Published problems
23
Maintained records
19
Source-linked entries
4
Current state unknown
0
Source checks overdue
0

Selection and checking

Staff select identifiable source items across several mathematical fields, check the wording and scope, retain source labels and observation dates, and preview the record against the publication contract. A separate staff action publishes it. No raw import candidate enters the public catalog.

Maintained records add a named decision in an OpenMath collection, a rationale and a recheck date. The present cluster covers known prime results, their related formulations and one bounded Lean exercise. Independent mathematical review remains pending.

“Checked” means that a cited document or source correspondence was inspected on that date. It does not mean every later paper or solution claim was reviewed. An upstream date is never inferred from the observation date. Historical sources remain historical even when visited recently.

Indexed source versions

metadata-link · Not established; links and OpenMath paraphrases only

AIM · Caccetta–Häggkvist workshop survey ↗

Directed graph questions and partial results from the 2006 workshop

Blair D. Sullivan; hosted by American Institute of Mathematics · Observed Oct 21, 2026 · Source date Apr 14, 2006 · Check every 180 days

Store metadata and original OpenMath paraphrases; follow the original source for authoritative wording.

Registry, attribution & update policy
Version ID
aim-caccetta@2006-04-14-sha256-98251ac3
Revision
2006-04-14-sha256-98251ac3
Update method
Manual checked import; new observations require staff preview and publication
Identifiers
Canonical source URL plus explicit item/declaration locator; no fuzzy identity merge
Attribution
Blair D. Sullivan; hosted by American Institute of Mathematics

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Miller · computer-assisted finite BSD cases ↗

Miller · computer-assisted finite BSD cases

Robert L. Miller · Observed Oct 10, 2026 · Source date Dec 21, 2011 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-1010.2431@arxiv-v3
Revision
arxiv-v3
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Robert L. Miller

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Jetchev–Skinner–Wan · rank-one BSD p-part ↗

Jetchev–Skinner–Wan · rank-one BSD p-part

Dimitar Jetchev; Christopher Skinner; Xin Wan · Observed Oct 10, 2026 · Source date Dec 21, 2015 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-1512.06894@arxiv-v1
Revision
arxiv-v1
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Dimitar Jetchev; Christopher Skinner; Xin Wan

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Rodgers–Tao · Newman constant is nonnegative ↗

Rodgers–Tao · Newman constant is nonnegative

Brad Rodgers; Terence Tao · Observed Oct 10, 2026 · Source date Jul 3, 2021 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-1801.05914@arxiv-v5
Revision
arxiv-v5
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Brad Rodgers; Terence Tao

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Tao · quantitative bounds for critically bounded solutions ↗

Tao · quantitative bounds for critically bounded solutions

Terence Tao · Observed Oct 21, 2026 · Source date Jul 10, 2020 · Check every 90 days

No upstream full text is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-1908.04958@arxiv-v2
Revision
arxiv-v2
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Terence Tao

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Platt–Trudgian · rigorous finite verification ↗

Platt–Trudgian · rigorous finite verification

Dave Platt; Tim Trudgian · Observed Oct 10, 2026 · Source date Apr 21, 2020 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2004.09765@arxiv-v1
Revision
arxiv-v1
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Dave Platt; Tim Trudgian

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Kang–Protas · Ladyzhenskaya–Prodi–Serrin conditions ↗

Kang–Protas · Ladyzhenskaya–Prodi–Serrin conditions

Di Kang; Bartosz Protas · Observed Oct 21, 2026 · Source date Oct 11, 2021 · Check every 90 days

No upstream full text is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2110.06130@arxiv-v1
Revision
arxiv-v1
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Di Kang; Bartosz Protas

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Guth–Maynard · zero-density estimates ↗

Guth–Maynard · zero-density estimates

Larry Guth; James Maynard · Observed Oct 10, 2026 · Source date Apr 7, 2026 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2405.20552@arxiv-v2
Revision
arxiv-v2
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Larry Guth; James Maynard

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Burungale–Skinner–Tian–Wan · zeta elements ↗

