Falsify, Repair, Repeat: Auditable Local Repair of Typed Dynamical Equations

Equation discovery can fit observed trajectories while retaining the wrong term, regime, or delay. We introduce Falsify–Repair–Repeat (FRR), a bounded scientific agent for auditing and locally repairing executable dynamical laws. Statistical verifiers turn failed tests into typed witnesses, a constrained policy selects grammar-valid edits, and numerical tools retain authority over refitting, acceptance, replay, and abstention. The selector is replaceable, but every structural change must survive executable validation and accumulated tests. This separation lets heterogeneous scientific agents share comparable evidence and decision records without exposing unrestricted control over the model. We characterize the finite repair basin, conditional recovery, replay preservation, budgeted termination, and an optional error-spending construction under conditionally valid tests. Across one-edit, compound-error, held-out, and null studies, typed editing supplies the principal behavioral and structural gains, while replay and abstention expose preservation–performance and risk–coverage trade-offs. Deterministic FRR reaches 85.6% semantic success on the one-edit benchmark; paired intervals support behavioral improvement through AST distance three, and independent ordinary-ODE rollouts improve from unseen initial conditions. Distant SINDy candidates instead trigger almost no action, revealing that basin entry remains a discovery problem. The proposal-agnostic interface therefore turns local equation repair, within an explicitly bounded typed neighborhood, into a traceable scientific decision process.