# Round-3 revised candidate — Kármán performance

**Status:** targeted M04 revision completed; second-audit candidate, not final manuscript approval and not self-declared ready. This revision separates near-prose from provenance, makes Legacy Kármán Re100 the principal result, and retains V5 Re100 only as secondary support.

## Section question and bounded answer

**Question.** Under the named Kármán contracts, what does learned wake-signature matching achieve, and what independent field-matching evidence remains after the signal objective is separated from spatial evaluation?

**Bounded answer.** Under the Legacy `karman_re100` target/controlled/zero contract and its registered downstream ROI, the frozen PPO trajectory is closer to the target than physical zero in both complete-cycle mean-field and eight-slot phase-resolved L2; its normalized six-channel DTW is complementary evidence, not the field claim. V5 Re100 supplies secondary evidence that high-scoring checkpoint discovery repeats across five seeds while late retention varies, so the result remains named-condition field matching rather than a pooled or robust cross-chain conclusion.

## Layer 1 — concise near-prose draft

The principal comparison is the Legacy Kármán Re100 target, physical zero and frozen PPO trajectory, evaluated within one Legacy solver and geometry contract. Here `Re100` is the code convention `U_0(2D)/\nu=100` (`U_0=0.01`, `D=20`, `\nu=0.004`), equivalent to single-cylinder `Re_D=50`; it is not the V5 Re100 case under another name. In the registered rectangle `-6\le (x-x_s)/D\le14`, `|(y-y_0)/D|\le5`, with Legacy `x_s=800`, the controlled field is closer to the Legacy target than the corresponding physical-zero field. [Legacy field authority; Module 03]

The signal result is consistent with that field comparison but does not define it. Under the same 30-step window, lag channel and target-channel normalization, the Legacy controlled role has a six-channel target-normalized DTW similarity score of `0.932899`, higher than the zero role’s `0.625127`; the corresponding native reward-compatible similarity scores are `0.952132` for controlled and `0.688244` for zero. Higher scores indicate greater similarity. These are role-local Legacy quantities, not V5 scores, and they are never interpreted as errors or distances. DTW records signal alignment and similarity; it is not a spatial norm, physical delay or causal response. [Legacy Re100 `dtw_summary.json`; Module 03]

The independent field result is carried by spatial L2. For complete accepted cycles, the Legacy controlled mean-field error is `E_mean=0.085771`, versus `0.475206` for zero, giving `\eta_mean=0.819508`. The corresponding eight-slot phase diagnostic is `E_phase8=0.112680`, versus `0.630878` for zero, giving `\eta_phase8=0.821392`. Here `E_mean` is the `U_0`-normalized area-RMS difference between complete-cycle arithmetic mean fields, whereas `E_phase8` is the RMS over eight independently phased nearest saved boundary snapshots; neither uses a solver-exact persisted common-fluid mask. Thus, for this named Legacy comparator and ROI, the field result agrees across persistent mean and phase-resolved diagnostics, without implying that all downstream flow states are identical. [Legacy `wake_l2.py` row; Module 03]

The agreement has a defined dynamic boundary. Legacy target and controlled roles each contain eight complete-cycle fields and nine accepted crossings, while zero contains four complete cycles and five crossings; the controlled relative frequency mismatch is `0.004831`, compared with `0.376794` for zero. This supports the bounded reading that the controlled trajectory is closer to the target under both declared field estimands, but the phase metric remains a one-snapshot-per-slot diagnostic rather than a repeated-crossing ensemble. The companion V5 `kar_re100` package is secondary: five seeds repeatedly found high-reward checkpoints, and the retained deterministic evaluation selected seed 45 with reward `0.931258` and DTW `0.918458`; late retention ratios ranged from `0.162632` to `0.858143`. This supports a discovery/retention distinction, not Legacy/V5 pooling or a general convergence claim. [Legacy metadata; V5 retained evaluation authority]

The result therefore hands two bounded questions forward. To Module 05, the Legacy Re100 field comparison establishes the performance target for testing whether a reduced action law reproduces the controlled trajectory under the same Legacy plant and window; it does not identify action-law complexity. To Module 06, the exact Legacy mean/phase L2 roles and their separate windows provide the performance baseline for mean/dynamic field organization, while the field metric remains geometry-guarded and descriptive rather than causal. [Module 03; current field authorities]

