The second revision proposes a uniform O(1) bound, strengthening the first revision’s slowly dimension-dependent estimate.
Source publication and attributed assessments are distinct from independent OpenMath review.
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
The second revision proposes a uniform O(1) bound, strengthening the first revision’s slowly dimension-dependent estimate.
Replaces an earlier passage. View versioned records →
Passage ID: kls-conjecture:entry:song-new:v1
Source item: song-new
Source record: kls-conjecture:source:song:v2
Replaces passage: kls-conjecture:entry:song:v1
Zhao Song · Xinzhi Zhang · Preprint · Publication date Oct 1, 2026
The first revision proposes inverse Cheeger bound O(4^log* n), giving Poincaré bound O(16^log* n).
Source publication and attributed assessments are distinct from independent OpenMath review.
The first revision proposes inverse Cheeger bound O(4^log* n), giving Poincaré bound O(16^log* n).
Passage ID: kls-conjecture:entry:song:v1
Source item: song
Source record: kls-conjecture:source:song:v1
Recorded authorship
Zhao Song · Xinzhi Zhang
Zhao Song, Xinzhi Zhang
The authors describe AI-assisted proof exploration and verification. Contribution claims belong to this source revision and do not constitute independent assessment.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Source terms ↗Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v5
Source assessment
Proposed
Uniform bound proposed by Song and Zhang in revision two
The later manuscript proposes a constant independent of dimension; independent mathematical assessment is pending.
Source date Oct 4, 2026 · Observed Oct 13, 2026
Proof explanation
Song second-revision account
Source assessment
Proposed
Slowly dimension-dependent bound proposed in revision one
Inverse Cheeger constant scales as 4^log*(n+2); the Poincaré bound uses its square.
Source date Oct 1, 2026 · Observed Oct 13, 2026
Research activity
Review the current proof proposals
Compare the current revisions, the high-order tilt criterion and the later cumulant/suspension argument.
No independent review verdict or executable formal proof is recorded in this source selection.
History
The second revision proposes a constant bound
Question
Kannan–Lovász–Simonovits conjecture
Further reading
Read the mathematical argument; inspect its Claim for assessment and scope.
History
The convex-geometric conjecture
History
A slowly dimension-dependent bound is proposed
Recorded authorship
Zhao Song · Xinzhi Zhang
Zhao Song, Xinzhi Zhang
Song and Zhang credit GPT-6 Astra, GPT-5.6 Sol and Claude Fable 5/5.1 for extensive proof exploration and checking, with authors directing priorities and retaining responsibility.
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
An O(1) Bound for the KLS Constant — second revision
An O(4^log* n) Bound for the KLS Constant — first revision
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Source terms ↗