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Proposes a dimension-free Poincaré bound for isotropic log-concave measures through cumulant estimates, localization and suspension.
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.
For isotropic log-concave measures, Lee and Vempala obtained C_P(μ) ≤ C√n (Ann. Math. 2024); Chen established a sub-polynomial bound (GAFA 2021); Klartag and Lehec proved a poly-logarithmic bound (GAFA 2022); and Klartag proved C_P(μ) ≤ C log n (2023).
Passage ID: kls-conjecture:entry:bkl-history:v1
Source item: introduction-history
Source record: kls-conjecture:source:bkl:v1
Proposes a dimension-free Poincaré bound for isotropic log-concave measures through cumulant estimates, localization and suspension.
Passage ID: kls-conjecture:entry:bkl:v1
Source item: bkl
Source record: kls-conjecture:source:bkl:v1
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v5
Source assessment
Proved
A sub-polynomial bound (Chen 2021)
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026
Source assessment
Proved
A logarithmic bound (Klartag 2023)
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026
Source assessment
Proved
A poly-logarithmic bound (Klartag & Lehec 2022)
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026
Source assessment
Proved
A square-root bound (Lee & Vempala 2024)
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026
Source assessment
Proved
Conditional mathematical implication in the cited source
This affine-transfer implication does not establish the premise or a numerical value of C. Singular covariance requires a formulation on its affine support.
Observed Oct 13, 2026
Source assessment
Proposed
Uniform bound proposed by Bizeul, Klartag and Lehec
Theorem 1.1 asserts a universal Poincaré bound. No formal execution or independent mathematical assessment is recorded here.
Source date Oct 4, 2026 · Observed Oct 13, 2026
Proof explanation
Bizeul–Klartag–Lehec account
Question
Kannan–Lovász–Simonovits conjecture
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
Another manuscript presents a proof
Further reading
Read the mathematical argument; inspect its Claim for assessment and scope.
Recorded authorship
Pierre Bizeul · Boaz Klartag · Joseph Lehec
Pierre Bizeul, Boaz Klartag, Joseph Lehec
The authors credit ChatGPT with many proof ideas and arguments, and credit the suspension idea and exposition to the human authors. Their approach uses a criterion of Song and Zhang; these are distinct papers with a mathematical dependency, not wholly independent proofs.
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
Presenting a proof of the Kannan–Lovász–Simonovits conjecture
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