## Layer 2 — compact provenance ledger

| Claim / quantity | Exact source and artifact | Chain; solver/geometry; case/seed/role; Re | Comparator and metric/estimand | ROI/window and status |
|---|---|---|---|---|
| Principal target/zero/controlled roles | `src/drl_pinball/data/reproduction/legacy/karman_re100/{target,zero,controlled}/metadata.json`; schema `drl-pinball-legacy-acquisition-v2` | Legacy solver/API; `1280×512`; `karman_re100`; controlled frozen model `d1a3o12_re100.zip` with frozen `norm.json`; Re code 100 = `U0(2D)/nu=100`, `Re_D=50` | target live builder trajectory; zero physical-zero/uncontrolled counter-bias trajectory; controlled frozen-policy trajectory | `SI=800`, 480 warm-up, 160 post-step boundaries; 8 phase fields; read, authority-bound, artifact-audit deferred for raw payloads |
| Registered field ROI | `src/drl_pinball/eval/wake_l2.py`, schema `drl-pinball-wake-l2-v2`; Module 03 §4 | Legacy; `D=20`, `x_s=800`, conservative solid extent 636 | fixed inclusive ROI; no outcome-dependent mask | lattice bounds `x=680..1080`, `y=156..355`; geometry-guarded ROI, solver-exact mask not persisted; read and agreed with Module 03 |
| Legacy complete-cycle mean L2 | Exact `_evaluate` row from current Legacy roles, using `wake_l2.py`; row values reproduced from bound role artifacts | Legacy; Re code 100; controlled vs target and zero vs target; no seed field in Legacy role | `E_mean_ctl=0.08577102245825166`; `E_mean_zero=0.47520632385441813`; `eta_mean=0.8195078260689812`; `U0`-normalized ROI RMS difference of complete-cycle mean fields | accepted rising centre-probe `u_y` crossings; target 9, controlled 9, zero 5; 8, 8 and 4 complete cycles; current authority value, raw artifact audit deferred |
| Legacy phase L2 | Same exact `_evaluate` row and `phase_fields.npz` role schema | Legacy; Re code 100; controlled/zero versus target | `E_phase8_ctl=0.11267999504986256`; `E_phase8_zero=0.6308775162147815`; `eta_phase8=0.8213916455195072`; eight-slot nearest-boundary RMS | independent role phasing, canonical slots; one snapshot per slot, not repeated-crossing ensemble; current authority value, artifact-audit deferred |
| Legacy current/normalized DTW similarity | `controlled/dtw_summary.json`, `zero/dtw_summary.json`, `target/dtw_summary.json`; native implementation `legacy_test/core/dtw_metrics.py` and offline metrics contract | Legacy; `karman_re100`; controlled and zero role histories versus target; no V5 transfer | target-normalized six-channel cycle DTW similarity score: controlled `0.9328993565511687`, zero `0.6251268882807846`; native similarity score: controlled `0.9521319744438127`, zero `0.6882437288676819`; higher is better and controlled is higher under both contracts; these are not errors or distances | historical window/`CONV_LEN=30`, lag channel 3, target-channel max-abs normalization; read, current role authority, artifact-audit deferred |
| Dynamic boundary | Legacy role metadata plus the exact field-evaluation row | Legacy Re100; target/controlled/zero | controlled relative frequency mismatch `0.004831181571494927`; zero `0.3767940098934097`; period CV controlled `0.00020952970987246327`, zero `0.06474211289191471` | physical time is Legacy-relative; relative same-case diagnostic only; bounded observation, not cross-chain frequency evidence |
| V5 secondary five-seed support | `src/drl_pinball/train/results/latest/tables/latest_results_summary.json`; `latest_eval_summary.csv`; `train/output/kar_re100_seed41–45/meta.json` | V5/CelerisLab; `2000×600`; `kar_re100`; seeds 41–45; code Re100 = `Re_D=50` | best rewards `0.9266385, 0.9301960, 0.9160065, 0.9221958, 0.9411612`; selected retained evaluation seed 45 reward `0.931258`, DTW `0.918458` | 500 iterations; retained evaluation 360 steps, last-180 tail; historical `legacy-policy-v1` compatibility, not current-contract retraining; read authority, artifact-audit deferred |
| V5 retention support | Same V5 `latest_results_summary.json` retention records | V5; same five named seeds and case | validated last-50 retention ratios `0.6703388, 0.2004286, 0.1626321, 0.8581434, 0.6373129` | training-retention diagnostic; best-versus-retained distinction explicit; normalizer pairing required only for reproducibility/selected-policy panel, not for this textual seed-retention claim |
| V5 Re400 boundary, if retained in figure | Current summary authority and current wake-L2 summary authority | V5/CelerisLab; `kar_re400`, seed 43; code Re400; support chain only | `E_mean_ctl=0.177469` vs zero `0.221541`, but `E_phase8_ctl=0.490471` vs zero `0.450626`; `eta_mean≈0.1989`, `eta_phase8=-0.08842` | same periodic field contract; current authority diagnostic, artifact-audit deferred; do not use as Legacy principal evidence |

