# Verification Pulses and the Cost of Escaping Wrong Consensus

arXiv: https://arxiv.org/abs/2610.00256 · HTML: https://mlsanity.com/paper/2610.00256/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 13 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Consensus is Not Verification: Why Crowd Wisdom Strategies Fail for LLM Truthfulness](https://mlsanity.com/paper/2603.06612/) (2026)
- [Physics of Agents: Statistical Mechanics Predicts Collective Behavior of AI Agents](https://mlsanity.com/paper/2608.16578/) (2026)
- [Steering opinion dynamics through control of social networks](https://mlsanity.com/paper/2404.09849/) (2024)
- [Phase transition of the 3-majority opinion dynamics with noisy interactions](https://mlsanity.com/paper/2112.03543/) (2021)
- [Optimal control in opinion dynamics models: towards a unified framework](https://mlsanity.com/paper/2207.01300/) (2022)

## Abstract (arXiv)

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. For a general nonlinear response, we derive the minimum fuel required to cross a basin boundary under a peak verification constraint. For a finite population, an exact birth--death calculation gives the probability of subsequent wrong consensus after a pulse. Our main asymptotic result identifies the critical budget window: a leading term Nlog(x0/b) and a correction of order √ N, with separate variance contributions from repeated verification targets and autonomous amplification after verification stops. 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. 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. A distributional audit also finds that modest mean-prediction error can conceal a large underestimate of terminal consensus occupancy. The results support risk-calibrated reset scheduling under a specified update contract, while explicitly separating it from distinct-target checking and unrestricted evidence broadcast.