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The evidence supports exact schema-induced conditioning, not a systems advantage over CARS, and the evaluated method makes no generic finite-trie scalability claim.
It is proved that common-mode error is not identifiable from internal judge scores alone and proposed a bounded two-anchor Bernstein certificate for finite-search error and regret.
This work formulate PRM stress testing as a quality-diversity search problem using MAP-Elites, retaining the most severe correctness-flipping edit in each behavior-space region while separating search coverage from exploit coverage, and characterize what such archives certify.
CODS is introduced, a critic-guided selector that alternates between fitting an algorithm-matched critic and acquiring high-residual transitions before freezing a reusable subset, a reusable selection procedure, not a formal coreset guarantee.
FlowNeg is introduced, a context-conditioned hierarchical generative flow network that amortizes reward-proportional sampling without normalizing a composite reward over the entity set: given a positive triple and corruption side, it selects a type, then an entity.
The realizable share of oracle opportunity is small and certifiable: strong routers beat the best fixed model, and most of the gap remains, while the selection-valid confidence intervals are small and certifiable.
A finite-horizon composition law for Gaussian certification from M independent coordinates, a familywise certifier protecting every coordinate and time up to T pays optimal normalized squared half-width of order log(eM) + log log(e^eT), within the sample-mean-centered rectangular class.
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