Burungale–Skinner–Tian–Wan · zeta elements

Ashay Burungale; Christopher Skinner; Ye Tian; Xin Wan · Observed Oct 10, 2026 · Source date Sep 11, 2024 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2409.01350@arxiv-v2
Revision
arxiv-v2
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Ashay Burungale; Christopher Skinner; Ye Tian; Xin Wan

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Markman · cycles from secant sheaves ↗

Markman · cycles from secant sheaves

Eyal Markman · Observed Oct 10, 2026 · Source date Jun 8, 2025 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2502.03415@arxiv-v2
Revision
arxiv-v2
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Eyal Markman

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Floccari–Fu · Weil fourfolds and powers ↗

Floccari–Fu · Weil fourfolds and powers

Salvatore Floccari; Lie Fu · Observed Oct 10, 2026 · Source date Feb 10, 2026 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2504.13607@arxiv-v2
Revision
arxiv-v2
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Salvatore Floccari; Lie Fu

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Floccari–Fu · Weil fourfolds and powers ↗

Floccari–Fu · Weil fourfolds and powers

Salvatore Floccari; Lie Fu · Observed Oct 10, 2026 · Source date Feb 10, 2026 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2504.13607@journal-2026-103876
Revision
journal-2026-103876
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Salvatore Floccari; Lie Fu

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Banwait–Huang · effective BSD twist families ↗

Banwait–Huang · effective BSD twist families

Barinder S. Banwait; Xiaoyu Huang · Observed Oct 10, 2026 · Source date Jun 4, 2026 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2601.16044@arxiv-v3
Revision
arxiv-v3
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Barinder S. Banwait; Xiaoyu Huang

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Bellotti–Trudgian–Yang · explicit zero-free region ↗

Bellotti–Trudgian–Yang · explicit zero-free region

Chiara Bellotti; Timothy S. Trudgian; Andrew Yang · Observed Oct 10, 2026 · Source date Mar 23, 2026 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2603.21490@arxiv-v1
Revision
arxiv-v1
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Chiara Bellotti; Timothy S. Trudgian; Andrew Yang

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Alpöge–Furman · simple zeros on the line ↗

Alpöge–Furman · simple zeros on the line

Levent Alpöge; Ralph Furman · Observed Oct 10, 2026 · Source date Aug 19, 2026 · Check every 30 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2608.13637@arxiv-v2
Revision
arxiv-v2
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Levent Alpöge; Ralph Furman

metadata-link · External full-text redistribution rights not asserted

Broe · Tate for abelian fourfolds over finite fields ↗

Broe · Tate for abelian fourfolds over finite fields

Matt Broe · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; full text stays upstream.

Registry, attribution & update policy
Version ID
arxiv-2608.28651@arxiv-v1
Revision
arxiv-v1
Update method
Manual primary-source revision check; changes require a new immutable source version.
Identifiers
Stable bibliographic identity, explicit revision and exact source-entry locators.
Attribution
Matt Broe

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Lamzouri · another proof and further proportions ↗

Lamzouri · another proof and further proportions

Youness Lamzouri · Observed Oct 10, 2026 · Source date Sep 8, 2026 · Check every 30 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2609.02882@arxiv-v2
Revision
arxiv-v2
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Youness Lamzouri

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Li · withdrawn CM-fourfold powers preprint ↗

Li · withdrawn CM-fourfold powers preprint

Ningyi Li · Observed Oct 10, 2026 · Source date Oct 8, 2026 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-2609.27916@arxiv-v2-withdrawn
Revision
arxiv-v2-withdrawn
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Ningyi Li

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Arapura · motivation for Hodge cycles ↗

Arapura · motivation for Hodge cycles

Donu Arapura · Observed Oct 10, 2026 · Source date Dec 16, 2005 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
arxiv-math-0501348@arxiv-v3
Revision
arxiv-v3
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Donu Arapura

metadata-link · Source document rights apply; OpenMath publishes original paraphrases.

The Černý Conjecture for One-Cluster Automata via Annular Spectral Descent ↗

Introduction; main positive-level results; Section 10, Definition 10.1, Lemma 10.2 and Corollary 10.8.

Yinfeng Zhu · Observed Oct 14, 2026 · Source date unavailable · Check every 90 days

Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.

