Proved
Conditional mathematical implication in the cited source ↗
Observed Oct 13, 2026
Theorem · version 1
Transporting the proposed bound beyond isotropic measures
Statement
If every isotropic log-concave probability measure has Poincaré constant at most C, then every full-dimensional log-concave probability measure μ with covariance Σ satisfies C_P(μ) ≤ C ‖Σ‖op.
Assumptions
- Finite nonsingular covariance and a log-concave probability density.
- The same universal constant C is assumed in the isotropic theorem.
Scope
This affine-transfer implication does not establish the premise or a numerical value of C. Singular covariance requires a formulation on its affine support.
Evidence
Source reports
Connections
In this problem · publication v3 · Selected context
Kannan–Lovász–Simonovits conjecture →
Conditional implication · Proved
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v5
Kannan–Lovász–Simonovits conjecture →
Conditional implication · Proved
Relationship not independently reviewed. This concerns its use in this problem.
Sources
Presenting a proof of the Kannan–Lovász–Simonovits conjecture →
- Theorem 1.1 and proof/AI acknowledgement → · Original passage ↗
Recorded wording
Proposes a dimension-free Poincaré bound for isotropic log-concave measures through cumulant estimates, localization and suspension.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Pierre Bizeul · Boaz Klartag · Joseph Lehec · Preprint · Publication date Oct 4, 2026
Revision & attribution
Source revision: 2026-10-04. Observed Oct 13, 2026.
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.
History
Statement versions
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessment history · 1
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proved
Conditional mathematical implication in the cited source ↗
Observed Oct 13, 2026 · Source passage →
Record details
- Claim ID
- claim-kls-conjecture-consequence
- Statement version
- 1
- SHA-256
- d0aec6e422cdec5a9a802054ea79ff9382159323b74a2e929b345022586ea068