Publication v1

Record details

Kannan–Lovász–Simonovits conjecture →

Coverage & review

Coverage of this curation

Original question, distinct results, proof provenance, selected history and an explanatory schematic.

Formal proofs: No linked formal proof project for the full KLS theorem was found in these primary sources. The October proposals remain under assessment; publication and model checks are not independent validation.

AI-assisted work: Song–Zhang and Bizeul–Klartag–Lehec own separate manuscripts. Their AI disclosures assign models proof exploration, ideas and checking; the authors retain mathematical responsibility. Bizeul–Klartag–Lehec explicitly use a Song–Zhang criterion, which is kept visible as a dependency.

Search scope & review

Selected primary papers, exact formal declarations, project provenance and official descriptions checked on 13 October 2026.

Checked Oct 13, 2026 · independent review pending.

  • Independent mathematical assessment of both current proposals is pending.
  • No full-theorem formal proof was found in the selected primary sources.
  • Exact numerical universal constants and a comprehensive earlier-bound history are not supplied by this curated reader.

General status observations

An O(1) Bound for the KLS Constant — second revision ↗

Uniform bound proposed by Song and Zhang in revision two · observed Oct 13, 2026

Source status dated Oct 4, 2026 · observed Oct 13, 2026

The later manuscript proposes a constant independent of dimension; independent mathematical assessment is pending.

Source identities & rights

An O(4^log* n) Bound for the KLS Constant — first revision ↗

Zhao Song, Xinzhi Zhang · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
kls-conjecture:source:song:v1
Revision
arXiv:2610.01447v1
Content SHA-256
11ded7a039724f1c925273968ead3ff1695e3161f11df5f40db7ee50ff1c1355
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

An O(1) Bound for the KLS Constant — second revision ↗

Zhao Song, Xinzhi Zhang · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
kls-conjecture:source:song:v2
Revision
arXiv:2610.01447v2
Content SHA-256
c69ea9c264ec83518df1ee205443fa54efe647c3c175344cbe5c75d7d091ce3d
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

Presenting a proof of the Kannan–Lovász–Simonovits conjecture ↗

Pierre Bizeul, Boaz Klartag, Joseph Lehec · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
kls-conjecture:source:bkl:v1
Revision
2026-10-04
Content SHA-256
fb51ab0d94171ac7de2a3009efb5249e44ee66de5c9a1dc5899bdb843de29df9
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

Publication history

Problem ID
problem-kls-conjecture
Publication checksum
aef3bb9b2e68b712a9a65c1ba4c472381885177ca26414415c63dd9c14c5493e
Published
2026-10-13T15:56:20.861602+00:00
Publication reason
Source-linked pilot import; independent mathematical review remains pending.
  1. Version 1 · Oct 13, 2026

    Source-linked pilot import; independent mathematical review remains pending.

  2. Version 2 · Oct 13, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  3. Version 3 · Oct 13, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  4. Version 4 · Oct 14, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  5. Version 5 · Oct 21, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

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