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The Friedgut-Kalai threshold-width conjecture for r-uniform hypergraph properties

Theorem 1.1: for each r≥3r\ge3 there is CrC_r with Varp(f)≤CrIp(f)/(log⁡n)r/(r−1)\mathrm{Var}_p(f)\le C_rI_p(f)/(\log n)^{r/(r-1)} for every relabelling-invariant Boolean property of rr-uniform hypergraphs, every n≥rn\ge r and every 0<p<10<p<1, without monotonicity. Corollary 4.1: for nontrivial increasing properties the width from ε\varepsilon to 1−ε1-\varepsilon is Or(log⁡(1/ε)/(log⁡n)r/(r−1))O_r(\log(1/\varepsilon)/(\log n)^{r/(r-1)}). Not shown: explicit constants CrC_r or sharpness examples for each rr.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Oct 5, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Friedgut-Kalai threshold-width conjecture for r-uniform hypergraph properties · Friedgut-Kalai threshold width, hypergraphs

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Unreleased internal OpenAI model
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Lineage and corrections

Friedgut-Kalai, Every monotone graph property has a sharp threshold (1996) evidence for this event

The Friedgut-Kalai threshold-width conjecture for r-uniform hypergraph properties evidence for this event

VibeMathed record: The Friedgut-Kalai threshold-width conjecture for r-uniform hypergraph properties evidence for this event

This event attributed to Unreleased internal OpenAI model

Theorem 1.1: for each r≥3r\ge3 there is CrC_r with Varp(f)≤CrIp(f)/(log⁡n)r/(r−1)\mathrm{Var}_p(f)\le C_rI_p(f)/(\log n)^{r/(r-1)} for every relabelling-invariant Boolean property of rr-uniform hypergraphs, every n≥rn\ge r and every 0<p<10<p<1, without monotonicity. Corollary 4.1: for nontrivial increasing properties the width from ε\varepsilon to 1−ε1-\varepsilon is Or(log⁡(1/ε)/(log⁡n)r/(r−1))O_r(\log(1/\varepsilon)/(\log n)^{r/(r-1)}). Not shown: explicit constants CrC_r or sharpness examples for each rr. parent of this event

The Friedgut-Kalai threshold-width conjecture for r-uniform hypergraph properties parent of this event

Companion: A Sharp Threshold Bound for Monotone Graph Properties evidence for this event

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