Remark: Family 127. The asymptotic Gotsman–Linial conjecture

Proves that a degree-at-most-$d$ polynomial threshold function on the uniform $n$-dimensional Boolean cube has average sensitivity at most $8d\sqrt{n}$, uniformly for $1\le d\le n$. Average sensitivity counts expected output changes under single-bit flips. This establishes the asymptotic Gotsman–Linial conjecture, allowing polynomial zeros with $\mathrm{sign}(0)=1$.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.