DynamisLab/docs/JFM_WYQ/FIGURE_PLANS/SECTION_06_FIGURE_SPEC.md

Section 6 figure specifications — Kármán mean fields and CCD

Status: textual production specification. Inventory and existing drafts do not imply manuscript-panel readiness.

Shared scientific identity

• Physical case: periodic Kármán cloak, parabolic-inflow/no-slip-wall channel configuration; inherited code label 100 retained in provenance only; use a neutral reference source-case label pending velocity-reference authority.
• Mean-field roles: target, physical zero, constant reference at the exact retained DRL physical action mean, and DRL.
• Primary mean estimand: coordinate-weighted vector RMS target error of retained role means on the exact four-role common solver-fluid mask, inclusive 34<=x/D<=54, |y/D|<=5, 80,200 fluid points. Persisted velocity is already nondimensional.
• Residual identity: separately centred DRL cycle/bin field minus the separate constant-control 19-cycle ensemble phase template; 19 DRL cycles × 10 bins, N=190, no cross-role pairing.
• Internal provenance only: current corrected result and publication paths may retain internal chain identifiers; captions use the physical configuration above.

S6-1 — Mean streamwise correction and vector-error accounting

Argumentative job

Show the physically legible streamwise pattern first—passive deficit relative to target and controlled addition relative to physical zero—then bind it to the exact two-component scalar error-reduction estimand. Establish mean dominance without calling it a physical/causal contribution.

Exact layout

• Top row, four equal field panels (a–d): mean_target[u_x], mean_zero[u_x], mean_constant_mean[u_x], mean_drl[u_x].
• Bottom-left, two wider signed-difference panels (e–f): mean_zero[u_x] - mean_target[u_x]; mean_drl[u_x] - mean_zero[u_x].
• Bottom-right, one compact ledger (g): target-error markers/bars at zero 0.4694352273, constant 0.1110140739, DRL 0.0857787860; ordered brackets zero→constant=0.3584211534, constant→DRL=0.0252352879, total 0.3836564413; labels 93.42% and 6.58% explicitly as shares of the measured scalar error reduction.
• Crop every field to the declared ROI; show body/ROI context only in a small locator inset if needed, because bodies lie upstream of this ROI.

Variables and subtraction order

• Panels (a–d): retained mean streamwise velocity, not speed or vector magnitude.
• Panel (e): physical zero minus target. Negative values denote lower streamwise velocity than target under the repository coordinate/sign convention.
• Panel (f): DRL minus physical zero. Positive values denote streamwise velocity added relative to passive zero.
• The two fields are compared visually as signed complements; do not label one as an exact negative of the other.
• Ledger uses both u_x and u_y; it is not computed from panels (e–f) alone.

Roles, case, metric, ROI, mask and window

• Roles: target / physical zero / constant reference / DRL from one corrected four-role campaign.
• Case/configuration: periodic Kármán cloak, parabolic inflow and no-slip channel walls, inherited code label 100.
• Metric: E_r=[sum_K w_k ||mean(q_r)-q_target||_2^2/sum_K w_k]^(1/2); coordinate weights duplicated across both velocity components.
• ROI/mask: inclusive 34<=x/D<=54, |y/D|<=5; exact intersection of all four solver-derived fluid masks; 80,200 points.
• Window: retained means bound by the corrected role campaigns; do not substitute Section-4 complete-cycle standardized means. Exact retained role/window provenance must be copied into the final production manifest: role identities, parent source leaves and hashes, retained row/slice bounds, cycle/bin windows, mask/weight contract, array orientation/transposition, render command/revision, crop/scale/clipping, and output hashes. Until that record exists, production remains dependency-gated.

Data and artifact sources

• Exact arrays: /home/frank14f/optane/DynamisLab/ccd/karman-dynamic/canonical/results/roi-mean/arrays.npz.
• Result summary/manifest: same directory summary.json, manifest.json; source manifest hash f7f6141042678e52314a4d8f76d589108da8e844c8ce504f8f523a6f88a17e73.
• Repository authority: src/CCD_analysis/{RESULTS_INDEX.md,FINAL_RESULTS.md,MATHEMATICAL_DERIVATION.md,FIGURES_AND_DATA.md} and src/CCD_analysis/karman_dynamic/{CORRECTED_MATH_CONTRACT.md,dynamic_increment.py,publication.py}.
• Existing drafts: external and repository reader copy publication-review-fix-per-cycle-20260808T1736+0800/{01_roi_mean_performance,02_roi_mean_target_error_fields,03_roi_mean_corrections}.{png,pdf}.
• Existing render source: src/CCD_analysis/karman_dynamic/publication.py.

Readiness

• Arrays/values: ready and authority-bound.
• Existing useful panels: draft-ready only. 02 already contains zero-target for u_x/u_y; 01 supplies the scalar ledger; 03 supplies constant-zero and DRL-constant but not the requested DRL-zero.
• Requested composite: dependency-gated new render. DRL-zero must be directly calculated as mean_drl - mean_zero from the stored means and recorded in a future output manifest with input paths/hashes, subtraction order, units, orientation and output hash; no substitution by DRL-constant is allowed. No CFD or new scientific estimator is required.
• Independent sign check: weighted ROI mean-u_x cosine of requested fields -0.9961 and relative residual 0.1662 were computed read-only for design verification. Do not print these values unless the coordinator extends current claim authority.

