发表机构
Independent Researcher（独立研究者）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究分析外部验证预算的时序与寻址对逃离错误共识的影响，推导关键预算窗口，并通过实验证明风险校准的重置调度优于随机检查。
AI 中文摘要
外部验证可以纠正单个输出，同时却使自我强化的人口停留在错误共识的盆地中。我们研究在异步二进制寄存器中，固定验证预算的时序和寻址如何影响恢复。对于一般的非线性响应，我们推导出在峰值验证约束下跨越盆地边界所需的最小燃料。对于有限人口，精确的出生-死亡计算给出了脉冲后随后出现错误共识的概率。我们的主要渐近结果确定了关键的预算窗口：主导项 $N\log(x_0/b)$ 和 $\sqrt N$ 量级的修正项，其中包含来自重复验证目标和验证停止后自主放大的独立方差贡献。区别是显著的：对于16个多数更新槽位和14个初始错误槽位，9次随机检查跨越了平均场预算阈值，而在精确模型中，需要23次才能实现95%的最终恢复。一项前瞻性规定的实验记录了13,392条语言模型响应，包括校准和108条保留轨迹。校准产生了不同的拟合响应区间，但所有四个调整后的调度比较区间都包含零。分布审计还发现，适度的均值预测误差可能掩盖终端共识占用率的严重低估。结果支持在指定更新契约下进行风险校准的重置调度，同时明确将其与不同目标检查和不受限制的证据广播区分开来。
英文摘要
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 $N\log(x_0/b)$ and a correction of order $\sqrt N$, with separate variance contributions from repeated verification targets and autonomous amplification after verification stops. 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.
Comments18 pages, 5 figures; code and raw experimental records: https://github.com/shi1720/verification-pulses