Registry, attribution & update policy
Version ID
cerny-synchronization:source:paper:v1
Revision
v1
Update method
Compare the pinned source before publishing another immutable revision.
Identifiers
Stable source identity; exact source passages are versioned.
Attribution
Yinfeng Zhu

metadata-link · Source document rights apply; OpenMath publishes original paraphrases.

Chernoff’s density is log-concave ↗

Published Bernoulli 20(1), 231–244; ordinary log-concavity and the stronger curvature conjecture.

Fadoua Balabdaoui, Jon A. Wellner · Observed Oct 14, 2026 · Source date unavailable · Check every 90 days

Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.

Registry, attribution & update policy
Version ID
chernoff-density:source:original:v1
Revision
v2
Update method
Compare the pinned source before publishing another immutable revision.
Identifiers
Stable source identity; exact source passages are versioned.
Attribution
Fadoua Balabdaoui, Jon A. Wellner

metadata-link · Source document rights apply; OpenMath publishes original paraphrases.

Chernoff’s Density Is Strongly Log-Concave ↗

Theorem 1; reciprocal-Airy representation, exponential peeling, convolution identity, compactness and AI Usage.

Xianyang Zhang, Quan Zhou · Observed Oct 14, 2026 · Source date unavailable · Check every 90 days

Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.

Registry, attribution & update policy
Version ID
chernoff-density:source:paper:v1
Revision
v1
Update method
Compare the pinned source before publishing another immutable revision.
Identifiers
Stable source identity; exact source passages are versioned.
Attribution
Xianyang Zhang, Quan Zhou

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Bombieri · official RH description ↗

Bombieri · official RH description

Enrico Bombieri · Observed Oct 10, 2026 · Source date unavailable · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
clay-bombieri-riemann@official-description
Revision
official-description
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Enrico Bombieri

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Deligne · official Hodge description ↗

Deligne · official Hodge description

Pierre Deligne · Observed Oct 10, 2026 · Source date unavailable · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
clay-deligne-hodge@official-description
Revision
official-description
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Pierre Deligne

metadata-link · Not established; links and OpenMath paraphrases only

Clay · Millennium Problems ↗

Seven Millennium Prize Problems; five selected here

Clay Mathematics Institute · Observed Oct 1, 2026 · Source date unavailable · Check every 30 days

Store metadata and original OpenMath paraphrases; follow the original source for authoritative wording.

Registry, attribution & update policy
Version ID
clay-millennium@observed-2026-10-01
Revision
observed-2026-10-01
Update method
Manual checked import; new observations require staff preview and publication
Identifiers
Canonical source URL plus explicit item/declaration locator; no fuzzy identity merge
Attribution
Clay Mathematics Institute

metadata-link · Not established; links and OpenMath paraphrases only

Clay · Millennium Problems ↗

Seven Millennium Prize Problems; five selected here

Clay Mathematics Institute · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Store metadata and original OpenMath paraphrases; follow the original source for authoritative wording.

Registry, attribution & update policy
Version ID
clay-millennium@observed-2026-10-10
Revision
observed-2026-10-10
Update method
Manual checked import; new observations require staff preview and publication
Identifiers
Canonical source URL plus explicit item/declaration locator; no fuzzy identity merge
Attribution
Clay Mathematics Institute

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Wiles · official BSD description ↗

Wiles · official BSD description

Andrew Wiles · Observed Oct 10, 2026 · Source date unavailable · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
clay-wiles-bsd@official-description
Revision
official-description
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Andrew Wiles

metadata-link · Original document rights remain with its authors.

Cycle double cover in Lean ↗

The source endpoint covers finite loopless bridgeless multigraphs via a formalized eight-flow theorem and a conversion to cycle covers.

OpenAI, openai/cdc-lean project · Observed Oct 13, 2026 · Source date Jul 9, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
cycle-double-cover:source:lean:v1
Revision
577e9d9ea326d520f80672ee69b830bf1d513df5
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
OpenAI, openai/cdc-lean project

metadata-link · Original document rights remain with its authors.

A proof of the cycle double cover conjecture ↗

A new argument is reported to construct a cycle double cover for every finite loopless bridgeless multigraph.

OpenAI · Observed Oct 13, 2026 · Source date Jul 10, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
cycle-double-cover:source:proof:v1
Revision
2026-07-10
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
OpenAI

metadata-link · Original document rights remain with its authors.

