("close") + samples=[] + def capture(sim,record,action,step,D,accepted,reverse,mask): + samples.append((step,np.asarray(action).copy())) + row={name:np.zeros(schema["tail"][0]) for name,schema in runner.TRANSIENT_ARRAY_SCHEMAS.items() if name not in ("field_L2_star","field_Linf_star")} + row["clock"]=np.array([step,step*.01/D]); row["action_omega"]=np.asarray(action); row["torque_body"]=np.array([0.,1.,-1.]); row["power_body"]=row["torque_body"]*row["action_omega"] + field=np.full((3,4,2),float(step)); return row,field,np.ones((3,4),bool),np.ones((3,4)) + monkeypatch.setattr(runner,"_capture_transient_v2",capture) + contract={"roles":["symmetric-a0.1"],"action_schedule":{"symmetric-a0.1":{"pulse_end_index":1,"release_index":1}},"body_order":list(runner.TRANSIENT_BODY_ORDER),"gap_order":list(runner.TRANSIENT_GAP_ORDER),"station_order_x_over_D":list(runner.TRANSIENT_STATION_ORDER),"torque":{"ownership":"actuator_on_fluid"}} + written={} + monkeypatch.setattr(runner,"write_transient_artifact",lambda out,contract,role,arrays:written.update(arrays=arrays) or {}) + continuation=([np.zeros((3,4,2)) for _ in range(3)],np.ones((3,4),bool)) + runner._run_transient_v2_role(record,checkpoint,tmp_path/"role","symmetric-a0.1",contract,[0.,.1,-.1],2,1,1.,FakeSimulation,{}, {},np.ones((3,4),bool),pulse_steps=1,continuation=continuation) + assert [x[0] for x in samples]==[0,1,2] + assert np.array_equal(samples[0][1],[0.,.1,-.1]) and np.array_equal(samples[1][1],record["action_omega"]) + assert np.array_equal(written["arrays"]["clock"][:,0],[0.,1.,2.]) + assert written["arrays"]["field_L2_star"][1,0]>0. + + +def test_stage3_transient_reference_authentication_fails_closed(tmp_path,monkeypatch): + import steady_pinball_theory.runner as runner + endpoint={"manifest_payload_sha256":"accepted-hash"}; record={"action_omega":[0.,.2,-.2]}; arrays={"ux":np.zeros((2,2)),"uy":np.zeros((2,2))} + accepted_manifest={"manifest_payload_sha256":"wrong-hash","spec":{"kind":"accepted"},"result":{"qualification_passed":True}} + monkeypatch.setattr(runner,"load_validate_artifact",lambda path:(accepted_manifest,arrays)) + with pytest.raises(ValueError,match="not accepted-parent"): + runner._transient_references(record,endpoint,arrays,tmp_path/"accepted",tmp_path/"reverse") + + +def _stage3_analysis_contract(roles): + import steady_pinball_theory.runner as runner + schedules={} + for role in roles: + pulsed=role!="continue-accepted" + schedules[role]={"initial_action_omega":[0.,.2,-.2],"release_action_omega":[0.,.2,-.2],"pulse_end_index":1 if pulsed else None,"release_index":1 if pulsed else 0} + return {"schema":runner.TRANSIENT_CAMPAIGN_SCHEMA,"roles":roles,"campaign_kind":"nonlinear-return","action_schedule":schedules,"action_schedule_semantics":{ + "pulse_end_index":"sample reached after the final pulsed evolution interval; the release action is installed before this sample is captured; null when no pulse is applied", + "release_index":"first sample under the release action and the pulse-end normalization index; equals pulse_end_index for pulsed roles and is zero for unpulsed roles", + "field_distance":"field_L2_star and field_Linf_star are synchronized role-minus-continuation distances on the common fluid mask, never distances from the role's own release state", + }} + + +def test_stage3_nonlinear_return_zero_normalization_writes_bounded_unavailable(tmp_path,monkeypatch): + import steady_pinball_theory.runner as runner + roles=["continue-accepted","symmetric-a0.1"] + arrays=_stage3_arrays(); arrays["field_L2_star"][1,0]=0. + loaded={role:({},_stage3_arrays()) for role in roles}; loaded["symmetric-a0.1"]=({},arrays) + monkeypatch.setattr(runner,"load_transient_campaign",lambda *args,**kwargs:(_stage3_analysis_contract(roles),loaded)) + result=runner.analyze_nonlinear_return_v2(tmp_path/"campaign",tmp_path/"analysis") + assert result["classification"]=="BOUNDED" + assert result["availability"]=="UNAVAILABLE_REACQUISITION_REQUIRED" + assert result["runs"]=={} and "labels" not in result and "label" not in result + assert "finite and positive" in result["reason"] + assert (tmp_path/"analysis"/"analysis.json").is_file() + + +def test_stage3_nonlinear_return_valid_data_keeps_finite_horizon_label(tmp_path,monkeypatch): + import steady_pinball_theory.runner as runner + roles=["continue-accepted","symmetric-a0.1"] + arrays=_stage3_arrays(); arrays["field_L2_star"][:,0]=[0.,1.,.5,.2,.05] + loaded={"continue-accepted":({},_stage3_arrays()),"symmetric-a0.1":({},arrays)} + monkeypatch.setattr(runner,"load_transient_campaign",lambda *args,**kwargs:(_stage3_analysis_contract(roles),loaded)) + result=runner.analyze_nonlinear_return_v2(tmp_path/"campaign",tmp_path/"analysis-valid") + assert result["availability"]=="AVAILABLE_FINITE_HORIZON" + assert result["runs"]["symmetric-a0.1"]["label"]=="RETURN" + + +def test_stage3_causal_order_unresolved_without_delivery(tmp_path,monkeypatch): + import steady_pinball_theory.runner as runner + roles={role:({},_stage3_arrays(7)) for role in ("continue-accepted","zero","equal-amplitude-reverse")} + contract=_stage3_analysis_contract(list(roles)); contract["campaign_kind"]="causal-switch"; contract["array_schemas"]=runner.TRANSIENT_ARRAY_SCHEMAS + for role in ("zero","equal-amplitude-reverse"): + roles[role][1]["gap_Q"][:,2]=[0.,0.,2.,2.,2.,2.,2.] + roles[role][1]["station_deficits"][:,0]=[0.,0.,0.,2.,2.,2.,2.] + monkeypatch.setattr(runner,"load_transient_campaign",lambda *args,**kwargs:(contract,roles)) + result=runner.analyze_causal_switch_v2(tmp_path/"campaign",tmp_path/"causal",explicit_floor=1.) + for role in ("zero","equal-amplitude-reverse"): + assert result["roles"][role]["delivery_onset"]["interval"] is None + assert result["roles"][role]["mediator_before_delivery"]["status"]=="UNRESOLVED" + + + + +def test_stage3_migration_preserves_nonpower_arrays_and_authenticates(tmp_path,monkeypatch): + import hashlib,json + import steady_pinball_theory.runner as runner + monkeypatch.setattr(runner,"_validate_endpoint_reference",lambda binding: {}) + parent=tmp_path/"parent.chk"; parent.write_bytes(b"parent") + refs={name:{"path":str(tmp_path/name),"manifest_payload_sha256":"0"*64} for name in ("accepted_endpoint","reverse_endpoint")} + schedule={"continue-accepted":{"initial_action_omega":[0.,.2,-.2],"release_action_omega":[0.,.2,-.2],"pulse_end_index":None,"release_index":0}} + legacy=runner.transient_contract(campaign_kind="causal-switch",campaign_id="legacy",roles=["continue-accepted"],parent=parent,references=refs,diameter=2.,u_inf=1.,torque_ownership="fluid_on_body",action_schedule=schedule) + arrays=_stage3_arrays(); arrays["power_body"]=-arrays["torque_body"]*arrays["action_omega"] + source=tmp_path/"source"; source.mkdir(); runner.write_transient_artifact(source/"continue-accepted",legacy,"continue-accepted",arrays) + rows={"plus_omega":[[1,.1,.4]],"minus_omega":[[1,.1,-.4]],"zero":[[1,.1,0.]]} + evaluated=runner._evaluate_torque_oracle(rows,D=20.,U=.01,rho=1.,omega=.002,parity_tolerance=.1,zero_tolerance=.1) + oracle={"schema":runner.TORQUE_ORACLE_SCHEMA,"immutable":True,"setup":{"D":20.,"U":.01,"rho":1.,"exact_actions_by_role":{"plus_omega":.002,"minus_omega":-.002,"zero":0.}},**evaluated} + oracle["payload_sha256"]=hashlib.sha256(runner._canonical_json(oracle)).hexdigest(); oracle_dir=tmp_path/"oracle"; oracle_dir.mkdir(); (oracle_dir/"oracle.json").write_text(json.dumps(oracle)) + out=tmp_path/"corrected"; contract,roles=runner.migrate_transient_ownership(source,oracle_dir,out) + manifest,migrated=roles["continue-accepted"] + assert contract["torque"]["ownership"]=="actuator_on_fluid" + assert np.array_equal(migrated["power_body"],arrays["torque_body"]*arrays["action_omega"]) + for name in arrays: + if name!="power_body": assert np.array_equal(migrated[name],arrays[name]) + runner.load_validate_transient(out/"continue-accepted",validate_references=False) + with pytest.raises(runner.TransientReacquisitionRequired,match="superseded transient power sign"): + runner.load_validate_transient(source/"continue-accepted",validate_references=False) + with pytest.raises(FileExistsError,match="clobber"): runner.migrate_transient_ownership(source,oracle_dir,out) + oracle["roles"]["plus_omega"]["mean_raw_torque"]+=1 + (oracle_dir/"oracle.json").write_text(json.dumps(oracle)) + with pytest.raises(ValueError,match="oracle payload"): runner.load_validate_transient(out/"continue-accepted",validate_references=True) + + +def _fake_torque_oracle_root(tmp_path): + root=tmp_path/"CelerisLab" + for rel in ("src/CelerisLab/lbm/kernels/boundary/curved_boundary.cuh","src/CelerisLab/lbm/kernels/core/obs.cuh"): + path=root/rel; path.parent.mkdir(parents=True,exist_ok=True); path.write_text("// frozen fake source\n") + return root + + +def _fake_torque_factory(torques): + import json + from types import SimpleNamespace + instances=[] + class FakeSimulation: + def __init__(self, *, lbm_config_path, body_config_path): + body=json.loads(Path(body_config_path).read_text()); self.omega=body["objects"][0]["omega"] + self.tau=float(torques[self.omega]); self.bodies=SimpleNamespace(count=1,objects=[SimpleNamespace(obj_id=0)]); self.closed=False + instances.append(self) + def initialize(self): pass + def run(self, steps, zero_obs=True): assert steps>0 and zero_obs + def read_body(self, body_id, normalize=True): + assert body_id==0 and normalize is True + return SimpleNamespace(torque=np.array([self.tau])) + def read_torque(self, body_id, normalize=True): + assert body_id==0 and normalize is True + return np.array([self.tau]) + def close(self): self.closed=True + return FakeSimulation,instances + + +def test_fake_factory_torque_oracle_sign_pass_and_metadata(tmp_path): + import json + from steady_pinball_theory.runner import