# Final audited OID results

These values are transcribed from compact summary schema `oid-phase4-compact-summary/v2` and the four hash-bound `oid-phase3-5-loro/v2` reports. The final authority is `runs/active-two-scene-v2/OID_PHASE4_AUDIT_20260723T1510Z.json`, SHA-256 `9358105c7199793a2fd810885044295350da165a0f8e9026734ca1a51fc52ed8`. Overall status is **conditional**; this is neither formal `COMPLETE` nor publication-ready. The exact conditional evidence-package inventory is `provenance/freeze/OID_CONDITIONAL_FREEZE_20260723T173300Z.json`. It may bind large ignored NPZ artifacts available locally or through the checksum-bound archive; committed compact JSON/PNG/PDF evidence remains directly inspectable. The freeze boundary does not satisfy or imply strict-loader `COMPLETE`.

Notation below is `held-out: observed R²; p; selected rank/lag; deranged rank/lag and R²; gate; LR-state R²`. R² is the primary pooled H-weighted score with `H=I`; `p` is the selection-adjusted, periodic-excluded, 999-shift upper-tail value. The gate is strict: observed must exceed the independently reselected deranged score by more than 0.01.

## Full fold metrics

### `karman_re100/delta_sensors` — promoted

- `r1`: 0.9647492359741772; 0.001; 12/0; 8/0 and 0.9529281661830779; pass; 0.7940138566560129.
- `r2`: 0.9671412374198772; 0.001; 12/1; 4/2 and -1.1711745174619739; pass; 0.7795911464481013.
- `r3`: 0.9733209744094111; 0.001; 12/1; 4/2 and -0.8014458421252284; pass; 0.7906617978821034.

All folds pass. Allowed interpretation: cross-realization association between the active correction state and incremental sensors for these three declared Kármán runs.

### `karman_re100/delta_forces` — not promoted

- `r1`: 0.8362060373462964; 0.001; 12/0; 12/0 and 0.836190644072093; **fail**; -3.694109397100756.
- `r2`: 0.8676698843517285; 0.001; 12/0; 4/0 and -1.3936813970219277; pass; -3.7327113934088185.
- `r3`: 0.8720870883530646; 0.001; 12/0; 4/0 and -1.1558973413673468; pass; -4.885610517833002.

`r1` misses the +0.01 margin even though the circular-shift p-value is 0.001. Report the observed and negative-control metrics descriptively; do not claim cross-realization force association. All LR state-reconstruction values are negative, so force OID does not demonstrate held-out state reconstruction skill.

### `illusion_1.0L/delta_sensors` — promoted

- `r1`: 0.936949098650597; 0.001; 12/2; 12/0 and -1.1109272633898142; pass; 0.43373659801976727.
- `r2`: 0.9289598285270472; 0.001; 12/2; 4/2 and -0.07452448339998452; pass; 0.3115277061403373.
- `r3`: 0.9397635230916879; 0.001; 12/0; 4/0 and 0.7906267008654244; pass; 0.6020838090100447.

All folds pass. Allowed interpretation: cross-realization association between the active correction state and incremental sensors for these three declared Illusion 1L runs.

### `illusion_1.0L/delta_forces` — not promoted

- `r1`: 0.7018650862689654; 0.001; 12/2; 8/2 and 0.5165690842754724; pass; -0.7147414442200091.
- `r2`: 0.6941624670535564; 0.001; 12/2; 8/2 and 0.5445259244101487; pass; -1.193782965197573.
- `r3`: 0.480277024047119; 0.001; 12/2; 12/2 and 0.47420334115121254; **fail**; -1.7853195191016673.

`r3` misses the +0.01 margin. Report the observed and negative-control metrics descriptively; do not claim cross-realization force association. All LR state-reconstruction values are negative.

## What the audit establishes

- Six source-, timeline-, geometry-, mask-, metric-, and hash-verified canonical products exist. Kármán has 5,025 fluid/95 solid reduced cells; Illusion has 5,024 fluid/96 solid.
- All four formal jobs have three LORO folds, 999 finite circular-shift scores per fold, p-value resolution 0.001, fixed `rcond=1e-12`, no regularization, and verified report/model bindings.
- Sensors pass the stricter reselected-derangement +0.01 gate in every fold and are promoted for the declared realizations.
- Forces fail one fold per scene. This is scientific non-promotion, not an integrity failure.
- No field-mode figure is promoted because the audit does not authorize causal, universal, or mode-unique interpretation.

The historical declaration of three realizations is not proof that they sample a broad independent stochastic population. Every LORO model trains on only two runs; folds are dependent and hyperparameter selection has low realization-level resolution. The evidence does not quantify robustness across Reynolds number, geometry, policy, forcing, or operating condition.