Three-Bit Flows and Cycle Covers. Part I ↗

A separately authored manuscript reports a proof of cycle double cover using an AI-assisted workflow.

Shiva Kintali · Observed Oct 13, 2026 · Source date Jul 13, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
cycle-double-cover:source:separate:v2
Revision
2026-07-13
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
Shiva Kintali

metadata-link · Original source license and document rights apply.

A Formal Counterexample to the Cost-Preserving Single-Source Unsplittable Flow Conjecture ↗

A directed seven-vertex, nine-arc instance has fractional cost 58 and no congestion-allowed unsplittable routing of cost below 60.

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
dinitz-garg-goemans-flow:source:isabelle:v2
Revision
80985fd56a4cb63a90176bf4bfe456eaff949bfd
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

metadata-link · Original source license and document rights apply.

Independent Lean verification of Goemans’ cost counterexample ↗

The project verifies the rational and real cost conjecture refutations and exact optimum 60 for the displayed instance.

Jason Hickey · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
dinitz-garg-goemans-flow:source:lean:v2
Revision
ffba3523f0edd14be3460d039f22a6b98c02fd9e
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Jason Hickey

metadata-link · Original source license and document rights apply.

Single-Source Unsplittable Flows in Planar Graphs ↗

The paper states the original congestion theorem, Goemans’ cost-enhanced conjecture and a planar theorem with twice the largest-demand allowance.

Vera Traub, Laura Vargas Koch, Rico Zenklusen · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
dinitz-garg-goemans-flow:source:literature:v1
Revision
2023-08-04
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Vera Traub, Laura Vargas Koch, Rico Zenklusen

metadata-link · Original source license and document rights apply.

OpenAI unit-distance announcement ↗

The announcement dates the release and describes the AI discovery, external readers and separately credited exponent refinement.

OpenAI · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
erdos-unit-distances:source:announcement:v1
Revision
2026-05-20
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
OpenAI

metadata-link · Original source license and document rights apply.

Unit-distance counterexample in Lean ↗

The pinned submission proves a positive exponent gain for arbitrarily large finite Euclidean planar point sets.

plby/Erdos90 project · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
erdos-unit-distances:source:lean:v2
Revision
2062b0e6c9770c81e397bfe41148e90b92ca0567
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
plby/Erdos90 project

metadata-link · Original source license and document rights apply.

Planar Point Sets with Many Unit Distances ↗

Theorem 1.1 constructs arbitrarily large planar sets with a fixed positive exponent gain in their unordered unit-distance count.

OpenAI · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
erdos-unit-distances:source:proof:v1
Revision
2026-05-20
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
OpenAI

metadata-link · Original source license and document rights apply.

Erdős problem 90: unit distances ↗

The maintained problem entry records the near-linear upper-bound question, its 1946 origin and the 2026 disproof, while retaining the unresolved extremal growth question.

Erdős Problems · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
erdos-unit-distances:source:question:v1
Revision
Observed 2026-10-13
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Erdős Problems

metadata-link · Original source license and document rights apply.

Remarks on the Disproof of the Unit Distance Conjecture ↗

The companion paper provides a human-digested argument and background for the exponent gain, including the classical upper bound.

Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, Melanie Matchett Wood · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
erdos-unit-distances:source:remarks:v1
Revision
2026-05-20
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, Melanie Matchett Wood

metadata-link · Original source license and document rights apply.

Remarks on the Breakdown of Smooth Solutions for the 3-D Euler Equations ↗

The classical continuation criterion makes integrated supremum vorticity a necessary divergence diagnostic at finite-time smooth breakdown.

J. Thomas Beale, Tosio Kato, Andrew Majda · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
euler-regularity:source:bkm:v1
Revision
1984
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
J. Thomas Beale, Tosio Kato, Andrew Majda

metadata-link · Original source license and document rights apply.

Finite Time Blowup for the Euler Equation ↗

The manuscript states smooth compactly supported unforced Euler data with finite maximal lifespan.

OpenAI · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
euler-regularity:source:paper:v1
Revision
2026-09-08
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
OpenAI

metadata-link · Original source license and document rights apply.