TORQUE_ORACLE_SCHEMA, qualify_torque_oracle + root=_fake_torque_oracle_root(tmp_path); factory,instances=_fake_torque_factory({.002:.4,-.002:-.39,0.0:.005}) + source={"celeris_import_root":str(root.resolve()),"celeris_git_commit":"fake","celeris_git_dirty":False} + out=tmp_path/"oracle" + result=qualify_torque_oracle(out,intended_celeris_root=root,simulation_factory=factory,source_environment=source,cooldown=False) + assert result["schema"]==TORQUE_ORACLE_SCHEMA and result["qualification"]=="PASS" + assert result["celeris_torque_channel_work_sign"]=="actuator_on_fluid" and result["strict_pass"] is True + assert result["ownership_established"]==result["force_ownership"]=="not_established" + assert result["newton_pair_force_ownership_inference"]=="prohibited_from_torque_oracle" + assert len(instances)==3 and len({id(instance) for instance in instances})==3 and all(instance.closed for instance in instances) + assert result["setup"]["fresh_simulation_per_role"] is True and result["setup"]["read_semantics"]["normalize"] is True + assert result["setup"]["two_dimensional_per_unit_span"] is True and result["roles"]["plus_omega"]["C_P"]>0 + assert set(result["source_identity"]["force_torque_kernel_source_hashes"])=={ + "src/CelerisLab/lbm/kernels/boundary/curved_boundary.cuh","src/CelerisLab/lbm/kernels/core/obs.cuh"} + stored=json.loads((out/"oracle.json").read_text()); assert stored["payload_sha256"]==result["payload_sha256"] + with pytest.raises(FileExistsError,match="clobber"): + qualify_torque_oracle(out,intended_celeris_root=root,simulation_factory=factory,source_environment=source,cooldown=False) + + +def test_fake_factory_torque_oracle_sign_failure_is_bounded(tmp_path): + from steady_pinball_theory.runner import qualify_torque_oracle + root=_fake_torque_oracle_root(tmp_path); factory,_=_fake_torque_factory({.002:-.4,-.002:.4,0.0:0.0}) + result=qualify_torque_oracle(tmp_path/"bounded",intended_celeris_root=root,simulation_factory=factory, + source_environment={"celeris_import_root":str(root.resolve())},cooldown=False) + assert result["qualification"]=="BOUNDED" and result["strict_pass"] is False + assert result["ownership_established"]==result["celeris_torque_channel_work_sign"]=="not_established" + assert result["force_ownership"]=="not_established" + assert result["gates"]["same_sign_torque_and_rotation_both_directions"] is False + assert result["gates"]["positive_omega_tau_actuator_power_both_directions"] is False + + +# Stage-5 publication-v3 audit guards. +def test_publication_v3_exact_qin_metric_and_conservative_scaling(): + import steady_pinball_theory.runner as runner + x=np.arange(5.); y=np.arange(6.); X,Y=np.meshgrid(x,y) + qin={"x":x,"y":y,"ux":np.ones_like(X),"uy":np.zeros_like(X),"fluid_mask":np.ones_like(X,dtype=bool)} + qctl={**qin,"ux":qin["ux"].copy(),"uy":qin["uy"].copy()}; qctl["ux"][:,4]+=0.25 + direct,_,j,mask=runner._publication_metric(qin,qctl,center_x=-6.,D=1.,U=1.) + assert j==4 and mask.sum()==2 and direct["E_inf_vector"]==.25 + ux=-Y.astype(float); uy=X.astype(float); omega,use=conservative_masked_vorticity(x,y,ux,uy,np.ones_like(X,dtype=bool)) + assert np.allclose(omega[use]*2/4,1.) # (dv/dx-du/dy)D/U + + +def test_publication_v3_hash_auth_missing_and_tamper(tmp_path): + import hashlib,json + import steady_pinball_theory.runner as runner + p=tmp_path/"x.json"; p.write_text('{}') + with pytest.raises(ValueError,match="authentication"): runner._load_hashed_json(p,"x") + value={"schema":"x"}; value["payload_sha256"]=hashlib.sha256(runner._canonical_json(value)).hexdigest(); p.write_text(json.dumps(value)) + assert runner._load_hashed_json(p,"x")["schema"]=="x" + value["schema"]="tampered"; p.write_text(json.dumps(value)) + with pytest.raises(ValueError,match="authentication"): runner._load_hashed_json(p,"x") + + +def test_publication_v3_render_config_no_clobber_and_report_contract(): + import inspect + import steady_pinball_theory.runner as runner + matplotlib,loc=runner._configure_publication_rendering() + assert matplotlib.get_backend().lower()=="agg" and loc in ("C","C.UTF-8") and __import__('os').environ["TZ"]=="UTC" + source=inspect.getsource(runner.publish_article) + assert 'CreationDate":None' in source and 'ModDate":None' in source and 'if out.exists(): raise FileExistsError' in source + assert source.count("主公式组 1")==1 and source.count("主公式组 2")==1 and source.count("主公式组 3")==1 and source.count("主公式组 4")==1 + for term in ("第一部分","第二部分","第三部分","第四部分","第五部分","第六部分","存储/时间项","物体邻近梯度","没有闭合残差","q_ctl,q_in"): + assert term in source + + +# Steady-results display publisher guards. +def test_display_vorticity_csv_mask_and_no_clobber(tmp_path): + import csv + import steady_pinball_theory.runner as runner + x=np.arange(5.); y=np.arange(5.); X,Y=np.meshgrid(x,y); fluid=np.ones((5,5),bool); fluid[2,2]=False + qin={"x":x,"y":y,"ux":np.ones_like(X),"uy":np.zeros_like(X),"fluid_mask":fluid} + a={**qin,"ux":np.ones_like(X)-Y,"uy":X.copy()} + spec={"D":2.,"config_lbm":{"physics":{"velocity":1.}}} + f=runner._display_fields(a,qin,spec) + assert not f["vorticity_mask"][2,1] and np.isnan(f["vorticity_star"][2,1]) + assert np.allclose(f["vorticity_star"][f["vorticity_mask"]],4.) + solid=runner._display_solid_mask(x,y,np.array([[0.,0.],[2.,0.],[4.,0.]]),.5) + assert solid[0,0] and solid[0,2] and solid[0,4] and not solid[1,1] + case={"name":"stable-reverse-s5.2","s":5.2,"arrays":a,"fields":f,"U":1.,"x_D":x,"y_D":y,"source_sha256":"a"*64} + out=tmp_path/"profiles.csv"; columns=runner._write_display_profiles(out,[case],stations=(2.,)) + assert columns[:3]==("case","s","x_over_D") + with out.open(newline="") as stream: rows=list(csv.DictReader(stream)) + assert tuple(rows[0])==columns and len(rows)==5 and rows[2]["fluid_mask"]=="0" and rows[2]["ux_over_U"]=="" + stage=tmp_path/"stage"; stage.mkdir(); destination=tmp_path/"immutable"; destination.mkdir() + with pytest.raises(FileExistsError,match="clobber"): runner._publish_directory_no_replace(stage,destination) + + +def test_display_stationary_status_and_diagnostic_csv(tmp_path): + import csv + import steady_pinball_theory.runner as runner + stationary={"result":{"qualification_required":False,"qualification_role":"unsteady_reference","qualification_passed":True,"settling":{"qualified":False,"value":.0657}}} + accepted={"result":{"qualification_required":True,"qualification_role":"required_steady_endpoint","qualification_passed":True,"settling":{"qualified":True,"value":1e-6}}} + assert runner._display_qualification(stationary)=="unsteady_reference_not_required_to_settle" + assert runner._display_qualification(accepted)=="settling_qualified_steady_endpoint" + bad={"result":dict(stationary["result"],settling={"qualified":True,"value":0.})} + with pytest.raises(ValueError,match="unsteady-reference"): runner._display_qualification(bad) + rows=[{"case":"accepted-s3.55","oracle_bound_C_P":15.026583843864495,"partial_ledger_status":"endpoint_spatial_partial_not_closed","residual":"","source_artifact_sha256":"a"*64}] + columns=runner._write_dict_csv(tmp_path/"diagnostics.csv",rows) + assert columns==("case","oracle_bound_C_P","partial_ledger_status","residual","source_artifact_sha256") + with (tmp_path/"diagnostics.csv").open(newline="") as stream: saved=list(csv.DictReader(stream)) + assert float(saved[0]["oracle_bound_C_P"])==15.026583843864495 and saved[0]["residual"]=="" + +def test_display_profile_rows_keep_common_fluid_and_conservative_blanks(tmp_path): + import csv + import steady_pinball_theory.runner as runner + x=np.arange(5.); y=np.arange(5.); X,Y=np.meshgrid(x,y); fluid=np.ones((5,5),bool); fluid[2,2]=False + qin={"x":x,"y":y,"ux":np.ones_like(X),"uy":np.zeros_like(X),"fluid_mask":fluid}; a={**qin,"ux":np.ones_like(X)-Y,"uy":X.copy()} + fields=runner._display_fields(a,qin,{"D":2.,"config_lbm":{"physics":{"velocity":1.}}}); case={"name":"accepted-s3.55","s":3.55,"arrays":a,"fields":fields,"U":1.,"x_D":x,"y_D":y,"source_sha256":"b"*64} + runner._write_display_profiles(tmp_path/"profiles.csv",[case],stations=(1.,)) + with (tmp_path/"profiles.csv").open(newline="") as stream: rows=list(csv.DictReader(stream)) + assert len(rows)==len(y) and sum(r["fluid_mask"]=="1" for r in rows)==len(y) + assert rows[2]["ux_over_U"]!="" and rows[2]["vorticity_star"]=="" + assert all(r["source_artifact_sha256"]=="b"*64 for r in rows) + + +# Evidence and reader-document closeout guards. +def test_evidence_index_covers_physical_tree_and_replacements(): + import json + root=Path(__file__).resolve().parents[1]/"evidence" + index=json.loads((root/"INDEX.json").read_text()) + physical={p.name for bucket in ("authoritative","archive") for p in (root/bucket).iterdir() if p.is_dir()} + listed=set(index["authoritative"])|set(index["archive"]) + assert listed==physical + assert set(index["artifact_catalog"])==physical + for source,replacement in index["replacement_map"].items(): + assert source in physical and replacement in index["authoritative"] + assert index["artifact_catalog"][source]["replacement"]==replacement + assert index["authoritative_presentation"]=="steady-results-display-v2-20260809" + assert "steady-results-display-20260809" in index["archive"] + assert index["replacement_map"]["steady-results-display-20260809"]==index["authoritative_presentation"] + for old in ("steady-article-publication-20260809","steady-article-publication-v2-20260809","steady-article-publication-v3-20260809"): + assert index["publication_supersession"][old]=="steady-article-publication-v3b-20260809" + + +def test_transient_dispositions_and_reader_docs_are_complete(): + import json + root=Path(__file__).resolve().parents[1]; index=json.loads((root/"evidence"/"INDEX.json").read_text()) + expected={ + "steady-causal-v2-d20-s3.55-20260808T2200":"steady-causal-v2c-d20-s3.55-20260808T2245", + "steady-causal-analysis-v3-d20-s3.55-20260808T2200":"steady-causal-analysis-v3c-d20-s3.55-20260808T2245", + "steady-return-v2-d20-s3.55-20260808T2225":"steady-return-v2c-d20-s3.55-20260808T2250", + "steady-return-analysis-v2-bounded-d20-s3.55-20260808T2225":"steady-return-analysis-v2c-d20-s3.55-20260808T2250", + } + for old,new in expected.items(): + assert old in index["archive"] and index["replacement_map"][old]==new + assert old in index["diagnostic_disposition"] + for name in ("README.md","RESULTS.md","HISTORY_AND_LESSONS.md","DERIVATION.md","LITERATURE.md"): + assert (root/name).is_file() + assert (root/"evidence"/"README.md").is_file() + readme=(root/"README.md").read_text(); results=(root/"RESULTS.md").read_text(); history=(root/"HISTORY_AND_LESSONS.md").read_text() + assert "publish-results-display" in readme and "steady-results-display-v2-20260809" in readme + assert "CCD is **pending/not frozen" in results + assert "navigation not evidence" in history + + +# Standalone lattice-exact plotting helper guards. +def test_plot_results_discrete_center_white_and_pixel_contract(tmp_path): + from PIL import Image + from steady_pinball_theory.plot_results import discrete_colormap, crop_indices + edges, _, cmap = discrete_colormap("RdBu_r", -2., 2., 21, center_white=True) + assert len(edges) == 22 and np.allclose(cmap.colors[10], [1, 1, 1, 1]) + source=Path(__file__).resolve().parents[1]/"plot_results.py" + text=source.read_text(); assert "displayed/exported vorticity analytically zero" in text + assert "plates/error" in text and "family_scales" in text + x=np.arange(-3.,12.); y=np.arange(-4.,5.); ix,iy=crop_indices(x,y) + assert (len(ix),len(iy))==(13,7) + path=tmp_path/"raw.png"; Image.new("RGBA",(len(ix),len(iy))).save(path) + assert Image.open(path).size==(len(ix),len(iy)) + + +def test_plot_results_area_weighted_l2_and_publish_contract(tmp_path): + from steady_pinball_theory.plot_results import area_weighted_vector_l2, publish + du=np.full((3,4),3.); dv=np.full((3,4),4.); mask=np.ones((3,4),bool); weights=np.arange(1,13,dtype=float).reshape(3,4) + assert area_weighted_vector_l2(du,dv,mask,weights,2.)==2.5 + stage=tmp_path/"stage"; stage.mkdir(); (stage/"marker").write_text("new") + out=tmp_path/"figures"; out.mkdir(); (out/"marker").write_text("old") + with pytest.raises(FileExistsError,match="overwrite"): publish(stage,out,False) + assert (out/"marker").read_text()=="old" + publish(stage,out,True); assert (out/"marker").read_text()=="new" diff --git a/src/steady_pinball_theory/theory.py b/src/steady_pinball_theory/theory.py index d992492..733d6b5 100644 --- a/src/steady_pinball_theory/theory.py +++ b/src/steady_pinball_theory/theory.py @@ -1,66 +1,1263 @@ -"""MFS outer/strip potential-flow representation with prescribed circulation.""" +"""Validated potential-flow references with prescribed geometric-CCW circulation. + +Outer MFS/exact helpers solve impermeability with independent body periods; they +are not rotating-wall no-slip or Gamma(Omega) closures (DERIVATION.md §§3–7, 24). +Vasconcelos–Föppl and Kármán helpers are quarantined mathematical oracles only. +""" from __future__ import annotations from dataclasses import dataclass import numpy as np +_TWOPI = 2.0 * np.pi -def _images(y0: float, H: float, layers: int, vortex: bool): - for k in range(-layers,layers+1): - yield y0+4*k*H, 1.0 - yield 2*H-y0+4*k*H, -1.0 if vortex else 1.0 + +def _points(points): + p = np.asarray(points, dtype=float) + if p.ndim == 1 and p.shape == (2,): + p = p[None, :] + if p.ndim != 2 or p.shape[1] != 2 or not np.isfinite(p).all(): + raise ValueError("points must be a finite (N,2) array") + return p + + +def _integer(name, value, minimum): + if isinstance(value, (bool, np.bool_)) or not isinstance(value, (int, np.integer)): + raise ValueError(f"{name} must be an integer") + if value < minimum: + raise ValueError(f"{name} must be >= {minimum}") + return int(value) + + +def _geometry(centers, radius, circulations=None, H=None): + c = np.asarray(centers, dtype=float) + if c.ndim != 2 or c.shape[1] != 2 or len(c) == 0 or not np.isfinite(c).all(): + raise ValueError("centers must be a nonempty finite (B,2) array") + if not np.isscalar(radius) or not np.isfinite(radius) or radius <= 0: + raise ValueError("radius must be finite and positive") + if circulations is not None: + g = np.asarray(circulations, dtype=float) + if g.shape != (len(c),) or not np.isfinite(g).all(): + raise ValueError("circulations must be one finite value per center") + else: + g = None + if len(c) > 1: + d = np.linalg.norm(c[:, None, :] - c[None, :, :], axis=2) + np.fill_diagonal(d, np.inf) + if np.any(d <= 2.0 * radius): + raise ValueError("cylinders must be strictly non-overlapping") + if H is not None: + if not np.isscalar(H) or not np.isfinite(H) or H <= 0: + raise ValueError("H must be finite and positive") + if np.any(np.abs(c[:, 1]) + radius >= H): + raise ValueError("every cylinder must lie strictly inside the strip") + return c, float(radius), g, None if H is None else float(H) + + +def _images(y0, H, layers, vortex): + for k in range(-layers, layers + 1): + yield y0 + 4 * k * H, 1.0 + yield 2 * H - y0 + 4 * k * H, -1.0 if vortex else 1.0 def singular_velocity(points, source, *, H=None, layers=0, vortex=False): - p=np.asarray(points,float); x0,y0=map(float,source); vel=np.zeros_like(p) - imgs=[(y0,1.0)] if H is None else list(_images(y0,float(H),int(layers),vortex)) - for yi,sgn in imgs: - dx=p[:,0]-x0; dy=p[:,1]-yi; r2=dx*dx+dy*dy - if np.any(r2 <= 1e-24): raise ValueError("evaluation at singularity") - if vortex: vel += sgn*np.column_stack((-dy/r2,dx/r2))/(2*np.pi) - else: vel += sgn*np.column_stack((dx/r2,dy/r2))/(2*np.pi) + p = _points(points) + z = np.asarray(source, dtype=float) + if z.shape != (2,) or not np.isfinite(z).all(): + raise ValueError("source must be a finite 2-vector") + layers = _integer("layers", layers, 0) + if H is not None and (not np.isfinite(H) or H <= 0): + raise ValueError("H must be finite and positive") + vel = np.zeros_like(p) + imgs = [(z[1], 1.0)] if H is None else _images(z[1], float(H), layers, vortex) + for yi, sign in imgs: + dx, dy = p[:, 0] - z[0], p[:, 1] - yi + r2 = dx * dx + dy * dy + if np.any(r2 <= 1e-24): + raise ValueError("evaluation at singularity") + if vortex: + vel += sign * np.column_stack((-dy / r2, dx / r2)) / _TWOPI + else: + vel += sign * np.column_stack((dx / r2, dy / r2)) / _TWOPI + if not np.isfinite(vel).all(): + raise FloatingPointError("nonfinite singular velocity") return vel +def cylinder_velocity(points, center, radius, *, u_inf=1.0, circulation=0.0): + """Exact exterior velocity; positive circulation is geometrically CCW.""" + p = _points(points) + center = np.asarray(center, dtype=float) + values = np.asarray([radius, u_inf, circulation], dtype=float) + if center.shape != (2,) or not np.isfinite(center).all() or not np.isfinite(values).all(): + raise ValueError("center and flow parameters must be finite") + if radius <= 0: + raise ValueError("radius must be positive") + d = p - center + r2 = np.einsum("ij,ij->i", d, d) + if np.any(r2 < radius * radius * (1.0 - 1e-13)): + raise ValueError("exact velocity is defined only on the cylinder exterior") + x, y = d[:, 0], d[:, 1] + r4 = r2 * r2 + ux = u_inf * (1.0 + radius**2 * (y * y - x * x) / r4) + uy = -2.0 * u_inf * radius**2 * x * y / r4 + ux -= circulation * y / (_TWOPI * r2) + uy += circulation * x / (_TWOPI * r2) + return np.column_stack((ux, uy)) + + @dataclass class MFSSolution: - centers: np.ndarray; radius: float; strengths: np.ndarray; source_points: np.ndarray - circulations: np.ndarray; u_inf: float; H: float|None; image_layers: int + centers: np.ndarray + radius: float + strengths: np.ndarray + source_points: np.ndarray + circulations: np.ndarray + u_inf: float + H: float | None + image_layers: int + def velocity(self, points): - p=np.asarray(points,float); v=np.zeros_like(p); v[:,0]=self.u_inf - for q,z in zip(self.strengths,self.source_points): - v += q*singular_velocity(p,z,H=self.H,layers=self.image_layers) - for g,z in zip(self.circulations,self.centers): - v += g*singular_velocity(p,z,H=self.H,layers=self.image_layers,vortex=True) + p = _points(points) + v = np.zeros_like(p) + v[:, 0] = self.u_inf + for q, z in zip(self.strengths, self.source_points): + v += q * singular_velocity(p, z, H=self.H, layers=self.image_layers) + for gamma, z in zip(self.circulations, self.centers): + v += gamma * singular_velocity( + p, z, H=self.H, layers=self.image_layers, vortex=True + ) + if not np.isfinite(v).all(): + raise FloatingPointError("nonfinite MFS velocity") return v def solve_mfs(centers, radius, circulations, *, u_inf=1.0, n_boundary=96, source_ratio=0.65, H=None, image_layers=20): - c=np.asarray(centers,float); gam=np.asarray(circulations,float) - if c.shape != (len(gam),2): raise ValueError("centers/circulations mismatch") - th=(np.arange(n_boundary)+0.5)*2*np.pi/n_boundary - normals=np.column_stack((np.cos(th),np.sin(th))) - bpts=np.concatenate([ci+radius*normals for ci in c]) - nrms=np.tile(normals,(len(c),1)) - spts=np.concatenate([ci+source_ratio*radius*normals for ci in c]) - base=np.zeros_like(bpts); base[:,0]=u_inf - for g,ci in zip(gam,c): base += g*singular_velocity(bpts,ci,H=H,layers=image_layers,vortex=True) - rhs=-np.einsum('ij,ij->i',base,nrms) - # Eliminate one source per body so every body's net source is exactly zero. - cols=[] + """Neumann MFS solve; circulations are prescribed geometric-CCW periods.""" + c, radius, gam, H = _geometry(centers, radius, circulations, H) + if not np.isscalar(u_inf) or not np.isfinite(u_inf): + raise ValueError("u_inf must be finite") + n_boundary = _integer("n_boundary", n_boundary, 8) + image_layers = _integer("image_layers", image_layers, 0) + if not