Mathematical FrontierNetworkSubmit movement

Discoveries / combinatorics

Source authenticated

The Ascoli-He-Park-Talagrand graph-decomposition conjecture at the expectation threshold

Theorem 1.1: there are absolute k≥2k\ge2 and L≥1L\ge1 such that for every n≥2n\ge2 and every graph HH on at most nn vertices, E(H)=E(H1)⊔⋯⊔E(Hk)E(H)=E(H_1)\sqcup\dots\sqcup E(H_k) with pc(Hi;n)≤Lq(H;n)p_c(H_i;n)\le Lq(H;n) for each ii. Pieces may be empty or share vertices, and the partition depends only on HH and nn. It does not give a single copy of HH at threshold Lq(H;n)Lq(H;n) (the separate embeddings need not glue), and kk, LL are not explicit.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

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 Ascoli-He-Park-Talagrand graph-decomposition conjecture at the expectation threshold · AHPT graph-decomposition conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Lineage and corrections

VibeMathed record: The Ascoli-He-Park-Talagrand graph-decomposition conjecture at the expectation threshold evidence for this event

This event attributed to Unreleased internal OpenAI model

Ascoli, He, Park, Talagrand, A reformulation of the discrete Convexity Conjecture (2026) evidence for this event

Theorem 1.1: there are absolute k≥2k\ge2 and L≥1L\ge1 such that for every n≥2n\ge2 and every graph HH on at most nn vertices, E(H)=E(H1)⊔⋯⊔E(Hk)E(H)=E(H_1)\sqcup\dots\sqcup E(H_k) with pc(Hi;n)≤Lq(H;n)p_c(H_i;n)\le Lq(H;n) for each ii. Pieces may be empty or share vertices, and the partition depends only on HH and nn. It does not give a single copy of HH at threshold Lq(H;n)Lq(H;n) (the separate embeddings need not glue), and kk, LL are not explicit. parent of this event

Input: Talagrand's discrete-convexity conjecture evidence for this event

Family: Integral and fractional expectation thresholds are equivalent evidence for this event

The Ascoli-He-Park-Talagrand graph-decomposition conjecture at the expectation threshold parent of this event

The Ascoli-He-Park-Talagrand graph-decomposition conjecture at the expectation threshold evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verifyOpen canonical problemExplore evidence graph