## Relation to SR and CCD

OID fits a state-to-observable propagator and distinguishes LR and LE generalized inverses. CCD/CCA whitens covariance and optimizes normalized co-variation between two processes; a common dataset, lag, POD, or visually similar subspace is not equivalence. SR fits symbolic reduced relationships and may summarize variables or modal coefficients, but it neither supplies an OID inverse nor validates OID causality. Cross-method comparison requires the same state, incremental observable, clocks, mask, metric, split, rank, and evidence identity. No OID promotion transfers automatically to SR or CCD, and vice versa.

## Allowed and prohibited claims

Allowed:

- describe manifest-bound canonical provenance and exact geometry/mask/metric contracts;
- report all primary and supplementary metrics, including negative gates;
- claim cross-realization `delta_sensors` association for `karman_re100` and `illusion_1.0L`, explicitly limited to `r1`–`r3`;
- report `delta_forces` as descriptive metrics and valid negative-control outcomes;
- state that each force job failed its all-fold association gate.

Prohibited:

- cross-realization `delta_forces` association for either scene;
- causal, controllability, controller-design, universal, broad-population, or mode-unique interpretation;
- force-state reconstruction skill;
- use of legacy steady outputs as evidence;
- unqualified “Kármán cylinder Re=100”: the case ID is `karman_re100`, but `Re_code=100` uses `2D` and physical `Re_D=50` (`nu=0.004`, `U0=0.01`, `D=20`);
- formal `COMPLETE`, immutable promotion, or publication-ready status.

## Open limitations

- Only three declared realizations per scene, at one fixed setup; no broad stochastic-independence or operating-condition claim.
- The periodic-excluded circular-shift null assumes approximate stationarity/periodicity and introduces wraparound endpoint adjacency.
- All observed selections choose the largest candidate rank, 12; rank sensitivity is recorded, but the candidate ceiling remains a limitation.
- Candidate lags are limited to 0–2 saved samples and represent a single-delay approximation.
- `H=I` follows the declared incremental coordinates; alternate scientifically justified observable metrics were not promoted.
- The formal folds are truncated (`rcond=1e-12`), not algebraically exact, and no regularization sensitivity is promoted.
- Individual mode uniqueness and causal mechanism are unsupported; no field modes are part of the compact presentation.
- Formal lineage is verified-existing but not strict-loader `COMPLETE`: no historical run-level manifest binds the full transition.
- The legacy steady case remains contradictory and excluded (`force Fx` reduction -11.391794204711914; full-field enstrophy reduction -9.052556311718561).

## Correction history

The final v2 result supersedes, but does not erase, earlier provenance:

1. Legacy products labelled cross-covariance/PLS-SVD directions as OID. They lacked the fitted Schlegel propagator and distinct LR/LE inverses; they are now `PLS-type` diagnostics only.
2. A contiguous trajectory holdout was previously described as independent validation. It was leakage-safe in time but not independent-realization validation; final analysis uses explicit LORO.
3. Earlier observables used absolute controlled telemetry rather than controlled-minus-blocked telemetry. Final canonical products bind `delta_forces` and `delta_sensors` on the exact field timeline.
4. A field-level telemetry callback read a value published only at control boundaries, producing invalid zero intermediate telemetry. Those runs are quarantined; the corrected callback reads synchronized per-step observations without changing the policy clock.
5. Index pairing and replay could not establish exact same-parent counterfactual alignment. Final products require equal IDs/lattice steps/times from same-parent controlled and zero-baseline branches, with a separate numerical twin gate.
6. The archived reduced mask was geometrically defective. Canonical rebuild reproduces the defect as a check, then applies exact Legacy rasterization, crop/stride, solid-zero quadrature, and audited cell counts.
7. Earlier POD paths risked inconsistent snapshot normalization/energy accounting and repeated expensive fits. Final weighted snapshot POD matches direct weighted SVD, uses the full-spectrum denominator, honors zero-weight solids, and caches one maximum-rank training fit before truncation.
8. Numerical solves previously depended on mixed library defaults. Final folds use one explicit `rcond=1e-12` across covariance, propagator, generated range, and LR/LE solves and report numerical ranks/defects.
9. Earlier “phase surrogate” wording and fixed-selection controls understated selection effects. Final reports use periodic-excluded circular shifts with complete surrogate reselection and independently reselected realization derangement.
10. Historical COMPLETE state cannot be reconstructed from relocated artifacts. The final audit intentionally remains conditional and fail-closed.

Archived paths are provenance-only and non-executable. Current claims must resolve through `runs/ACTIVE_EVIDENCE.json`, the six active canonical manifests, four active formal reports, the final audit, the conditional freeze manifest, and their recorded hashes.