np.isscalar(source_ratio) or not np.isfinite(source_ratio) or not 0 < source_ratio < 1: + raise ValueError("source_ratio must satisfy 0 < source_ratio < 1") + theta = (np.arange(n_boundary) + 0.5) * _TWOPI / n_boundary + normals = np.column_stack((np.cos(theta), np.sin(theta))) + bpts = np.concatenate([ci + radius * normals for ci in c]) + nrms = np.tile(normals, (len(c), 1)) + spts = np.concatenate([ci + source_ratio * radius * normals for ci in c]) + base = np.zeros_like(bpts) + base[:, 0] = float(u_inf) + for gamma, ci in zip(gam, c): + base += gamma * singular_velocity( + bpts, ci, H=H, layers=image_layers, vortex=True + ) + rhs = -np.einsum("ij,ij->i", base, nrms) + cols = [] for ib in range(len(c)): - ref=spts[ib*n_boundary+n_boundary-1] - vr=singular_velocity(bpts,ref,H=H,layers=image_layers) - for j in range(n_boundary-1): - v=singular_velocity(bpts,spts[ib*n_boundary+j],H=H,layers=image_layers)-vr - cols.append(np.einsum('ij,ij->i',v,nrms)) - A=np.column_stack(cols); coeff,resid,rank,sv=np.linalg.lstsq(A,rhs,rcond=1e-12) - strengths=np.zeros(len(spts)); k=0 + ref = spts[(ib + 1) * n_boundary - 1] + vr = singular_velocity(bpts, ref, H=H, layers=image_layers) + for j in range(n_boundary - 1): + v = singular_velocity( + bpts, spts[ib * n_boundary + j], H=H, layers=image_layers + ) - vr + cols.append(np.einsum("ij,ij->i", v, nrms)) + A = np.column_stack(cols) + coeff, _, rank, sv = np.linalg.lstsq(A, rhs, rcond=1e-12) + if rank != A.shape[1]: + raise np.linalg.LinAlgError(f"rank-deficient MFS system: rank {rank}/{A.shape[1]}") + if not np.isfinite(coeff).all() or not np.isfinite(sv).all() or sv[-1] <= 0: + raise FloatingPointError("nonfinite or singular MFS solve") + strengths = np.zeros(len(spts)) + k = 0 for ib in range(len(c)): - q=coeff[k:k+n_boundary-1]; k+=n_boundary-1 - strengths[ib*n_boundary:ib*n_boundary+n_boundary-1]=q - strengths[ib*n_boundary+n_boundary-1]=-np.sum(q) - sol=MFSSolution(c,float(radius),strengths,spts,gam,float(u_inf),H,int(image_layers)) - residual=np.einsum('ij,ij->i',sol.velocity(bpts),nrms) - return sol,{"boundary_Linf":float(np.max(np.abs(residual))),"boundary_L2":float(np.sqrt(np.mean(residual**2))), - "rank":int(rank),"unknowns":int(A.shape[1]),"condition":float(sv[0]/sv[-1])} + q = coeff[k:k + n_boundary - 1] + k += n_boundary - 1 + strengths[ib * n_boundary:(ib + 1) * n_boundary - 1] = q + strengths[(ib + 1) * n_boundary - 1] = -np.sum(q) + sol = MFSSolution(c, radius, strengths, spts, gam, float(u_inf), H, image_layers) + residual = np.einsum("ij,ij->i", sol.velocity(bpts), nrms) + diag = { + "collocation_Linf": float(np.max(np.abs(residual))), + "collocation_RMS": float(np.sqrt(np.mean(residual**2))), + "rank": int(rank), "unknowns": int(A.shape[1]), + "singular_value_max": float(sv[0]), "singular_value_min": float(sv[-1]), + "condition": float(sv[0] / sv[-1]), + "coefficient_L2": float(np.linalg.norm(strengths)), + "coefficient_Linf": float(np.max(np.abs(strengths))), + "zero_source_error": [float(abs(x.sum())) for x in strengths.reshape(len(c), -1)], + } + return sol, diag + + +def _boundary_sample(centers, radius, n_boundary): + c, radius, _, _ = _geometry(centers, radius) + n_boundary = _integer("n_boundary", n_boundary, 8) + theta = (np.arange(n_boundary) + 0.5) * _TWOPI / n_boundary + normals = np.column_stack((np.cos(theta), np.sin(theta))) + bpts = np.concatenate([ci + radius * normals for ci in c]) + nrms = np.tile(normals, (len(c), 1)) + tangents = np.column_stack((-nrms[:, 1], nrms[:, 0])) + body_index = np.repeat(np.arange(len(c)), n_boundary) + return c, radius, bpts, nrms, tangents, body_index, theta, n_boundary + + +def _zero_mean_per_body(values, body_index, n_bodies, n_boundary): + out = np.asarray(values, dtype=float).copy() + for ib in range(n_bodies): + sl = body_index == ib + mean = float(np.mean(out[sl])) + out[sl] -= mean + return out + + +def wall_tangential_speed(centers, radius, omega, *, n_boundary=96): + """No-slip tangential speed u_theta=Omega a on each body boundary sample.""" + c, radius, bpts, _, tangents, body_index, _, _ = _boundary_sample( + centers, radius, n_boundary) + omega = np.asarray(omega, dtype=float) + if omega.shape != (len(c),) or not np.isfinite(omega).all(): + raise ValueError("omega must be one finite value per body") + rel = bpts - c[body_index] + speed = omega[body_index] * float(radius) + return {"points": bpts, "tangents": tangents, "speed": speed, + "body_index": body_index, "n_boundary": n_boundary} + + +def displacement_transpiration_rhs(centers, radius, omega, base_velocity, *, + n_boundary=96, delta_star_scale=0.05): + """Zero-net-per-body transpiration v_n=alpha d(U_e delta*)/ds proxy. + + The scale is a low-Re ansatz at h/D=0.5; it is not a lubrication closure. + """ + c, radius, bpts, nrms, tangents, body_index, _, n_boundary = _boundary_sample( + centers, radius, n_boundary) + wall = wall_tangential_speed(centers, radius, omega, n_boundary=n_boundary) + u_e = np.einsum("ij,ij->i", base_velocity(bpts), tangents) + delta_star = float(delta_star_scale) * radius / np.maximum(np.abs(u_e), 0.25) + product = u_e * delta_star + v_n = np.zeros(len(bpts)) + for ib in range(len(c)): + sl = body_index == ib + s = np.linspace(0.0, _TWOPI * radius, int(sl.sum()), endpoint=False) + v_n[sl] = np.gradient(product[sl], s) + v_n = _zero_mean_per_body(v_n, body_index, len(c), n_boundary) + return {"boundary_points": bpts, "normals": nrms, "v_n": v_n, + "body_index": body_index, "wall_speed": wall["speed"], + "edge_speed": u_e, "zero_mean_per_body": True} + + +def solve_mfs_neumann(centers, radius, normal_velocity, *, circulations=None, + u_inf=1.0, n_boundary=96, source_ratio=0.65, H=None, + image_layers=20): + """MFS Neumann solve with optional zero-mean transpiration on each body.""" + c, radius, gam, H = _geometry(centers, radius, circulations, H) + if gam is None: + gam = np.zeros(len(c)) + n_boundary = _integer("n_boundary", n_boundary, 8) + c, radius, bpts, nrms, _, body_index, _, _ = _boundary_sample( + c, radius, n_boundary) + vn = np.asarray(normal_velocity, dtype=float) + if vn.shape != bpts.shape[:1] or not np.isfinite(vn).all(): + raise ValueError("normal_velocity must align with boundary samples") + for ib in range(len(c)): + sl = body_index == ib + if abs(float(np.mean(vn[sl]))) > 1e-10: + raise ValueError("normal_velocity must have zero mean on every body") + base = np.zeros_like(bpts) + base[:, 0] = float(u_inf) + for gamma, ci in zip(gam, c): + base += gamma * singular_velocity( + bpts, ci, H=H, layers=image_layers, vortex=True) + rhs = vn - np.einsum("ij,ij->i", base, nrms) + theta = (np.arange(n_boundary) + 0.5) * _TWOPI / n_boundary + normals0 = np.column_stack((np.cos(theta), np.sin(theta))) + spts = np.concatenate([ci + source_ratio * radius * normals0 for ci in c]) + cols = [] + for ib in range(len(c)): + ref = spts[(ib + 1) * n_boundary - 1] + vr = singular_velocity(bpts, ref, H=H, layers=image_layers) + for j in range(n_boundary - 1): + v = singular_velocity( + bpts, spts[ib * n_boundary + j], H=H, layers=image_layers) - vr + cols.append(np.einsum("ij,ij->i", v, nrms)) + A = np.column_stack(cols) + coeff, _, rank, sv = np.linalg.lstsq(A, rhs, rcond=1e-12) + if rank != A.shape[1]: + raise np.linalg.LinAlgError(f"rank-deficient MFS Neumann system: {rank}/{A.shape[1]}") + strengths = np.zeros(len(spts)) + k = 0 + for ib in range(len(c)): + q = coeff[k:k + n_boundary - 1] + k += n_boundary - 1 + strengths[ib * n_boundary:(ib + 1) * n_boundary - 1] = q + strengths[(ib + 1) * n_boundary - 1] = -np.sum(q) + sol = MFSSolution(c, radius, strengths, spts, gam, float(u_inf), H, image_layers) + residual = np.einsum("ij,ij->i", sol.velocity(bpts), nrms) - vn + diag = { + "collocation_Linf": float(np.max(np.abs(residual))), + "collocation_RMS": float(np.sqrt(np.mean(residual**2))), + "rank": int(rank), "condition": float(sv[0] / sv[-1]), + "zero_source_error": [float(abs(x.sum())) for x in strengths.reshape(len(c), -1)], + } + return sol, diag + + +def solve_mfs_transpiration(centers, radius, omega, *, branch, u_inf=1.0, + delta_star_scale=0.05, **kwargs): + """Zero-circulation outer field plus moving-wall transpiration response.""" + zero, _ = solve_mfs(centers, radius, np.zeros(len(np.asarray(centers))), u_inf=u_inf, **kwargs) + if branch == "plus-minus": + om = np.asarray([0.0, +abs(omega), -abs(omega)], dtype=float) + elif branch == "minus-plus": + om = np.asarray([0.0, -abs(omega), +abs(omega)], dtype=float) + else: + raise ValueError("branch must be 'plus-minus' or 'minus-plus'") + if float(np.max(np.abs(om))) <= 0.0: + zero, d0 = solve_mfs(centers, radius, np.zeros(len(np.asarray(centers))), u_inf=u_inf, **kwargs) + return {"base": zero, "transpiration": zero, "rhs": {"v_n": np.zeros(1)}, + "diagnostics": d0, "zero_rotation": True} + rhs = displacement_transpiration_rhs( + centers, radius, om, zero.velocity, delta_star_scale=delta_star_scale, + n_boundary=kwargs.get("n_boundary", 96)) + resp, diag = solve_mfs_neumann( + centers, radius, rhs["v_n"], circulations=np.zeros(len(np.asarray(centers))), + u_inf=u_inf, **kwargs) + return {"base": zero, "transpiration": resp, "rhs": rhs, "diagnostics": diag} + + +def gap_couette_poiseuille_section(gap_height, u_wall_a, u_wall_b, *, + dp_dx=0.0, nu=None): + """Parallel-plate Couette–Poiseuille section oracle (finite-gap ansatz). + + Returns oriented mass flux Q_g, momentum flux J_g, mean velocity, and power + scale per unit span. Not a lubrication-theory claim at h/D=0.5. + """ + h = float(gap_height) + ua = float(u_wall_a) + ub = float(u_wall_b) + if h <= 0 or not np.isfinite([h, ua, ub, dp_dx]).all(): + raise ValueError("invalid Couette–Poiseuille inputs") + if nu is None and dp_dx != 0.0: + raise ValueError("nonzero dp_dx requires explicit finite positive nu") + if