### Authority/interface reconciliation with Module 03

- **Agreement:** Module 03 and `wake_l2.py` agree on `drl-pinball-wake-l2-v2`, registered `[-6D,+14D]×[-5D,+5D]` ROI, `D=20`, `E_mean` as complete-cycle mean-field RMS, `E_phase8` as eight independently phased nearest-snapshot diagnostic, `eta=1-E_role/E_zero`, and geometry-guarded/no-persisted-exact-mask status.
- **Agreement:** Module 03’s Legacy Re100 role semantics agree with the current metadata: Legacy target is live builder-generated, zero is physical-zero/uncontrolled, controlled is frozen Legacy PPO; Legacy roles use their own chain and are not V5 continuations.
- **Conflict/clarification:** Module 03 says every role must carry target identity/hash when available; Legacy metadata binds run-generated target-array hashes separately for target, controlled and zero. These hashes differ because the trajectories are independently generated; they must not be treated as one shared target identity without an explicit target-role reconciliation. This is a provenance clarification, not a numerical conflict.
- **Deferral:** Module 03’s normalizer/VecNormalize contract applies to V5 retained policy reproducibility. It does not condition the Legacy field text above, whose frozen Legacy `norm.json` is directly bound in the controlled and zero metadata. Same-selection V5 model/normalizer verification is therefore a selected-policy reproducibility/panel dependency, not a blocker to the Legacy principal result.

## Figure, equation and table contracts

1. **Principal target/zero/controlled Legacy plate.** Show Legacy Re100 target, zero and controlled fields with chain, role, phase slot/window and fixed vorticity limits. It supports visual comparator context and can accompany the exact L2 rows; it does not prove mask exactness, causality or V5 equivalence.
2. **L2-first result panel.** Report Legacy Re100 absolute `E_mean`, `E_phase8` and zero-relative `eta` before the DTW companion. Caption must state ROI, `U0`, accepted-crossing window, eight-slot nearest-snapshot semantics and geometry-guarded mask status. It does not establish a universal cloak score or repeated-crossing uncertainty.
3. **DTW companion.** Show Legacy controlled/zero target-normalized DTW similarity scores and label native versus target-normalized similarity pipelines. State explicitly that higher is better (`0.932899` controlled versus `0.625127` zero normalized; `0.952132` controlled versus `0.688244` zero native) and never label these values as errors or distances. The panel supports signal-level matching under the declared window; it does not become field L2, a delay or a causal test.
4. **V5 seed/retention inset.** Show best discovery and late-retention spread only as secondary support, with selected seed 45, historical compatibility path and best/retained labels. A same-selection model/normalizer pair is required for a reproducibility or selected-policy panel, not for the textual statement that retention varies.
5. **Equations.** Use Module 03 canonical `E_mean`, `E_phase8` and `eta` definitions; do not add a second DTW equation here unless Module 03 requires it. Distinguish spatial L2 from any pipeline Level-2/Level-3 or Stage-3 validation gate.

## Claim ladder

**Green — supported at named scope**

- Legacy `karman_re100` controlled is closer to its target than its physical-zero comparator in both the complete-cycle mean-field and eight-slot phase-resolved registered spatial L2 rows above.
- Legacy controlled target-normalized DTW similarity is higher than zero under the declared role-local normalized cycle contract; native similarity is reported separately, and higher is better for both.
- V5 Re100 has five retained seeds with repeated best-checkpoint discovery and seed-dependent late retention; this is secondary support, not pooled field evidence.

**Amber — bounded interpretation**

- The Legacy Re100 result is consistent with learned wake-signature matching producing a controlled trajectory whose declared downstream field is closer to target over the registered ROI.
- Agreement of mean and phase L2 under this Legacy role supports a stronger named-case reading than DTW alone, while phase-slot and mask limitations remain attached.
- The V5 seed pattern motivates separating discovery from retention and does not transfer a V5 result into the Legacy action-law interpretation.

**Red — prohibited without new evidence**

- A global statement that field matching always survives beyond reward, pooled Legacy/V5 values, or a single cross-chain Kármán score.
- DTW as physical delay, causal response, field equivalence or mechanism.
- Robust/general convergence, universal Re transfer, stability, optimal sensor placement, exact solver-mask L2, or statistical uncertainty from the current phase slots.
- V5 selected-policy reproducibility claims without the matching model/normalizer pair; this restriction does not block the Legacy principal text.