Sharp small-deviation inequalities for sums of independent nonnegative random variables ↗

Proves two parameter-range lower bounds, with the finite-n bound sharp when δ ≥ 1.

Weibo Fu, Yanjun Han, Guanyang Wang, Jun Yan, Peng Zhang, Zhengqing Zhou · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
feige-conjecture:source:fu:v1
Revision
2026-07-27
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
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Weibo Fu, Yanjun Han, Guanyang Wang, Jun Yan, Peng Zhang, Zhengqing Zhou

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Lean proof of the sharp unit-slack Feige bound ↗

The headline theorem asserts optimality of (n/(n+1))^n for every positive finite n in the strict unit-slack event.

Guanyang Wang, Peng Zhang · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

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Version ID
feige-conjecture:source:lean:v1
Revision
19c61d6cb556d1e967dbb0ada9f293c290837867
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Guanyang Wang, Peng Zhang

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On Samuels’ Conjecture ↗

Claims Samuels’ sharp mean-vector formula and the full sharp Feige formula for every δ > 0.

Zhi Ling · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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feige-conjecture:source:ling:v1
Revision
2026-08-18
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Zhi Ling

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On Feige’s conjecture ↗

Gives a separate argument for the unit-slack inequality and the bound δ(n/(n+δ))^n for 0 < δ ≤ 1 under unit means.

Zipei Nie, Jiaye Wei · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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feige-conjecture:source:nie:v1
Revision
2026-07-27
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Zipei Nie, Jiaye Wei

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On the Navier–Stokes Millennium Prize Problem ↗

The announcement describes the mathematical/model workflow, later formalization, and concurrent forced-Euler work with a different scope.

OpenAI · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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fluid-regularity:source:announcement:v1
Revision
2026-09-08
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OpenAI

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Navier–Stokes and Euler formal proof sources ↗

The project reports complete main-result formalizations, zero sorry counts and only standard logical axioms at the listed endpoints.

OpenAI · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

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Version ID
fluid-regularity:source:lean:v2
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f9e8bc5b38b6e212696e8a30e3e91517af887bbd
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OpenAI

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Poincaré comparator integration verification ↗

Poincaré comparator integration verification

FrenzyMath contributors · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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frenzymath-poincare-verification@432c38f2aa5a30efb13871292d17b4a3309a496a
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432c38f2aa5a30efb13871292d17b4a3309a496a
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FrenzyMath contributors

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Poincaré comparator integration verification ↗

Poincaré comparator integration verification

FrenzyMath contributors · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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frenzymath-poincare-verification@432c38f2aa5a30efb13871292d17b4a3309a496a-metadata-v2
Revision
432c38f2aa5a30efb13871292d17b4a3309a496a; bibliographic metadata corrected 2026-10-12
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FrenzyMath contributors

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An AI-Assisted Formalization of the Poincaré Conjecture ↗

An AI-Assisted Formalization of the Poincaré Conjecture

Zhiyuan Zhang; Axel Delaval; Leheng Chen; Jinxuan Chen; Jie Xu; Yuxuan Liao; Jiedong Jiang; Chunlei Liu; Bin Dong · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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frenzymath-poincare@arxiv-2610.08329v1
Revision
arxiv-2610.08329v1
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Zhiyuan Zhang; Axel Delaval; Leheng Chen; Jinxuan Chen; Jie Xu; Yuxuan Liao; Jiedong Jiang; Chunlei Liu; Bin Dong

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Small Counterexamples to the Gaussian Moments Conjecture ↗

Gives a cubic four-variable witness and a quartic three-variable witness, both with zero pure moments and nonzero mixed moments of every order.

Christopher D. Long · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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gaussian-moments:source:long:v1
Revision
2026-07-20
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Christopher D. Long

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The Gaussian Moments Conjecture and the Jacobian Conjecture ↗

Introduces Gaussian moment vanishing, proves the one-variable case and gives a global implication to the Jacobian conjecture.

