The verifier is part of the simulator: letting an agent pick its evidence view makes PDEBench accept a law missing diffusion

An equation-discovery agent can change a fixed verifier's conclusion merely by choosing which computed numerical summary is admitted as evidence, while the simulated trajectory, candidate library, verifier and thresholds stay fixed. Weak-form equation discovery had treated building the quadrature well as the established task, with test functions setting the scales at which the equation is observed; here the choice of which already-computed summary to admit becomes the scored action. With the true advection–diffusion equation among 92 candidate-term combinations, seven temporal samples and five oscillatory test functions make the verifier declare necessary physics absent and earn the highest score of 13.77, while 25 samples and two test functions recover both terms and score 10.87.

The failure needs neither a score nor a language model: when the time grid is too coarse, the oscillatory weak-form integrals are underintegrated, so discretization error is read as model mismatch and a complete candidate library appears incomplete. Changing only the summary lowers the median best residual as the sample count rises, and the median normalized target and design discrepancies fall alongside it. On matched episodes the residual separates the omission task perfectly at the fine view (AUROC 1.000) and barely at seven samples (0.589); the external PySINDy WeakPDE STLSQ implementation omits a generating term in 15 of 600 coarse fits versus 3 of 600 fine fits.

Exact maximization of the public score systematically produces false rejections, because the score rewards decisive verdicts and rises with reported misfit when rejecting. On 50 untouched seeds and 1,800 matched episodes per implementation, exact maximization rejects the library on every in-library episode, with coarse view A03 worst and A02 next at 356 of 1,500. Both the spectral and centered finite-difference implementations give 1,500 false rejections at 100% coverage, and the 300 correct verdicts are exactly the omitted-family episodes; on PDEBench's 900 episodes, score maximization returns 69 false identifications and three false rejections, with all 69 identifications omitting diffusion and selecting the 25-sample/two-mode view.

Requiring four prescribed views to agree on verdict and support cuts wrong verdicts from 41 for the fixed fine view to 3, paid for in abstention. Across 1,800 episodes the agreement rule leaves 3 wrong verdicts and 362 undecided at 79.89% coverage, against 41 wrong and 317 undecided at 82.39% coverage for the fixed fine view. All three residual errors are false rejections against generating truth at the coarsest grid, where the locked reference is also wrong; on PDEBench the agreement rule emits no false verdict but abstains on 255 episodes, while the fixed fine view answers all 900 correctly.

The demonstrated setting is equation discovery on simulated trajectories: one-dimensional matched episodes spanning five in-library families and one omitted family, plus a PDEBench transfer on coupled two-dimensional diffusion–reaction data, all simulated rather than physical observations. The intended readers are researchers and engineers who design or audit equation-discovery agents and their verification interfaces.

The language-model evidence comes from one provider under single-turn forced choice, with trust probes and action choices made in separate calls; the agent selects among prescribed views rather than constructing its own, and agreement against an adaptive agent is untested. The agreement rule underperforms the fixed fine view on PDEBench, and the authors call it a safeguard rather than a certificate; retrospective retuning of the score constants reduces errors to 13 of 180 at best.