The Kannan-Lovász-Simonovits conjecture
Claims the conjecture in full, for all isotropic log-concave measures: with universal. The route bounds the third cumulant, propagates the estimate to cumulants of every order by Eldan's stochastic localization, realizes derivatives of tilt averages as mixed cumulants through a suspension construction, and closes with the Song-Zhang criterion. The previous best bounds were Klartag's and Song and Zhang's (1 October 2026). Priority: Song and Zhang revised their preprint on 4 October 2026, the day this paper was posted, to claim the same bound by their own route; the two are parallel claims of the same result. Consequences include the thin-shell and variance conjectures, already known to follow from KLS.
Exact FrontierDelta
Scope and record
Occurred: Oct 4, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. 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 Kannan-Lovász-Simonovits conjecture · KLS conjecture
Confidence: Not scored
Registry verification: unreviewed · preprint · candidate
Attribution
VibeMathed
registry · event recorded by
ChatGPT (version not stated)
model · ai model contributor · OpenAI
Pierre Bizeul
human · human collaborator
Boaz Klartag
human · human collaborator
Joseph Lehec
human · human collaborator
Lineage and corrections
This event attributed to Pierre Bizeul
VibeMathed record: The Kannan-Lovász-Simonovits conjecture evidence for this event
The Kannan-Lovász-Simonovits conjecture parent of this event
This event attributed to Joseph Lehec
The KLS conjecture for quadratic forms (earlier AI result) evidence for this event
Kannan, Lovász and Simonovits, Isoperimetric problems for convex bodies (1995) evidence for this event
This event attributed to ChatGPT (version not stated)
Claims the conjecture in full, for all isotropic log-concave measures: with universal. The route bounds the third cumulant, propagates the estimate to cumulants of every order by Eldan's stochastic localization, realizes derivatives of tilt averages as mixed cumulants through a suspension construction, and closes with the Song-Zhang criterion. The previous best bounds were Klartag's and Song and Zhang's (1 October 2026). Priority: Song and Zhang revised their preprint on 4 October 2026, the day this paper was posted, to claim the same bound by their own route; the two are parallel claims of the same result. Consequences include the thin-shell and variance conjectures, already known to follow from KLS. parent of this event
The Kannan-Lovász-Simonovits conjecture evidence for this event
This event attributed to Boaz Klartag
Song and Zhang, An O(1) bound for the KLS constant (arXiv:2610.01447, revised 4 October) evidence for this event
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