Auditing Learned Mean-Field Equilibrium Claims: Claim-Conditioned Response and Flow Evidence

Mean-field game solvers return a policy together with a population flow, but standard endpoint evidence does not determine whether this pair supports an equilibrium claim. A high return need not imply response optimality; a best response to a declared flow need not generate that flow; and passive trajectories may not expose either failure. We instantiate the broader Claim-Aware Protocol Auditing (CAPA) pattern for MFGs as MF-CAPA, a post-hoc auditor that separates response optimality from population consistency, restricts evidence to executable trajectory interventions, and returns CERTIFY, REFUTE, or ABSTAIN. The central distinction is that auditing a fixed claim need not identify the game. For finite quotient models, we define a claim-conditioned trajectory-KL characteristic time, prove that audit characteristic time can be arbitrarily smaller than the time required for model identification, and derive an expected-time lower bound for decisively terminating audits and an almost-sure upper rate. An anytime mixture confidence sequence controls adaptive stopping, while the intervention interface and sound semantic bounders determine whether a verdict is supportable. In actual sequential trials, passive aliases yield only 3/200 and 1/200 decisive stops (3 and 0 wrong), versus 200/200 for each active condition. Across two separately family-wise-calibrated suites of 60 final-candidate/control cells using exact best-response probes and exact mean-field transitions, every decisive audit agrees with exact two-axis truth and all 90 single-axis/wrong-flow controls are refuted; a separate 360-cell study across three native MFGLib learners again yields no wrong decisive decision. Structured numerical relaxations illustrate robust-box verification, distinct from auditing an unknown true model. MF-CAPA provides an evidence contract for deciding which learned equilibrium declarations the available interventions support; it audits supplied candidates rather than introducing a new equilibrium solver.