nu is None: + nu_value = None + u_mean = 0.5 * (ua + ub) + profile = lambda eta: ua + (ub - ua) * eta + else: + nu_value = float(nu) + if not np.isfinite(nu_value) or nu_value <= 0: + raise ValueError("nu must be finite and positive when provided") + u_mean = 0.5 * (ua + ub) - h * h * dp_dx / (12.0 * nu_value) + profile = lambda eta: ua + (ub - ua) * eta - dp_dx * h * h / (2.0 * nu_value) * eta * (1.0 - eta) + eta = np.linspace(0.0, 1.0, 201) + u = profile(eta) + q_g = float(h * u_mean) + j_g = float(h * np.sum(.5*((u*u)[:-1]+(u*u)[1:])*np.diff(eta))) + shear = (ub - ua) / h - (0.0 if nu_value is None else 0.5 * h * dp_dx / nu_value) + power = float(abs(shear * (ub - ua) * h)) + return {"Q_g": q_g, "J_g": j_g, "u_mean": float(u_mean), + "gap_height": h, "u_wall_a": ua, "u_wall_b": ub, + "dp_dx": float(dp_dx), "power_scale": power} + + +def _gap_wall_speeds(centers, radius, omega, branch): + """Gap-facing tangential speeds for rear–rear and front–rear segments.""" + c = np.asarray(centers, dtype=float) + if branch == "plus-minus": + om = np.asarray([0.0, +abs(omega), -abs(omega)], dtype=float) + elif branch == "minus-plus": + om = np.asarray([0.0, -abs(omega), +abs(omega)], dtype=float) + else: + raise ValueError("branch must be 'plus-minus' or 'minus-plus'") + r = float(radius) + # Gap-facing cardinals from contract oracle geometry. + upper_gap = om[1] * r + lower_gap = -om[2] * r + front_upper = om[0] * r + front_lower = -om[0] * r + rear_rear_h = float(np.linalg.norm(c[1] - c[2]) - 2.0 * r) + front_upper_h = float(np.linalg.norm(c[0] - c[1]) - 2.0 * r) + front_lower_h = float(np.linalg.norm(c[0] - c[2]) - 2.0 * r) + return { + "rear_rear": gap_couette_poiseuille_section(rear_rear_h, upper_gap, lower_gap), + "front_upper": gap_couette_poiseuille_section(front_upper_h, front_upper, upper_gap), + "front_lower": gap_couette_poiseuille_section(front_lower_h, front_lower, lower_gap), + } + + +def gap_jet_velocity_field(points, center_a, center_b, radius, gap_oracle, *, + jet_decay=0.35, strength=1.0): + """Localized gap-momentum jet along the shortest open segment.""" + p = _points(points) + a = np.asarray(center_a, dtype=float) + b = np.asarray(center_b, dtype=float) + d = b - a + length = float(np.linalg.norm(d)) + if length <= 2.0 * radius: + raise ValueError("invalid gap geometry") + tangent = d / length + normal = np.array([-tangent[1], tangent[0]]) + mid = 0.5 * (a + b) + t = np.clip(np.einsum("ij,j->i", p - a, tangent), radius, length - radius) + closest = a + t[:, None] * tangent + dist = np.linalg.norm(p - closest, axis=1) + envelope = np.exp(-(dist / (jet_decay * radius)) ** 2) + u_mag = float(strength) * float(gap_oracle["u_mean"]) + vel = envelope[:, None] * (u_mag * normal) + return vel + + +def wake_gaussian_deficit(points, *, x0, amplitude, width, u_conv=1.0, diffusivity=0.02): + """Convected Gaussian streamwise deficit; parameters from near field only.""" + p = _points(points) + x = p[:, 0] - float(x0) + y = p[:, 1] + if float(u_conv) <= 0 or float(width) <= 0: + raise ValueError("u_conv and width must be positive") + sigma2 = float(width) ** 2 + np.maximum(0.0, 2.0 * float(diffusivity) * x / float(u_conv)) + sigma = np.sqrt(sigma2) + decay = np.exp(-np.maximum(x, 0.0) * float(u_conv) / max(4.0 * float(diffusivity), 1e-12)) + du = -float(amplitude) * decay * np.exp(-0.5 * (y / sigma) ** 2) + return np.column_stack((du, np.zeros_like(du))) + + +def composite_model_fields(points, *, centers, radius, omega, branch, s=None, + coeffs=None, H=15.0, u_inf=1.0, n_boundary=96, + source_ratio=0.65, image_layers=40, + delta_star_scale=0.05, jet_decay=0.35, + wake_x0=2.0, wake_diffusivity=0.02): + """Evaluate q_MFS0, q_VI, q_gap, q_wake and weighted composite q_SA.""" + p = _points(points) + c = np.asarray(centers, dtype=float) + if coeffs is None: + coeffs = {"alpha_vi": 1.0, "alpha_gap": 1.0, "wake_amplitude": 0.0, + "wake_width": 0.5, "gamma": 0.0} + mfs0, _ = solve_mfs(c, radius, np.zeros(len(c)), u_inf=u_inf, H=H, + n_boundary=n_boundary, source_ratio=source_ratio, + image_layers=image_layers) + q0 = mfs0.velocity(p) + vi = solve_mfs_transpiration( + c, radius, float(omega), branch=branch, u_inf=u_inf, H=H, + n_boundary=n_boundary, source_ratio=source_ratio, + image_layers=image_layers, delta_star_scale=delta_star_scale) + q_vi = vi["transpiration"].velocity(p) - q0 + gaps = _gap_wall_speeds(c, radius, omega, branch) + q_gap = np.zeros_like(p) + for key, pair in (("rear_rear", (c[1], c[2])), + ("front_upper", (c[0], c[1])), + ("front_lower", (c[0], c[2]))): + q_gap += gap_jet_velocity_field( + p, pair[0], pair[1], radius, gaps[key], + jet_decay=jet_decay, strength=float(coeffs.get("alpha_gap", 1.0))) + q_wake = wake_gaussian_deficit( + p, x0=wake_x0, amplitude=float(coeffs.get("wake_amplitude", 0.0)), + width=float(coeffs.get("wake_width", 0.5)), u_conv=u_inf, + diffusivity=wake_diffusivity) + if abs(float(coeffs.get("gamma", 0.0))) > 0: + basis = circulation_basis("rear_opposite") + gfield, _ = solve_mfs(c, radius, float(coeffs["gamma"]) * basis, u_inf=u_inf, + H=H, n_boundary=n_boundary, source_ratio=source_ratio, + image_layers=image_layers) + q_gamma = gfield.velocity(p) - q0 + else: + q_gamma = np.zeros_like(p) + alpha_vi = float(coeffs.get("alpha_vi", 1.0)) + composite = q0 + alpha_vi * q_vi + q_gap + q_wake + q_gamma + return { + "q_mfs0": q0, "q_vi": q_vi, "q_gap": q_gap, "q_wake": q_wake, + "q_gamma": q_gamma, "q_sa": composite, "gaps": gaps, + "transpiration_rhs": vi["rhs"], "coeffs": dict(coeffs), + } + + +def _free_vortices(positions, strengths, centers=None, radius=None): + x = _points(positions) + kappa = np.asarray(strengths, dtype=float) + if len(x) == 0 or kappa.shape != (len(x),) or not np.isfinite(kappa).all(): + raise ValueError("strengths must be one finite value per nonempty vortex position") + if len(x) > 1: + separation = np.linalg.norm(x[:, None, :] - x[None, :, :], axis=2) + np.fill_diagonal(separation, np.inf) + if np.any(separation <= 1e-12): + raise ValueError("free vortices must be distinct") + if centers is not None: + distance = np.linalg.norm(x[:, None, :] - centers[None, :, :], axis=2) + if np.any(distance <= radius * (1.0 + 1e-12)): + raise ValueError("free vortices must lie strictly outside every cylinder") + return x, kappa + + +def mutual_vortex_velocity(positions, strengths): + """Physical mutual induction, with every singular self term omitted.""" + x, kappa = _free_vortices(positions, strengths) + velocity = np.zeros_like(x) + for i in range(len(x)): + for j in range(len(x)): + if i != j: + velocity[i] += kappa[j] * singular_velocity( + x[i:i + 1], x[j], vortex=True)[0] + if not np.isfinite(velocity).all(): + raise FloatingPointError("nonfinite mutual vortex velocity") + return velocity + + +@dataclass +class MFSBodyResponse: + """Reusable unbounded zero-period MFS Neumann-response discretization.""" + centers: np.ndarray + radius: float + boundary_points: np.ndarray + normals: np.ndarray + source_points: np.ndarray + matrix: np.ndarray + n_boundary: int + + def response(self, vortex_positions, vortex_strengths): + x, kappa = _free_vortices( + vortex_positions, vortex_strengths, self.centers, self.radius) + incident = np.zeros_like(self.boundary_points) + for position, strength in zip(x, kappa): + incident += strength * singular_velocity( + self.boundary_points, position, vortex=True) + rhs = -np.einsum("ij,ij->i", incident, self.normals) + coeff, _, rank, sv = np.linalg.lstsq(self.matrix, rhs, rcond=1e-12) + if rank != self.matrix.shape[1]: + raise np.linalg.LinAlgError( + f"rank-deficient MFS response: rank {rank}/{self.matrix.shape[1]}") + if not np.isfinite(coeff).all() or not np.isfinite(sv).all() or sv[-1] <= 0: + raise FloatingPointError("nonfinite or singular MFS response solve") + strengths = np.zeros(len(self.source_points)) + k = 0 + for ib in range(len(self.centers)): + q = coeff[k:k + self.n_boundary - 1] + k += self.n_boundary - 1 + sl = slice(ib * self.n_boundary, (ib + 1) * self.n_boundary) + strengths[sl.start:sl.stop - 1] = q + strengths[sl.stop - 1] = -np.sum(q) + return MFSSolution( + self.centers.copy(), self.radius, strengths, + self.source_points.copy(), np.zeros(len(self.centers)), 0.0, None, 0) + + +def prepare_unbounded_body_response(centers, radius, *, n_boundary=96, + source_ratio=0.65): + """Preassemble the geometry-only MFS matrix for free-vortex responses.""" + c, radius, _, _ = _geometry(centers, radius) + n_boundary = _integer("n_boundary", n_boundary, 8) + if (not np.isscalar(source_ratio) or not np.isfinite(source_ratio) or + not 0 < source_ratio < 1): + raise ValueError("source_ratio must satisfy 0 < source_ratio < 1") + theta = (np.arange(n_boundary) + 0.5) * _TWOPI / n_boundary + normals0 = np.column_stack((np.cos(theta), np.sin(theta))) + boundary = np.concatenate([center + radius * normals0 for center in c]) + normals = np.tile(normals0, (len(c), 1)) + sources = np.concatenate([ + center + float(source_ratio) * radius * normals0 for center in c]) + columns = [] + for ib in range(len(c)): + reference = sources[(ib + 1) * n_boundary - 1] + reference_velocity = singular_velocity(boundary, reference) + for j in range(n_boundary - 1): + velocity = (singular_velocity(boundary, sources[ib * n_boundary + j]) + - reference_velocity) + columns.append(np.einsum("ij,ij->i", velocity, normals)) + matrix = np.column_stack(columns) + if np.linalg.matrix_rank(matrix, tol=1e-12) != matrix.shape[1]: + raise np.linalg.LinAlgError("rank-deficient MFS response geometry") + return MFSBodyResponse(c, radius, boundary, normals, sources, matrix, n_boundary) + + +def finite_vortex_rhs(base_solution, vortex_positions, vortex_strengths, *, + body_response=None): + """Unbounded point-vortex RHS with physical self omitted, response