Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 127-01. Average sensitivity of polynomial threshold functions
Manuscript map · lines 4885–4894
OpenAI@2026-10-07#rem:oai-p-127-01
Authors: OpenAI. Family 127.
Title: Average sensitivity of polynomial threshold functions.
Abstract: For every n ≥ 1 and $1{}le d{}le n$, we prove that a polynomial threshold function of degree at most d on the uniform Boolean cube has average sensitivity at most $8d{}sqrt n$. This proves the asymptotic form of the Gotsman–Linial conjecture. The bound is uniform in both parameters and uses the convention ${}mathop{{}mathrm{sgn}}{}nolimits (0)=1$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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