Auditing Discovery Claims: A Two-Sided Criterion for Agentic Science, with the Negative Side Decidable

Abstract

When a self-improving AI-for-science system claims a new capability, the evidence is usually a benchmark delta, a description-length gate, or a p-value. None separates a real gain from extra search, from a changed verifier, or from adaptation to a fallible oracle. We build a two-sided audit whose negative side is a formal fact: a pseudoknot-free oracle provably cannot represent a crossing base pair, so the prior verifier's range is bounded exactly, offline, before any run."New"is relative to the agent's prior self, never to the base model. First, how far a single fallible oracle can inflate a capability claim. An invented, solver-free operator solves 43/60 crossing RNA targets under the predictor it optimizes, above a context-free floor of 0/60; under three predictors, 1/60 survives. Paired on the same 43 targets, a predictor the operator never saw confirms 2 of its designs against 26 for a minimum-free-energy solver (p = 8e-7). No statistic computed from the system and its own oracle sees that gap. Second, agent-written procedures can beat a human-written one under a judge no objective can flatter, at a fraction of the compute. Of six frontier models, the two whose operators ran without timeouts carry over at 0.293 against our 0.095 (n = 951 paired units, target-clustered [+0.108, +0.297], p = 5e-5) while spending 4.6-10x fewer oracle calls. Three rungs: difference under an outside adjudicator (reached), not bought with compute (reached, both directions), mechanism identified and transferable (not reached; seven candidates tested, none moves the statistic). The ceiling is the panel itself: its three predictors share nearest-neighbour thermodynamic parameters, two agreeing at kappa = 0.673. The audit is as unsparing about our own system: matched undirected search is an exact zero, and a search-free probe puts 84% of our headline effect on targets a random sequence already solves.