retained.""" + if not isinstance(base_solution, MFSSolution) or base_solution.H is not None: + raise ValueError("base_solution must be an unbounded MFSSolution") + x, kappa = _free_vortices( + vortex_positions, vortex_strengths, + base_solution.centers, base_solution.radius) + if body_response is None: + per_body = len(base_solution.source_points) // len(base_solution.centers) + body_response = prepare_unbounded_body_response( + base_solution.centers, base_solution.radius, n_boundary=per_body) + if (not isinstance(body_response, MFSBodyResponse) or + body_response.centers.shape != base_solution.centers.shape or + not np.allclose(body_response.centers, base_solution.centers, + rtol=0.0, atol=1e-14) or + not np.isclose(body_response.radius, base_solution.radius, + rtol=0.0, atol=1e-14)): + raise ValueError("body_response geometry must match base_solution") + response = body_response.response(x, kappa) + rhs = (base_solution.velocity(x) + mutual_vortex_velocity(x, kappa) + + response.velocity(x)) + if not np.isfinite(rhs).all(): + raise FloatingPointError("nonfinite finite-vortex RHS") + return rhs + + + +def vas_foppl_hamiltonian(position, kappa): + """Vasconcelos et al. (2012), eq. (7); quarantined Föppl oracle (not steady claim).""" + point = np.asarray(position, dtype=float) + if point.shape != (2,) or not np.isfinite(point).all(): + raise ValueError("position must be a finite 2-vector") + if not np.isscalar(kappa) or not np.isfinite(kappa) or kappa <= 0: + raise ValueError("kappa must be finite and positive") + x, y = point + r2 = x * x + y * y + if y <= 0 or r2 <= 1.0: + raise ValueError("Vas symmetric coordinates require y > 0 and r^2 > 1") + logarithm_argument = y * (r2 - 1.0) / np.sqrt((r2 - 1.0)**2 + 4.0 * y * y) + return float(y * (1.0 - 1.0 / r2) + - 0.5 * float(kappa) * np.log(logarithm_argument)) + + +def vas_critical_hamiltonian(kappa): + """Hamiltonian level at Vas eq. (13) infinity saddle, paper eq. (26).""" + if not np.isscalar(kappa) or not np.isfinite(kappa) or kappa <= 0: + raise ValueError("kappa must be finite and positive") + return float(0.5 * kappa * (1.0 - np.log(0.5 * kappa))) + + +def vas_foppl_rhs(position, kappa): + """Canonical RHS (dx/dt,dy/dt)=(dH/dy,-dH/dx) for the Vas Hamiltonian.""" + point = np.asarray(position, dtype=float) + vas_foppl_hamiltonian(point, kappa) + x, y = point + r2 = x * x + y * y + gap = r2 - 1.0 + denominator = gap * gap + 4.0 * y * y + dlog_dx = 2.0 * x / gap - 2.0 * x * gap / denominator + dlog_dy = 1.0 / y + 2.0 * y / gap - 2.0 * y * (gap + 2.0) / denominator + dH_dx = 2.0 * x * y / (r2 * r2) - 0.5 * float(kappa) * dlog_dx + dH_dy = (1.0 - 1.0 / r2 + 2.0 * y * y / (r2 * r2) + - 0.5 * float(kappa) * dlog_dy) + return np.array([dH_dy, -dH_dx]) + + +def vas_foppl_equilibrium(radius): + """Return downstream Foppl (x0,y0,kappa) from Vas et al. eqs. (9)-(10).""" + if not np.isscalar(radius) or not np.isfinite(radius) or radius <= 1.0: + raise ValueError("radius must be finite and greater than one") + r0 = float(radius) + y0 = (r0 * r0 - 1.0) / (2.0 * r0) + x0 = np.sqrt(r0 * r0 - y0 * y0) + kappa = (r0 * r0 + 1.0) * (r0 * r0 - 1.0)**2 / r0**5 + return np.array([x0, y0]), float(kappa) + + +def exact_circle_vortex_response(vortex_position, vortex_strength, *, + center=(0.0, 0.0), radius=1.0): + """Exact zero-period response to one exterior vortex around one circle. + + A physical geometric-CCW vortex Gamma at z0 is paired with image -Gamma at + c+a^2(z0-c)/|z0-c|^2 and central +Gamma, restoring zero island circulation. + The regular self velocity retains both image terms (Routh rule). + """ + c, radius, _, _ = _geometry([center], radius) + position, strength = _free_vortices( + [vortex_position], [vortex_strength], c, radius) + z0 = position[0] + gamma = float(strength[0]) + relative = z0 - c[0] + image = c[0] + radius * radius * relative / np.dot(relative, relative) + + def velocity(points): + p = _points(points) + return gamma * (singular_velocity(p, c[0], vortex=True) + - singular_velocity(p, image, vortex=True)) + + regular_self = velocity(z0[None, :])[0] + hamiltonian = (gamma * gamma / (4.0 * np.pi) + * np.log((np.dot(relative, relative) - radius * radius) + / np.dot(relative, relative))) + return { + "image_position": image, "image_strength": -gamma, + "central_strength": gamma, "regular_self_velocity": regular_self, + "hamiltonian": float(hamiltonian), "velocity": velocity, + } + + +def staggered_karman_train(half_window, *, spacing=1.0, separation=0.281, + circulation=1.0): + """Finite unconfined Karman street; quarantined oracle (not steady claim path). + + Lower row: (m*a,-h/2), -Gamma. Upper row: ((m+1/2)*a,+h/2), +Gamma, + over the symmetric streamwise window |x| <= (half_window+1/2)*a. + """ + half_window = _integer("half_window", half_window, 0) + values = np.asarray([spacing, separation, circulation], dtype=float) + if not np.isfinite(values).all() or spacing <= 0 or separation <= 0: + raise ValueError("spacing and separation must be finite and positive") + lower_m = np.arange(-half_window, half_window + 1, dtype=float) + upper_m = np.arange(-half_window - 1, half_window + 1, dtype=float) + lower = np.column_stack((lower_m * float(spacing), + np.full(len(lower_m), -0.5 * float(separation)))) + upper = np.column_stack(((upper_m + 0.5) * float(spacing), + np.full(len(upper_m), 0.5 * float(separation)))) + positions = np.concatenate((lower, upper)) + strengths = np.concatenate((np.full(len(lower_m), -float(circulation)), + np.full(len(upper_m), float(circulation)))) + return positions, strengths + + +def karman_self_advection(spacing, separation, circulation): + """Positive-x infinite-street speed; quarantined Karman oracle only.""" + values = np.asarray([spacing, separation, circulation], dtype=float) + if not np.isfinite(values).all() or spacing <= 0 or separation <= 0: + raise ValueError("spacing and separation must be finite and positive") + return float(circulation) / (2.0 * float(spacing)) * np.tanh( + np.pi * float(separation) / float(spacing)) + + +def karman_stable_aspect(): + """Unconfined von Karman neutral aspect p0=h/a; quarantined oracle only.""" + return float(np.arcsinh(1.0) / np.pi) + + + +def point_vortex_hamiltonian(positions, strengths, *, reference_length=1.0): + """Finite-plane Hamiltonian matching mutual_vortex_velocity exactly. + + The reference length fixes the logarithm's dimensionless argument; no + configuration-dependent additive constant is introduced. + """ + x, kappa = _free_vortices(positions, strengths) + if (not np.isscalar(reference_length) or not np.isfinite(reference_length) + or reference_length <= 0): + raise ValueError("reference_length must be finite and positive") + i, j = np.triu_indices(len(x), 1) + distance = np.linalg.norm(x[i] - x[j], axis=1) + return float(-np.sum(kappa[i] * kappa[j] + * np.log(distance / float(reference_length))) / _TWOPI) + + +def point_vortex_rhs(positions, strengths, *, collision_distance=1e-6): + """Vectorized unbounded point-vortex RHS with collision fail-fast.""" + x, kappa = _free_vortices(positions, strengths) + if (not np.isscalar(collision_distance) or not np.isfinite(collision_distance) + or collision_distance <= 0): + raise ValueError("collision_distance must be finite and positive") + delta = x[:, None, :] - x[None, :, :] + radius2 = np.einsum("ijk,ijk->ij", delta, delta) + np.fill_diagonal(radius2, np.inf) + if np.min(radius2) <= float(collision_distance)**2: + raise ValueError("point-vortex collision threshold reached") + weights = kappa[None, :] / (_TWOPI * radius2) + velocity = np.column_stack((-np.sum(weights * delta[:, :, 1], axis=1), + np.sum(weights * delta[:, :, 0], axis=1))) + if not np.isfinite(velocity).all(): + raise FloatingPointError("nonfinite point-vortex RHS") + return velocity + + +def integrate_point_vortices_rk4(positions, strengths, *, horizon, time_step, + collision_distance=1e-6, + reference_length=1.0): + """Deterministic fixed-step classical RK4 point-vortex integration.""" + x, kappa = _free_vortices(positions, strengths) + values = np.asarray([horizon, time_step, collision_distance, + reference_length], dtype=float) + if (not np.isfinite(values).all() or horizon <= 0 or time_step <= 0 + or collision_distance <= 0 or reference_length <= 0): + raise ValueError("integration scales must be finite and positive") + states = [x.copy()] + times = [0.0] + hamiltonians = [point_vortex_hamiltonian( + x, kappa, reference_length=reference_length)] + time = 0.0 + while time < float(horizon): + dt = min(float(time_step), float(horizon) - time) + k1 = point_vortex_rhs(x, kappa, collision_distance=collision_distance) + k2 = point_vortex_rhs(x + 0.5 * dt * k1, kappa, + collision_distance=collision_distance) + k3 = point_vortex_rhs(x + 0.5 * dt * k2, kappa, + collision_distance=collision_distance) + k4 = point_vortex_rhs(x + dt * k3, kappa, + collision_distance=collision_distance) + x = x + dt * (k1 + 2*k2 + 2*k3 + k4) / 6.0 + if not np.isfinite(x).all(): + raise FloatingPointError("nonfinite RK4 state") + point_vortex_rhs(x, kappa, collision_distance=collision_distance) + time += dt + states.append(x.copy()) + times.append(time) + hamiltonians.append(point_vortex_hamiltonian( + x, kappa, reference_length=reference_length)) + return {"times": np.asarray(times), "states": np.asarray(states), + "hamiltonian": np.asarray(hamiltonians)} + + +@dataclass +class LaurentSolution: + centers: np.ndarray + radius: float + coefficients: np.ndarray + u_inf: float + + def velocity(self, points): + p = _points(points) + z = p[:, 0] + 1j * p[:, 1] + q = np.full(len(p), self.u_inf, dtype=complex) + order = self.coefficients.shape[1] + for center, coeffs in zip(self.centers, self.coefficients): + dz = z - complex(*center) + if np.any(np.abs(dz) <= self.radius): + raise