Where the Verifier Fails: A Category-Level Audit of Reward Signals in RLVR

Esther Xin audits the verifier rather than the model, applying metamorphic testing across 307,420 verdicts from four widely used RLVR verifiers to decompose exactly which answer forms consume the error budget.
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Certified false negatives. Equivalent answer variants are generated so that they preserve mathematical meaning by construction, which makes any rejection a provable false negative requiring no human adjudication.
The 94% figure describes one implementation, not the task. Self-validation ranges from 53.8% to 95.2% on identical inputs, a 41.3-point spread, and two configurations of the same library disagree on 49.9% of pairs.
The residual is punctuation, not parsing. Whitespace and punctuation account for 93.0% of in-contract failures for the default LaTeX configuration. A trailing period or newline dominates the budget.
A scale-invariance bug with teeth. A reference numeric cascade accepts off-by-one wrong answers as a step function of magnitude, from 0% below 10^4 to 100% at or above, because its relative tolerance is scale invariant.
Why this matters for agents. Every RLVR result and every benchmark number downstream of these verifiers inherits their error structure, and verifiers with similar aggregate error turn out to fail for opposite reasons.
Abstract
Reinforcement learning with verifiable rewards (RLVR) and standard benchmark evaluation both rely on an automatic verifier that turns a free text answer into a binary reward. Prior work reports that one evaluation harness accepts only about 94% of its own ground truth answers, blaming LaTeX parsing. That is an aggregate: it does not say which answer forms consume the error budget. We supply the decomposition. We apply metamorphic testing to the verifier rather than the model, generating certified equivalent answer variants, that is, rewrites that preserve mathematical meaning by construction, so that any rejection is a provable false negative needing no human adjudication. We then measure rejection per answer category across four widely used verifiers over 307,420 verdicts. We find three things. (1) Self validation ranges from 53.8% to 95.2% on identical inputs, a spread of 41.3 points. The published figure describes one implementation, not the task; two configurations of the same library disagree on 49.9% of pairs. (2) The residual is not spread across parsing categories but concentrated in whitespace and punctuation, which account for 93.0% of in contract failures for the default LaTeX configuration. A trailing period or newline dominates the budget. (3) Separating rejection from execution failure shows that verifiers with similar aggregate error fail for opposite reasons, and that a reference numeric cascade accepts off by one wrong answers as a step function of magnitude, from 0% below 10^4 to 100% at or above, because its relative tolerance is scale invariant.