We asked GPT-5 Pro to look for counterexamples among a public list of open problems (the Simons ``Real Analysis in Computer Science'' collection). After several numerical experiments, it suggested a counterexample for the Non-Interactive Correlation Distillation (NICD) with erasures question: namely, a Boolean function on 5 bits that achieves a strictly larger value of $\mathbb{E}|f(z)|$ than the 5-bit majority function when the erasure parameter is $p=0.40.$ In this very short note we record the finding, state the problem precisely, give the explicit function, and verify the computation step by step by hand so that it can be checked without a computer. In addition, we show that for each fixed odd $n$ the majority is optimal (among unbiased Boolean functions) in a neighborhood of $p=0$. We view this as a little spark of an AI contribution in Theoretical Computer Science: while modern Large Language Models (LLMs) often assist with literature and numerics, here a concrete finite counterexample emerged.

翻译：我们要求GPT-5 Pro在一个公开的开放问题列表（西蒙斯基金会"计算机科学中的实分析"专题集）中寻找反例。经过多次数值实验，该模型针对含擦除的非交互式相关蒸馏问题提出了一个反例：即一个5比特布尔函数，当擦除参数为$p=0.40$时，其$\mathbb{E}|f(z)|$的期望值严格大于5比特多数函数。在这篇简短的札记中，我们记录了该发现，精确阐述了问题，给出了显式函数表达式，并通过逐步手工验证计算过程以确保无需计算机即可核验。此外，我们证明了对于每个固定的奇数$n$，在$p=0$的邻域内多数函数（在无偏布尔函数中）是最优的。我们认为这是人工智能在理论计算机科学领域贡献的一个微小火花：虽然现代大语言模型通常协助文献梳理和数值计算，但此处却产生了一个具体的有限反例。