The observation that optimum circuit size changes by at most $O(n)$ under a one-point truth table perturbation is implicit in prior work on the Minimum Circuit Size Problem. This note states the bound explicitly for arbitrary fixed finite complete bases with unit-cost gates, extends it to general Hamming distance via a telescoping argument, and verifies it exhaustively at $n = 4$ in the AIG basis using SAT-derived exact circuit sizes for 220 of 222 NPN equivalence classes. Among 987 mutation edges, the maximum observed difference is $4 = n$, confirming the bound is tight at $n = 4$ for AIG.

翻译：关于最优电路规模在单点真值表扰动下变化不超过$O(n)$的观察，先前关于最小电路规模问题的研究中已有隐含论述。本笔记针对任意固定的有限完备基（采用单位代价门）明确陈述该界，通过伸缩和论证将其推广至一般汉明距离，并在AIG基下对$n=4$的情况进行穷举验证，利用SAT推导出的精确电路规模覆盖了222个NPN等价类中的220个。在987个突变边中，观察到的最大差值为$4=n$，证实了该界在$n=4$时对于AIG是紧的。