feat(theory): establish steady-cloak analytical baseline

Freeze the source-derived action contract and direct q-in objective so the new MFS strip model and serial CFD runner provide a compact, auditable basis for the steady-cloak study. Co-authored-by: Cursor <cursoragent@cursor.com>
2026-08-03 14:55:10 +08:00
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+# Reset campaign results and claim matrix
+
+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.
+
+## Sign oracle
+
+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:
+
+- `[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.
+
+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.
+
+## Rotation search
+
+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.
+
+## Numerical sensitivity
+
+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`.
+
+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.
+
+## Analytical representation and finite-Re interface
+
+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.
+
+## Claim matrix
+
+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.
+
+Bounded/descriptive:
+- empirical cold-start steadiness through `tU/D=250`;
+- circulation-dominated outer-flow interpretation;
+- lateral-domain sensitivity over `H/D=12-18`.
+
+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.