## Imports, exports and bridge

**Imports from Module 03:** canonical role/chain vocabulary; Legacy/V5 solver and Re boundaries; registered ROI; `E_mean`, `E_phase8`, `eta`, phase and mask semantics; spatial-L2 versus pipeline validation-level distinction. This revision reconciles those definitions above and records the one target-hash clarification.

**Exact exports to Module 05 — Kármán action law:** use Legacy `karman_re100` target/zero/controlled as the principal closed-loop performance comparator; preserve its Legacy solver/API, `Re_code=100`/`Re_D=50`, frozen policy and `norm.json`, `SI=800`, 480 warm-up plus 160 retained boundaries, complete-cycle window and role-local target/zero semantics. The field result is a performance arbiter for any reduced law; it does not itself identify a necessary, causal or unique action component.

**Exact exports to Module 06 — Kármán field/CCD:** use Legacy Re100 `E_mean_ctl=0.08577102245825166` versus zero `0.47520632385441813`, `eta_mean=0.8195078260689812`, and `E_phase8_ctl=0.11267999504986256` versus zero `0.6308775162147815`, `eta_phase8=0.8213916455195072`, with the registered Legacy ROI and geometry-guarded mask status. Treat these as separate mean and phase estimands; do not infer action correlation or causality from them. V5 seed/retention and Re400 disagreement remain support-chain context only. Although the standardized PPO and corrected CCD mean errors are numerically close and share the same nominal x extent, they arise from different role acquisitions and role sets, retained windows, masks, and weighting/normalization contracts; they are different estimands, are not combined arithmetically, and must not be described as replication, validation, agreement or triangulation.

**Final bridge.** The named Legacy comparator establishes what the learned policy achieved in the registered Kármán wake; Module 05 can now test action-law compression against that same result, and Module 06 can organize mean and phase field differences without turning the field metric into a causal explanation.

## Genuine blockers and scope-local deferrals

- **No blocker to this section text:** external/symlink-backed raw fields and absent solver-exact masks are `artifact-audit deferred` because current metadata, evaluator code and authority-bound rows identify the roles, comparator, window and exact summary values without conflict.
- **Panel/raw-audit dependency:** a newly redrawn field panel or independent artifact audit still requires access to the raw role payloads and exact manifest/hash check. Do not claim that this pass performed that audit.
- **V5 reproducibility dependency only:** same-selection `best_model.zip` plus matching VecNormalize is required to reproduce or redraw a selected V5 policy panel; it does not condition the Legacy principal field/DTW text or the textual seed-retention observation.
- **No unresolved Module 03 metric conflict:** canonical definitions agree; the target-array hash distinction is recorded as a clarification.

## Coverage ledger

| Status | Sources inspected | Evidence status / reason |
|---|---|---|
| `read` | Revised `.cursor/rules/jfm-round3-section-drafting.mdc`; Round3 master and quality; current Module 03; Round1 DRL/control, coverage audit and case-metrics dossiers; `WAKE_L2_AND_SENSOR_PLACEMENT_RESEARCH_NOTES.md`; `RESULTS.md`, `CLAIMS.md`, `WRITING_HANDOFF.md`, `eval/README.md`; `wake_l2.py`; Legacy Re100 metadata and DTW summaries; V5 result tables and Re100 metadata/calibration | Full read; current authority values extracted where stated; raw NPZ/model binaries not independently audited |
| `mapped` | `data/reproduction_plots/manifest.json`; current plot navigation and external role paths | Role/phase-slot mapping read; derived views, not numerical authority |
| `not-covered` | New CFD, retraining, external literature, independent mask reconstruction, new panel generation | Outside this revision; no claim depends on them |
| `external-inaccessible` | External Optane root is symlink-backed and raw field payloads are permission-restricted in ordinary inspection | Authority-led `artifact-audit deferred`; exact role/summary rows were still obtained through the bound evaluator and metadata |

## Anti-index / anti-AI audit

- Layer 1 is five concise prose-like paragraphs with source tags and scientific cadence; it does not contain repeated bold template labels, giant inline evidence blocks or training-path inventories.
- Layer 2 carries the complete provenance ledger, including chain, solver/geometry, case/role/seed, Re, comparator, metric, ROI/window, status and deferral state.
- The principal result is Legacy Re100; V5 is visibly secondary, and the 23-row aggregate is not used as the principal claim.
- L2 remains primary and DTW complementary; native and normalized DTW, mean and phase8, Legacy and V5 are not pooled.
- Best checkpoint, retained evaluation and late retention are separated; VecNormalize is scoped to V5 reproducibility/panel dependency rather than treated as a universal blocker.
- No global beyond-reward claim, causal language, generalization claim, invented number or silent target-hash merge is used.

**Disposition:** revised candidate submitted for second audit; not self-declared ready.