ValueError("Laurent velocity requires strict exterior points") + for n in range(1, order + 1): + q += -n * coeffs[n - 1] * self.radius**n / dz**(n + 1) + v = np.column_stack((q.real, -q.imag)) + if not np.isfinite(v).all(): + raise FloatingPointError("nonfinite Laurent velocity") + return v + + +def solve_laurent(centers, radius, *, u_inf=1.0, order=12, n_boundary=None): + """Independent zero-circulation unbounded Fourier/Laurent collocation.""" + c, radius, _, _ = _geometry(centers, radius) + if not np.isscalar(u_inf) or not np.isfinite(u_inf): + raise ValueError("u_inf must be finite") + order = _integer("order", order, 1) + n_boundary = 4 * order if n_boundary is None else _integer("n_boundary", n_boundary, 2 * order) + theta = (np.arange(n_boundary) + 0.173) * _TWOPI / n_boundary + normals0 = np.column_stack((np.cos(theta), np.sin(theta))) + points = np.concatenate([ci + radius * normals0 for ci in c]) + normals = np.tile(normals0, (len(c), 1)) + z = points[:, 0] + 1j * points[:, 1] + cols = [] + for center in c: + dz = z - complex(*center) + for n in range(1, order + 1): + basis = -n * radius**n / dz**(n + 1) + for phase in (1.0, 1.0j): + q = phase * basis + vel = np.column_stack((q.real, -q.imag)) + cols.append(np.einsum("ij,ij->i", vel, normals)) + A = np.column_stack(cols) + rhs = -float(u_inf) * normals[:, 0] + x, _, rank, sv = np.linalg.lstsq(A, rhs, rcond=1e-12) + if rank != A.shape[1] or not np.isfinite(x).all() or sv[-1] <= 0: + raise np.linalg.LinAlgError("rank-deficient or nonfinite Laurent solve") + coeff = np.empty((len(c), order), dtype=complex) + k = 0 + for ib in range(len(c)): + for n in range(order): + coeff[ib, n] = x[k] + 1j * x[k + 1] + k += 2 + sol = LaurentSolution(c, radius, coeff, float(u_inf)) + collocation_residual = A @ x - rhs + # A distinct angular grid checks the boundary trace independently of the + # solve nodes. The tiny radial offset only satisfies strict-exterior evaluation. + check_theta = (np.arange(3 * n_boundary + 1) + 0.61803398875) * _TWOPI / (3 * n_boundary + 1) + check_normals0 = np.column_stack((np.cos(check_theta), np.sin(check_theta))) + check_points = np.concatenate([ + ci + radius * (1.0 + 1e-10) * check_normals0 for ci in c + ]) + check_normals = np.tile(check_normals0, (len(c), 1)) + offgrid_residual = np.einsum( + "ij,ij->i", sol.velocity(check_points), check_normals + ) + return sol, { + "collocation_Linf": float(np.max(np.abs(collocation_residual))), + "off_collocation_Linf": float(np.max(np.abs(offgrid_residual))), + "off_collocation_RMS": float(np.sqrt(np.mean(offgrid_residual**2))), + "off_collocation_angles_per_body": int(len(check_theta)), + "rank": int(rank), "unknowns": int(A.shape[1]), + "condition": float(sv[0] / sv[-1]), + "coefficient_L2": float(np.linalg.norm(coeff)), + } + + +def dense_diagnostics(solution, *, n_angle=2048, wall_interval=None, n_wall=1001, + contour_factor=1.08, far_radius=50.0, n_far=720): + """Independent shifted-node boundary, circulation, wall, and far-field diagnostics.""" + n_angle = _integer("n_angle", n_angle, 32) + n_far = _integer("n_far", n_far, 32) + c, radius, _, _ = _geometry(solution.centers, solution.radius, solution.circulations, + solution.H) + theta = (np.arange(n_angle) + 0.271828) * _TWOPI / n_angle + normals = np.column_stack((np.cos(theta), np.sin(theta))) + bodies = [] + for ib, center in enumerate(c): + points = center + radius * normals + residual = np.einsum("ij,ij->i", solution.velocity(points), normals) + if len(c) > 1: + vectors = np.delete(c, ib, axis=0) - center + target = vectors[np.argmin(np.linalg.norm(vectors, axis=1))] + angle = np.arctan2(target[1], target[0]) + delta = np.angle(np.exp(1j * (theta - angle))) + gap = np.abs(delta) <= np.pi / 3 + else: + gap = np.ones(n_angle, dtype=bool) + outer = ~gap if np.any(~gap) else gap + bodies.append({ + "Linf": float(np.max(np.abs(residual))), + "RMS": float(np.sqrt(np.mean(residual**2))), + "gap_Linf": float(np.max(np.abs(residual[gap]))), + "outer_Linf": float(np.max(np.abs(residual[outer]))), + }) + if not np.isfinite(contour_factor) or contour_factor <= 1: + raise ValueError("contour_factor must exceed one") + circulations = [] + tangent = np.column_stack((-np.sin(theta), np.cos(theta))) + for center in c: + points = center + contour_factor * radius * normals + trace = np.einsum("ij,ij->i", solution.velocity(points), tangent) + circulations.append(float(contour_factor * radius * _TWOPI * np.mean(trace))) + phi = (np.arange(n_far) + 0.4142) * _TWOPI / n_far + origin = np.mean(c, axis=0) + far_points = origin + far_radius * np.column_stack((np.cos(phi), np.sin(phi))) + far_error = solution.velocity(far_points) - np.array([solution.u_inf, 0.0]) + out = { + "off_collocation_bodies": bodies, + "circulation_integrals": circulations, + "circulation_errors": (np.asarray(circulations) - solution.circulations).tolist(), + "far_radius": float(far_radius), + "far_field_Linf": float(np.max(np.linalg.norm(far_error, axis=1))), + "far_field_RMS": float(np.sqrt(np.mean(np.sum(far_error**2, axis=1)))), + } + if solution.H is not None: + if wall_interval is None or len(wall_interval) != 2: + raise ValueError("strip diagnostics require wall_interval=(xmin,xmax)") + xmin, xmax = map(float, wall_interval) + if not np.isfinite([xmin, xmax]).all() or xmin >= xmax: + raise ValueError("wall_interval must be finite and increasing") + n_wall = _integer("n_wall", n_wall, 16) + x = np.linspace(xmin, xmax, n_wall) + p = np.concatenate((np.column_stack((x, np.full_like(x, solution.H))), + np.column_stack((x, np.full_like(x, -solution.H))))) + residual = solution.velocity(p)[:, 1] + out["strip_wall"] = { + "interval": [xmin, xmax], "samples_per_wall": n_wall, + "Linf": float(np.max(np.abs(residual))), + "RMS": float(np.sqrt(np.mean(residual**2))), + } + return out + + +@dataclass +class MultipoleSolution: + """Unbounded MFS source expansion through a finite bodywise order.""" + centers: np.ndarray + source_coefficients: np.ndarray + circulations: np.ndarray + u_inf: float + source_radii: np.ndarray + + def velocity(self, points): + p = _points(points) + z = p[:, 0] + 1j * p[:, 1] + q = np.full(len(p), self.u_inf, dtype=complex) + for center, coeffs, rho in zip(self.centers, self.source_coefficients, + self.source_radii): + dz = z - complex(*center) + if np.any(np.abs(dz) <= rho): + raise ValueError("multipole reconstruction requires points outside source rings") + for n, coefficient in enumerate(coeffs, start=1): + q += -n * coefficient / dz**(n + 1) + for gamma, center in zip(self.circulations, self.centers): + dz = z - complex(*center) + if np.any(np.abs(dz) <= 1e-12): + raise ValueError("evaluation at vortex center") + q += -1j * gamma / (_TWOPI * dz) + velocity = np.column_stack((q.real, -q.imag)) + if not np.isfinite(velocity).all(): + raise FloatingPointError("nonfinite multipole velocity") + return velocity + + +def source_multipole_coefficients(solution, order): + """Return A[j,n-1] for W_source=sum A[j,n-1]/(z-c_j)^n.""" + if solution.H is not None: + raise ValueError("unbounded source multipoles are not a strip asymptotic basis") + order = _integer("order", order, 1) + count = len(solution.centers) + if len(solution.strengths) % count: + raise ValueError("source points must be grouped uniformly by body") + per_body = len(solution.strengths) // count + coefficients = np.empty((count, order), dtype=complex) + radii = np.empty(count) + for j, center in enumerate(solution.centers): + sl = slice(j * per_body, (j + 1) * per_body) + strengths = solution.strengths[sl] + delta = (solution.source_points[sl, 0] + 1j * solution.source_points[sl, 1] + - complex(*center)) + if abs(np.sum(strengths)) > 1e-10: + raise ValueError("each body must have zero source monopole") + radii[j] = np.max(np.abs(delta)) + for n in range(1, order + 1): + coefficients[j, n - 1] = -np.sum(strengths * delta**n) / (_TWOPI * n) + return coefficients, radii + + +def reconstruct_multipoles(solution, order): + coefficients, radii = source_multipole_coefficients(solution, order) + return MultipoleSolution(solution.centers.copy(), coefficients, + solution.circulations.copy(), solution.u_inf, radii) + + +def far_field_coefficients(solution): + """Direct unbounded log and 1/z potential coefficients about the origin.""" + if solution.H is not None: + raise ValueError("unbounded Laurent coefficients do not describe strip asymptotics") + source_z = solution.source_points[:, 0] + 1j * solution.source_points[:, 1] + center_z = solution.centers[:, 0] + 1j * solution.centers[:, 1] + log_coefficient = (np.sum(solution.strengths) - 1j * np.sum(solution.circulations)) / _TWOPI + dipole_coefficient = (-np.sum(solution.strengths * source_z) + + 1j * np.sum(solution.circulations * center_z)) / _TWOPI + return {"log": complex(log_coefficient), "dipole": complex(dipole_coefficient)} + + +def rear_opposite_affine(centers, radius, *, u_inf=1.0, n_boundary=96, + source_ratio=0.65): + """Solve C(Gamma)=C0+Gamma*dC and its optimal real cancellation.""" + centers = np.asarray(centers, dtype=float) + if centers.shape != (3, 2): + raise ValueError("rear-opposite basis requires exactly three centers") + zero, _ = solve_mfs(centers, radius, [0.0, 0.0, 0.0], u_inf=u_inf, + n_boundary=n_boundary, source_ratio=source_ratio) + unit, _ = solve_mfs(centers, radius, [0.0, 1.0, -1.0], u_inf=u_inf, + n_boundary=n_boundary, source_ratio=source_ratio) + c0 = far_field_coefficients(zero)["dipole"] + dc = far_field_coefficients(unit)["dipole"] - c0 + if abs(dc) <= 1e-14: + raise FloatingPointError("rear-opposite dipole sensitivity is zero") + gamma = -float(np.real(np.conj(dc) * c0)) / float(abs(dc)**2) + residual = c0 + gamma * dc + scale = max(abs(c0), abs(gamma * dc), 1.0) + return { + "C0": c0, "dC": dc, "gamma_opt": gamma, "residual": residual, + "exact": bool(abs(residual) <= 1e-10 * scale), + } + + +_STAGE4_BASES = { + "rear_opposite": np.array([0.0, 1.0, -1.0]) / np.sqrt(2.0), + "common_rear": np.array([0.0, 1.0, 1.0]) / np.sqrt(2.0), + "front_only": np.array([1.0, 0.0, 0.0]), +} + + +def circulation_basis(name): + """Frozen unit-L2 geometric-CCW circulation counterfactual.""" + if name not in _STAGE4_BASES: + raise ValueError(f"unknown circulation basis {name!r}") + return _STAGE4_BASES[name].copy() + + +def basis_affine(centers, radius, name, *, u_inf=1.0, n_boundary=96, + source_ratio=0.65): + """Return exact MFS affine field/coefficient data for a frozen unit basis.""" + centers = np.asarray(centers, dtype=float) + if centers.shape != (3, 2): + raise ValueError("Stage-4 bases require exactly three centers") + basis = circulation_basis(name) + zero, _ = solve_mfs(centers, radius, np.zeros(3), u_inf=u_inf, + n_boundary=n_boundary, source_ratio=source_ratio) + unit, _ = solve_mfs(centers, radius, basis, u_inf=u_inf, + n_boundary=n_boundary, source_ratio=source_ratio) + c0 = far_field_coefficients(zero) + c1 = far_field_coefficients(unit) + return { + "name": name, "basis": basis, "zero": zero, "unit": unit, + "log0": c0["log"], "dlog": c1["log"] - c0["log"], + "C0": c0["dipole"], "dC": c1["dipole"] - c0["dipole"], + } + + +def affine_velocity(affine, amplitude, points): + """Evaluate u0 + amplitude*(u1-u0), exactly affine up to roundoff.""" + p = _points(points) + v0 = affine["zero"].velocity(p) + return v0 + float(amplitude) * (affine["unit"].velocity(p) - v0) + + + +def velocity_jacobian(velocity, point, *, step=2e-5): + """Centered finite-difference Jacobian D_x u at one interior point.""" + x = np.asarray(point, dtype=float) + if x.shape != (2,) or not np.isfinite(x).all(): + raise ValueError("point must be a finite 2-vector") + if not np.isscalar(step) or not np.isfinite(step) or step <= 0: + raise ValueError("step must be finite and positive") + columns = [] + for k in range(2): + delta = np.zeros(2); delta[k] = float(step) + plus = np.asarray(velocity((x + delta)[None, :]), dtype=float) + minus = np.asarray(velocity((x - delta)[None, :]), dtype=float) + if plus.shape != (1, 2) or minus.shape != (1, 2): + raise ValueError("velocity must return an aligned (N,2) array") + columns.append((plus[0] - minus[0]) / (2.0 * step)) + jacobian = np.column_stack(columns) + if not np.isfinite(jacobian).all(): + raise FloatingPointError("nonfinite velocity Jacobian") + return jacobian + + +def classify_stagnation_root(velocity, point, *, jacobian_step=2e-5, + nondegenerate_sigma=1e-4): + """Return residual and implicit-function diagnostics for one root candidate.""" + if not np.isfinite(nondegenerate_sigma) or nondegenerate_sigma <= 0: + raise ValueError("nondegenerate_sigma must be finite and positive") + x = np.asarray(point, dtype=float) + value = np.asarray(velocity(x[None, :]), dtype=float) + if value.shape != (1, 2) or not np.isfinite(value).all(): + raise ValueError("velocity must return a finite aligned (N,2) array") + jacobian = velocity_jacobian(velocity, x, step=jacobian_step) + singular_values = np.linalg.svd(jacobian, compute_uv=False) + return { + "point": x.copy(), "residual": float(np.linalg.norm(value[0])), + "jacobian": jacobian, "determinant": float(np.linalg.det(jacobian)), + "singular_values": singular_values, + "nondegenerate": bool(singular_values[-1] >= nondegenerate_sigma), + } + + +def find_interior_stagnation_points( + velocity, centers, radius, *, bounds=(-2.0, 5.0, -2.5, 2.5), + seed_shape=(29, 25), exclusion_margin=0.08, root_tolerance=1e-9, + deduplication_radius=2e-5, jacobian_step=2e-5, + nondegenerate_sigma=1e-4, max_iterations=40): + """Finite-seed Newton sampled audit of interior velocity roots. + + This routine does not assert global root completeness and excludes boundary roots. + """ + c, radius, _, _ = _geometry(centers, radius) + if len(bounds) != 4 or not np.isfinite(bounds).all(): + raise ValueError("bounds must contain four finite values") + xmin, xmax, ymin, ymax = map(float, bounds) + if xmin >= xmax or ymin >= ymax: + raise ValueError("bounds must be increasing") + if (len(seed_shape) != 2 or any(isinstance(n, (bool, np.bool_)) or + not isinstance(n, (int, np.integer)) or n < 2 for n in seed_shape)): + raise ValueError("seed_shape must contain two integers >= 2") + scales = [exclusion_margin, root_tolerance, deduplication_radius, + jacobian_step, nondegenerate_sigma] + if not np.isfinite(scales).all() or any(x <= 0 for x in scales): + raise ValueError("audit tolerances and margin must be finite and positive") + max_iterations = _integer("max_iterations", max_iterations, 1) + minimum_distance = radius + float(exclusion_margin) + + def admissible(x): + return (xmin <= x[0] <= xmax and ymin <= x[1] <= ymax and + np.all(np.linalg.norm(c - x, axis=1) >= minimum_distance)) + + xs = np.linspace(xmin, xmax, int(seed_shape[0])) + ys = np.linspace(ymin, ymax, int(seed_shape[1])) + roots = [] + attempted = 0 + for seed in np.array(np.meshgrid(xs, ys, indexing="xy")).reshape(2, -1).T: + if not admissible(seed): + continue + attempted += 1 + x = seed.copy() + converged = False + for _ in range(max_iterations): + try: + f = np.asarray(velocity(x[None, :]), dtype=float)[0] + if not np.isfinite(f).all(): + break + if np.linalg.norm(f) <= root_tolerance: + converged = True + break + jacobian = velocity_jacobian(velocity, x, step=jacobian_step) + step = np.linalg.lstsq(jacobian, -f, rcond=None)[0] + except (ValueError, FloatingPointError, np.linalg.LinAlgError): + break + if not np.isfinite(step).all() or np.linalg.norm(step) > 2.0: + break + accepted = False + for damping in (1.0, 0.5, 0.25, 0.125, 0.0625): + trial = x + damping * step + if admissible(trial): + try: + trial_norm = np.linalg.norm(velocity(trial[None, :])[0]) + except (ValueError, FloatingPointError): + continue + if np.isfinite(trial_norm) and trial_norm < np.linalg.norm(f): + x = trial; accepted = True; break + if not accepted: + break + if converged and admissible(x): + info = classify_stagnation_root( + velocity, x, jacobian_step=jacobian_step, + nondegenerate_sigma=nondegenerate_sigma) + if info["residual"] <= root_tolerance and not any( + np.linalg.norm(x - old["point"]) <= deduplication_radius + for old in roots): + roots.append(info) + roots.sort(key=lambda item: (item["point"][0], item["point"][1])) + return { + "kind": "sampled root audit", "bounds": [xmin, xmax, ymin, ymax], + "seed_shape": [int(seed_shape[0]), int(seed_shape[1])], + "attempted_seeds": attempted, "exclusion_margin": float(exclusion_margin), + "root_tolerance": float(root_tolerance), + "deduplication_radius": float(deduplication_radius), + "jacobian_step": float(jacobian_step), "roots": roots, + } + + +def continue_stagnation_points(reference_audit, candidate_audit, *, + maximum_displacement=0.2): + """One-to-one nearest matching for two sampled root audits.""" + if not np.isfinite(maximum_displacement) or maximum_displacement <= 0: + raise ValueError("maximum_displacement must be finite and positive") + reference = list(reference_audit.get("roots", [])) + candidate = list(candidate_audit.get("roots", [])) + pairs = [] + remaining = set(range(len(candidate))) + for i, root in enumerate(reference): + if not remaining: + break + j = min(remaining, key=lambda k: np.linalg.norm( + root["point"] - candidate[k]["point"])) + displacement = float(np.linalg.norm(root["point"] - candidate[j]["point"])) + pairs.append({ + "reference_index": i, "candidate_index": j, + "displacement": displacement, + "candidate_residual": candidate[j]["residual"], + "candidate_determinant": candidate[j]["determinant"], + "candidate_singular_values": candidate[j]["singular_values"].copy(), + "nondegenerate": candidate[j]["nondegenerate"], + }) + remaining.remove(j) + flagged = (len(reference) != len(candidate) or len(pairs) != len(reference) or + bool(remaining) or any(pair["displacement"] > maximum_displacement or + not pair["nondegenerate"] for pair in pairs)) + return { + "pairs": pairs, "reference_count": len(reference), + "candidate_count": len(candidate), "unmatched_candidate_indices": sorted(remaining), + "maximum_displacement": float(maximum_displacement), "flagged": bool(flagged), + } + + + +def strip_basis_affine(centers, radius, name, *, H, u_inf=1.0, n_boundary=96, + source_ratio=0.65, image_layers=40): + """Exact finite-image MFS affine basis for a free-slip strip.""" + centers=np.asarray(centers,dtype=float) + if centers.shape!=(3,2): raise ValueError("strip bases require exactly three centers") + basis=circulation_basis(name) + zero,d0=solve_mfs(centers,radius,np.zeros(3),u_inf=u_inf,n_boundary=n_boundary, + source_ratio=source_ratio,H=H,image_layers=image_layers) + unit,d1=solve_mfs(centers,radius,basis,u_inf=u_inf,n_boundary=n_boundary, + source_ratio=source_ratio,H=H,image_layers=image_layers) + return {"name":name,"basis":basis,"zero":zero,"unit":unit,"H":float(H), + "image_layers":int(image_layers),"zero_diagnostics":d0,"unit_diagnostics":d1} + + +def strip_mode_field(y, x, H, coefficients, *, origin=0.0, through_flow=0.0): + """Evaluate exact decaying harmonic velocity modes downstream of origin. + + With phi_n=B_n exp(-k_n dx) cos(k_n(y+H)), differentiation gives + (u_x,u_y)=-k_n B_n exp(-k_n dx)(cos,sin). The input is the + velocity amplitude A_n=-k_n B_n, so independently projected cosine + and sine coefficients have equal signs; no fitting sign is inserted. + """ + y=np.asarray(y,dtype=float); x=np.asarray(x,dtype=float); a=np.asarray(coefficients,dtype=float) + if H<=0 or y.shape!=x.shape or a.ndim!=1 or not np.isfinite(y).all() or not np.isfinite(x).all() or not np.isfinite(a).all() or np.any(x

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