Harm Derksen, Arno van den Essen, Wenhua Zhao · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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gaussian-moments:source:original:v1
Revision
2015-06-17
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Harm Derksen, Arno van den Essen, Wenhua Zhao

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Gomila · proposed improved Newman bound ↗

Gomila · proposed improved Newman bound

Jude Gomila · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

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Version ID
gomila-newman-candidate@git-a74738deb6d5e0f76887cb36901da08b68dca705
Revision
git-a74738deb6d5e0f76887cb36901da08b68dca705
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Jude Gomila

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Counting flags in triangle-free digraphs ↗

Counting flags in triangle-free digraphs

Jan Hladký; Daniel Král’; Sergey Norin · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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hkn-triangle-bound@arxiv-0908.2791v4
Revision
arxiv-0908.2791v4
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Jan Hladký; Daniel Král’; Sergey Norin

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Aharoni’s rainbow cycle conjecture holds up to an additive constant ↗

Aharoni’s rainbow cycle conjecture holds up to an additive constant

Patrick Hompe; Tony Huynh · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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Version ID
hompe-huynh-rainbow@arxiv-2212.05697v4
Revision
arxiv-2212.05697v4
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Patrick Hompe; Tony Huynh

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ICARM · individual high-rank curve record ↗

ICARM · individual high-rank curve record

ICARM leaderboard; submitter ranksunbounded · Observed Oct 10, 2026 · Source date Aug 20, 2026 · Check every 90 days

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Version ID
icarm-curve-273@observed-2026-10-10
Revision
observed-2026-10-10
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Attribution
ICARM leaderboard; submitter ranksunbounded

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Counterexamples to the Jacobian conjecture in dimensions greater than two ↗

Algebraic analysis of the three-variable counterexample, including its non-injectivity; the two-dimensional complex case remains open.

Shuhong Gao · Observed Oct 13, 2026 · Source date Jul 31, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

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Version ID
jacobian-conjecture:source:analysis:v2
Revision
2026-07-31
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Shuhong Gao

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Alpöge counterexample in Lean ↗

The source proves constant formal polynomial Jacobian determinant, a three-point fiber, and failure of a polynomial inverse for the recorded Jacobian conjecture statement.

alerad/alpoge-lean project · Observed Oct 13, 2026 · Source date Jul 23, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

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Version ID
jacobian-conjecture:source:lean:v1
Revision
b8eec94711a9b73151929b78cbd7cb999a008590
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alerad/alpoge-lean project

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A Counterexample to the Jacobian Conjecture ↗

An explicit three-variable polynomial map has constant determinant −2 and a fiber containing three distinct rational points.

ULAM research manuscript (no author named) · Observed Oct 13, 2026 · Source date Jul 20, 2026 · Check every 90 days

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Version ID
jacobian-conjecture:source:witness:v2
Revision
2026-07-20
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ULAM research manuscript (no author named)

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Kemeny Rank Aggregation is NP-Hard for Three Voters ↗

Theorem 1; Sections 1–6, especially the MAX CUT reduction and three-ballot realization.

Dominik Peters · Observed Oct 14, 2026 · Source date unavailable · Check every 90 days

Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.

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Version ID
kemeny-three-voters:source:paper:v1
Revision
v1
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Dominik Peters

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Kent · AI-augmented BSD research substrate ↗

Kent · AI-augmented BSD research substrate

Owen P. Kent (repository owner) · Observed Oct 10, 2026 · Source date Jun 14, 2026 · Check every 90 days

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Version ID
kent-bsd-project@0e9519aaeb5c8b8c524f95925eecb970d86bc5b1-metadata-2026-10-10
Revision
0e9519aaeb5c8b8c524f95925eecb970d86bc5b1
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Owen P. Kent (repository owner)

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

Proposes a dimension-free Poincaré bound for isotropic log-concave measures through cumulant estimates, localization and suspension.

Pierre Bizeul, Boaz Klartag, Joseph Lehec · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

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Version ID
kls-conjecture:source:bkl:v1
Revision
2026-10-04
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Pierre Bizeul, Boaz Klartag, Joseph Lehec

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

The first revision proposes inverse Cheeger bound O(4^log* n), giving Poincaré bound O(16^log* n).

Zhao Song, Xinzhi Zhang · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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Version ID
kls-conjecture:source:song:v1
Revision
arXiv:2610.01447v1
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Zhao Song, Xinzhi Zhang

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

The second revision proposes a uniform O(1) bound, strengthening the first revision’s slowly dimension-dependent estimate.

