Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 186-01. A uniform influence bound for hypergraph properties
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OpenAI@2026-10-07#rem:oai-p-186-01
Authors: OpenAI. Family 186.
Title: A uniform influence bound for hypergraph properties.
Abstract: For every fixed integer r ≥ 3, we prove that every relabeling-invariant Boolean property of simple r-uniform hypergraphs on n vertices satisfies ${}mathop{{}mathrm{Var}}{}nolimits _p(f){}le C_r I_p(f)/({}log n){}{r/(r-1)}$. The constant depends only on r, and the bound holds uniformly for all $0{}lt p{}lt 1$ without a monotonicity assumption. For increasing properties, it gives the corresponding threshold-width bound with exponent $r/(r-1)$, proving the hypergraph threshold-width conjecture of Friedgut and Kalai.
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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