Counterexample to Majority Optimality in NICD with Erasures

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 \emph{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 \emph{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.