Color and sign conventions

• Four absolute mean-u_x panels: one shared sequential or diverging scale chosen from all four arrays; label units/nondimensionalization exactly from authority. If a sequential scale obscures deviations, use a physically meaningful common scale but never independently autoscale roles.
• Difference panels: one shared symmetric diverging scale centred at zero, preferably RdBu_r; positive must mean the named first role has larger u_x under the printed subtraction.
• Mask non-fluid cells; transpose stored (x,y) arrays for plotting. Never infer sign from color without a labelled color bar.
• Optional zero contours on both difference panels should use identical styling.

Caption claim

“Relative to the target, the passive pinball produces a downstream mean-streamwise deficit over much of the declared wake ROI, while DRL adds a largely opposite-signed streamwise correction relative to physical zero. This pattern is compatible with adding streamwise velocity where the passive configuration produces a deficit. The scalar ledger evaluates both velocity components on the exact common mask: the constant reference accounts for 93.42% of the measured zero-to-DRL scalar mean-field error reduction and the constant-to-DRL increment accounts for the remaining 6.58%.”

Explicit non-claims

No momentum restoration; no exact cancellation; no closed momentum/energy budget; no causal actuator effect; no mechanism; no physical contribution percentage; no energy/explained variance; no SR-term share; no Section-4 replication/agreement; no cross-case universality.

Supplement fallback

If the seven-panel composition is illegible, retain panels (e–g) in main text and move the four absolute means to Supplement S6-S0. If raw composite production fails, use the existing scalar ledger plus zero-target draft and state that DRL-zero is omitted; do not substitute DRL-constant under the wrong label.

S6-2 — Non-paired residual and action-coordinate phase organization

Argumentative job

Explain what CCD adds after the mean ledger: a low-rank representation of the separately centred residual associated with action coordinates and organized over phase. Keep the result descriptive and avoid a mode gallery.

Exact layout

• Panel (a), left 25%: residual construction schematic with the equation U_(c,b)=(q^D_(c,b)-bar q_D)-(hat q^C_b-bar q_C), 19×10, and a visible “cycles not paired” annotation.
• Panel (b), centre 25%: compact 3×3 action-coordinate matrix or bars: rows front, rear-symmetric, rear-antisymmetric; columns modes 1–3. State global mode-sign arbitrariness.
• Panels (c–d), right 50%: rank-3 mean residual reconstructions at two registered representative phase bins nearest 0 and pi (use four bins nearest 0,pi/2,pi,3pi/2 only if final-size legibility passes). Show signed u_x; use the exact registered bins from representative_phase_bins.
• Do not include all individual mode fields in main text. A small rank/stability note may state rank 3, not singular-strength shares.

Variables, roles and estimand

• Field residual uses both velocity components internally; displayed phase reconstruction is u_x and must be labelled as a component view.
• Constant phase template is the ensemble mean over its own 19 cycles. DRL and constant cycles are not paired.
• Observable is same-boundary DRL effective action in native front/upper/lower order, exact retained physical action mean removed, then empirical centering.
• Operator: A=P_c(W^(1/2)U_c)^T/(N sqrt(3)), N=190, Q=1; no whitening, standardization, lag, wrap or POD preprojection.

Domain, source and readiness

• Preferred display domain: pinball-inclusive 29<=x/D<=54, |y/D|<=5, exact common-fluid mask, 99,264 points, M=198528.
• Preferred result: /home/frank14f/optane/DynamisLab/ccd/karman-dynamic/canonical/results/pinball-domain-20260809T1925+0800/, manifest hash 7e107a895364ed3e34abf2be513a3ce9e12736766ec6383c5b831891802d5828.
• Repository plot arrays: src/CCD_analysis/data/karman-dynamic/canonical/publication-pinball-domain-20260809T1925+0800/plot_data.npz and plot_data.json.
• Existing drafts: 01_domain_estimand, 02_ccd_mode_identity, 03_phase_reconstruction, 04_raw_pod_vs_ccd PNG/PDF groups.
• Render sources: src/CCD_analysis/karman_dynamic/{domain_comparison.py,mode_diagnostics.py,pod_baseline.py}; standalone single-mode redraw helper src/CCD_analysis/plot_ccd.py is insufficient for the full composite.
• Readiness: source arrays and existing views ready; manuscript recomposition dependency-gated. Phase panels may be extracted/redrawn without new CFD. The residual schematic is specification-ready.

Color and sign conventions

• Phase residual u_x: one shared robust symmetric diverging limit across selected phases, centred at zero.
• Mode/action columns: if individual mode signs are shown, use the same sign convention as the bound publication and state that global sign is arbitrary. Physical phase sign is carried by coefficient × mode, not mode color alone.
• Stored plot arrays use (x,y) and require transpose for display. Overlay exact mask; body circles are geometry guides only.

