bundle/v0/CLAIM_MAPPING.md

# Official claim mapping

The scored claim set is pinned in `configs/official_claims_lock.json`. The live judge merges `{**legacy, **anchored}`, so the anchored six-claim record replaces the historical three-claim record for OpenReview `K1EPPO9t2c`. The `C1`, `C2`, and `C3` labels inside the frozen 14,000-task plan are internal evidence-route labels only. They are not judge-facing claims and changing them would invalidate the active run identity.

| Claim | Official anchored claim | Primary evidence | Conservative verdict rule |
|---|---|---|---|
| `A1` | The ambiguity-set geometry is learned as a bilevel OT-DRO problem. | Validated end-to-end portfolio and absolute-regression main suites, raw upper/lower-level lineage, solver feasibility, and per-iteration geometry. | Verify only when both main suites are complete with no capped or worsening-stop tasks. |
| `A2` | Theorem 5.1 gives convergence to a critical point under its stated conditions. | Enumerated source-anchored assumptions, a hash-bound proof artifact, and a separately bound independent-reviewer receipt. | Verification is hard-disabled until that complete contract exists. Finite trajectories and self-declared receipts never verify the theorem. |
| `A3` | Algorithm 1 differentiates through nonsmooth conic OT-DRO programs. | Source/formula audit plus nonsmooth and active-set boundary evidence for conservative implicit differentiation without continuous-differentiability assumptions. | The current six smooth finite-difference checks can support at most partial verification. They cannot verify A3. |
| `A4` | Portfolio relative improvement increases as sample size decreases. | Exact `k=2`, `J=30`, `n_b=20`, `gamma=0.05`, `beta=0.1` binding and the paper's exact Figure 2 relative-improvement estimand. | The frozen plan does not bind `k`, `J`, or the paper formula, so A4 remains inconclusive. Available slope analysis is extension-only sensitivity evidence. |
| `A5` | The shaped ambiguity set retains the specified high-probability coverage. | `portfolio_gaussian_main` coverage at every sample size, aggregated by distribution before bootstrapping. | Verify only when every lower 95% confidence bound reaches the predeclared `1 - beta = 0.9` target. |
| `A6` | Ten independent regression trials consistently reduce average loss versus baseline OT-DRO. | `regression_absolute_main` out-of-sample relative improvement at every sample size and for each of the ten distributions. | Verify only when every sample-size lower confidence bound is positive and every one of the ten distribution means is positive. |

The high-dimensional, discrete, Gaussian-mixture, squared-loss, and coverage-penalty-ablation suites remain valuable robustness analyses. They are reported under `extensions` and cannot create additional scored claims.