Audit Frontiers and Finite Budget Rank Decisions under Partial Observations

Partial observations can prove a predictive law wrong without saying what should replace it. We score updates of a finite predictive law by their worst case log score improvement over every latent world consistent with the observed law. A trust budget limits divergence from the reference; an audit budget limits divergence from the least committal law with the same observations. On a compact subanalytic set of available updates, the gain exponent, as a function of the audit precision, is eventually constant exactly when positive gain survives a zero audit. The comparison behind this criterion specializes preparation theory and bounds the gain by a finite maximum of minima of monomials in the two budgets, with constants independent of their ratio. In a conditional logit module, the vanishing orders of singular values determine the correction rank needed at each audit precision, and in a sixteen state tied network, bounds over every admissible action give exact minimum rank decisions at finite budgets. We also give certificates that hold uniformly over updates fitted to the same observations and a hardness construction whose instances share a second order jet. On a rain and sprinkler example, four of five deployed language models, told only how often the ground was wet, changed the unidentified split between rain and the sprinkler in almost every revision. In trained adapter families of two open weight models, that split moves at approximately first order over the measured edit scales, outside the module's second order assumption. This audit tests no theorem. All guarantees concern this finite interface, and no result is validated on a language model.