Caption claim

“After separate centring, the DRL fields are compared with an independently formed constant-control phase template; cycles are not paired. CCD associates the resulting rank-3 residual representation with centred same-boundary action coordinates and displays its phase organization. These are action-correlated correction-field modes, not causal responses or unique flow structures.”

Explicit non-claims

No paired counterfactual; no response time/lag; no causal direction; no actuator authority; no mechanism; no wall-vorticity interpretation; no explained variance from CCD singular strengths; no individual-mode stability claim; no SR derivation; no independent triangulation.

Supplement fallback

If action matrix plus phase fields remains crowded, main text keeps residual schematic + two phase reconstructions and moves action-coordinate matrix with all individual modes to S6-S1. Text then states the association without showing a mode gallery.

Shared normalized readiness

Plan specified; repository authorities and named repository copies read/path-confirmed, external absolute payloads mapped rather than newly audited, raw-array recomputation not-covered; S6-1/S6-2 estimands authority-bound but exact retained role/window and final render-manifest provenance dependency-gated; render redraw-required; disposition retain-with-gates. A partial plot manifest authenticates only available diagnostics, not completeness/readiness. Caption ceiling remains descriptive/noncausal and different-estimand; fallback uses existing scalar ledger plus zero-target, never a substituted difference.

S6-S1 — Raw POD boundary and CCD diagnostics (supplement)

Argumentative job and layout

Define familiar POD as a variance/energy-optimal field organization under the declared weighted metric without action information; compare its rank-3 subspace with CCD on the same centred residual. Use a compact principal-cosine strip/table plus optional aligned POD/CCD mode pairs and stability inset. Detailed mode parity and body-local rotation proxy, if retained, belong here.

Exact source and metric

• Same pinball-inclusive residual/domain/result as S6-2.
• Raw full-fit weighted POD Gram matrix G=U_c^T W U_c; no action observable selects POD.
• Principal cosines are singular values of Phi^T W Psi: [0.9999616609, 0.9998971005, 0.9976439804].
• Minimum declared bin/cycle rank-3 stability cosine 0.9974651867.
• Source: preferred 04_raw_pod_vs_ccd draft and compact result arrays; math in MATHEMATICAL_DERIVATION.md.

Readiness, caption and non-claims

Readiness: numerical and draft-view ready; publication recomposition required. Caption claim: POD and CCD span essentially the same tested rank-3 field subspace; CCD supplies action-coordinate association, not a distinct field basis. Do not claim CCD/POD superiority, exact identity, held-out prediction, independent uncertainty, unique modes, causal relevance or energy meaning for CCD singular strengths.

S6-S2 — Optional cross-cloak signed mean-u_x audit (supplement only)

Argumentative job

Test whether the visual zero-target / controlled-zero sign pattern recurs beyond the deep case without transferring its quantitative estimand or interpretation.

Candidate source inventory

• Linked root: src/drl_pinball/data/reproduction → external reproduction authority.
• Periodic phase_fields.npz normally stores mean_ux, mean_uy from complete cycles.
• Directly inspected available means:
  • parabolic/no-slip inherited Kármán labels karman_re50, karman_re100, karman_re200, karman_re400;
  • uniform/free-slip Reynolds cases kar_re60, five kar_re100 controlled realizations, kar_re200, kar_re400;
  • uniform/free-slip disturbance-size cases kar_d075, kar_d15, kar_d2.
• Existing images: src/drl_pinball/data/reproduction_plots/{legacy,v5}/*.png show phase-0 vorticity, not mean-u_x differences.
• Scripts: plot_reproduction_summary.py renders phase-0 vorticity; plot_flow_fields.py reads complete means but renders nonnegative vector target-error magnitude, not signed mean-u_x pairs.

Required layout and per-panel contract if commissioned

For each selected case, two adjacent fields: mean_zero[u_x]-mean_target[u_x] and mean_controlled[u_x]-mean_zero[u_x]. Print physical configuration, case, controlled realization/seed, complete-cycle role windows, mask policy and scale above each pair. Use shared symmetric scale within a case pair; use one global scale across cases only after unit/nondimensionalization and range audit. Never combine configurations in a common scalar score.

Readiness and dependencies

Source arrays: available for the cases listed. Existing signed plots: absent. Render code: absent for this exact panel. Panel readiness: S6-S2 remains blocked pending case selection, role/window and mask audit, nondimensionalization/scale decision, and a dedicated read-only renderer. A preliminary unweighted full-grid check found broadly opposite signs in most cases but weakening at harder/high-Re/large-disturbance conditions; it is diagnostic only and must not appear as a result.

Caption claim and non-claims

Allowed caption after audit: “Selected periodic cloak cases show qualitatively opposing passive-deficit and controlled-minus-passive mean-streamwise patterns under their own role and window contracts.” Prohibit common quantitative complementarity, exact cancellation, universal cloak mechanism, transfer of 93.42/6.58, transfer of the exact common-mask ROI, CCD interpretation, robustness/generalization, or momentum restoration.