AI-Generated Math Proof Contains Critical Error, Now Corrected.

A recent analysis uncovered a significant error in an AI-generated mathematical proof published in OpenAI's "Ten Advances in Mathematics and Theoretical Computer Science." Specifically, a greedy conditioning lemma used in a chapter on quantum parallel repetition contained a polarity error, where the continuation test was based on average success while the subsequent step required a large conditional failure probability. The paper provides an explicit counterexample, pinpoints the intended continuation condition, and supplies a complete, corrected proof. While the repair is local and doesn't alter the lemma's statement or later parameters, it serves as a crucial example of how mathematically plausible AI-generated arguments can subtly reverse complementary events, leading to critical flaws that require careful human auditing.