External verification can correct individual outputs while leaving a self-reinforcing population in the basin of a wrong consensus.
We study how the timing and addressing of a fixed verification budget affect recovery in an asynchronous binary register.
Derivation of Minimum Fuel
For a general nonlinear response, we derive the minimum fuel required to cross a basin boundary under a peak verification constraint.
Probability Calculation
For a finite population, an exact birth--death calculation gives the probability of subsequent wrong consensus after a pulse.
Asymptotic Result
Our main asymptotic result identifies the critical budget window: a leading term $N\log(x_0/b)$ and a correction of order $\sqrt N$, with separate variance contributions from repeated verification targets and autonomous amplification after verification stops.
Substantial Distinction
The distinction is substantial: with 16 majority-updated slots and 14 initially wrong, 9 random checks cross the mean-field budget threshold, whereas 23 are required for 95% eventual recovery in the exact model.
Experiment Results
A prospectively specified experiment records 13,392 language-model responses, including calibration and 108 held-out trajectories.
Calibration produces different fitted response regimes, but all four adjusted schedule-comparison intervals include zero.
Distributional Audit
A distributional audit also finds that modest mean-prediction error can conceal a large underestimate of terminal consensus occupancy.
Support for Risk-Calibrated Reset Scheduling
The results support risk-calibrated reset scheduling under a specified update contract, while explicitly separating it from distinct-target checking and unrestricted evidence broadcast.