Mathematical FrontierNetworkSubmit movement

Discoveries / geometry-topology

Source authenticated

The strong isotropic constant conjecture: simplices maximize the isotropic constant

Claims Theorem 1.1: for every n≥1n\ge1 and every convex body K⊂RnK\subset\mathbb R^n, LK≤(n!)1/n/((n+1)(n+1)/(2n)n+2)L_K\le(n!)^{1/n}/((n+1)^{(n+1)/(2n)}\sqrt{n+2}), with equality if and only if KK is a simplex. Also claims the sharp entropy bound h(f)≥m+12log⁡det⁡Cov(f)h(f)\ge m+\tfrac12\log\det\mathrm{Cov}(f) for every log-concave density on Rm\mathbb R^m, with equality exactly for affine images of products of one-sided exponentials, proved via Gaussian-to-target Brenier transport. Via Klartag (2018) it yields the non-symmetric Mahler inequality ∣K∣∣K∘∣≥(n+1)n+1/(n!)2|K||K^\circ|\ge(n+1)^{n+1}/(n!)^2, already listed from a separate manuscript of the same release. It gives no new information on the symmetric slicing constant or on symmetric Mahler.

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 strong isotropic constant conjecture: simplices maximize the isotropic constant · Simplex isotropic constant 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 strong isotropic constant conjecture: simplices maximize the isotropic constant evidence for this event

This event attributed to Unreleased internal OpenAI model

The strong isotropic constant conjecture: simplices maximize the isotropic constant evidence for this event

Claims Theorem 1.1: for every n≥1n\ge1 and every convex body K⊂RnK\subset\mathbb R^n, LK≤(n!)1/n/((n+1)(n+1)/(2n)n+2)L_K\le(n!)^{1/n}/((n+1)^{(n+1)/(2n)}\sqrt{n+2}), with equality if and only if KK is a simplex. Also claims the sharp entropy bound h(f)≥m+12log⁡det⁡Cov(f)h(f)\ge m+\tfrac12\log\det\mathrm{Cov}(f) for every log-concave density on Rm\mathbb R^m, with equality exactly for affine images of products of one-sided exponentials, proved via Gaussian-to-target Brenier transport. Via Klartag (2018) it yields the non-symmetric Mahler inequality ∣K∣∣K∘∣≥(n+1)n+1/(n!)2|K||K^\circ|\ge(n+1)^{n+1}/(n!)^2, already listed from a separate manuscript of the same release. It gives no new information on the symmetric slicing constant or on symmetric Mahler. parent of this event

The strong isotropic constant conjecture: simplices maximize the isotropic constant parent of this event

Scalar certificate checker verify_scalar.py (run here, ALL CHECKS PASSED) evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verifyOpen canonical problemExplore evidence graph