# Active judge merge

## Discovery tags

- icml2026-repro
- paper-JIbkbLYo3o

## Pinned merge rule

Both target-paper claim feeds are pinned at challenge revision
7b5b56aebf3abe590eab9f2c241a796125cab928. The active judge merge is:

1. start with claims.json;
2. apply claims_anchored.json at the same target paper key; and
3. use claims_anchored.json when the two feeds overlap.

Thus claims_anchored.json overrides claims.json for the active judge record.
The immutable target-paper hashes and ETags are in evidence-manifest.json.

## Active anchored judge evidence

All target-paper entries below retain status **unverified**. They document the
active judge feed, not additional proof validation or empirical replication.

1. For laminar set cover, the proposed dual-prediction algorithm achieves E[ALG] = (1+epsilon)*OPT + O(R*eta/epsilon) for any constant epsilon>0, where eta measures dual prediction error (Theorem 1.1).
2. For metrical task systems, the dual-prediction algorithm (Algorithm 3, an A*-style search minimizing d(s_{t-1},s)+c_t(s)+w_hat_t(s)) achieves a (1+eta/OPT)-competitive ratio driven by the span seminorm of Bellman-operator discrepancies (Theorem 3.1).
3. Optimal dual solutions are stable under instance perturbations, satisfying ||y1* - y2*||_1 = O(|X1 Delta X2|), whereas optimal primal solutions can change arbitrarily under a single-element perturbation (Lemma A.1).
4. Event predictions for caching are similarly shown to be unstable, since a single prediction error can cause the competitive ratio to collapse (Lemma A.3).
5. On the parking permit problem, the learning-augmented dual-prediction algorithm achieves 1.8x to 4.4x better competitive ratios than classical algorithms at K=9 permit types, and it outperforms baselines on the k-server problem using real bike-sharing data (Experiments section).
6. For general (non-laminar) set cover, even perfect dual predictions cannot beat the classical H_m competitive ratio under the standard LP formulation, showing laminar structure is necessary for the improvement (Lemma A.4).

## Crosswalk boundary

The retained source/theorem crosswalk covers the three legacy official claims
on pages 01–03 and preserves the eight verified anchor labels in the manifest.
This package adds no source, theorem, author-code, data, or experimental
validation for the additional anchored judge entries.