Zhao Song, Xinzhi Zhang · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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kls-conjecture:source:song:v2
Revision
arXiv:2610.01447v2
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Zhao Song, Xinzhi Zhang

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From Knots to Four-Manifolds ↗

From Knots to Four-Manifolds

Ciprian Manolescu · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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Version ID
manolescu-four-manifolds@icm-2026-doi-25M1806703
Revision
icm-2026-doi-25M1806703
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Ciprian Manolescu

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Mathlib · wanted Poincaré statements ↗

Mathlib · wanted Poincaré statements

Mathlib contributors · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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mathlib-poincare-wanted@9454a4c25a2b923eb55dba3098f2d6ae0484d09b
Revision
9454a4c25a2b923eb55dba3098f2d6ae0484d09b
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Mathlib contributors

licensed-excerpt · Apache-2.0

mathlib · natural-number prime definitions ↗

Natural-number primality and divisibility

mathlib contributors · Observed Oct 1, 2026 · Source date unavailable · Check every 180 days

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Version ID
mathlib-prime-defs@32d24245c7a12ded17325299fd41d412022cd3fe
Revision
32d24245c7a12ded17325299fd41d412022cd3fe
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mathlib contributors

licensed-excerpt · Apache-2.0

mathlib · infinitude of primes ↗

Natural-number prime statements

mathlib contributors · Observed Oct 1, 2026 · Source date unavailable · Check every 180 days

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Version ID
mathlib-prime-infinite@32d24245c7a12ded17325299fd41d412022cd3fe
Revision
32d24245c7a12ded17325299fd41d412022cd3fe
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mathlib contributors

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Topology through Four Centuries: Low Dimensional Manifolds ↗

Topology through Four Centuries: Low Dimensional Manifolds · ICM 2014 lecture slides

John Milnor · Observed Oct 21, 2026 · Source date unavailable · Check every 365 days

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milnor-four-centuries@icm-2014-slides-sha256-89cf5c46
Revision
icm-2014-slides-sha256-89cf5c46
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John Milnor

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The Poincaré Conjecture · official description ↗

The Poincaré Conjecture · official description

John Milnor · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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Version ID
milnor-poincare-description@clay-description-observed-2026-10-12
Revision
clay-description-observed-2026-10-12
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John Milnor

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Ricci Flow and the Poincaré Conjecture ↗

Ricci Flow and the Poincaré Conjecture

John Morgan; Gang Tian · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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Version ID
morgan-tian-poincare@clay-monograph-3-2007
Revision
clay-monograph-3-2007
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John Morgan; Gang Tian

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Clay Mathematics Institute: Navier–Stokes announcement ↗

CMI acknowledges the announcement and describes its deliberately unhurried evaluation process. It does not record a prize award.

Clay Mathematics Institute · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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Version ID
navier-stokes:source:clay-announcement:v1
Revision
2026-09-11
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Clay Mathematics Institute

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Existence and Smoothness of the Navier–Stokes Equation ↗

The official problem specifies alternatives A/B for unforced regularity and C/D for forced breakdown, with separate decay, periodicity and energy conditions.

Charles L. Fefferman · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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navier-stokes:source:clay:v1
Revision
2000
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Charles L. Fefferman

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Finite Time Blowup for Navier–Stokes ↗

The manuscript states forced breakdown from rest with compactly supported smooth forcing, bounded kinetic energy and unbounded velocity; it also states a periodic corollary.

OpenAI · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

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navier-stokes:source:paper:v1
Revision
2026-09-08
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OpenAI

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OpenAI · proposed full BSD from low Selmer corank ↗

OpenAI · proposed full BSD from low Selmer corank

OpenAI · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

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Version ID
openai-bsd-low-selmer@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Revision
fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Update method
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Attribution
OpenAI

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OpenAI · proposed Goldfeld analytic densities and 2-converse ↗

OpenAI · proposed Goldfeld analytic densities and 2-converse

OpenAI · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

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Version ID
openai-goldfeld@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Revision
fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Update method
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Attribution
OpenAI

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OpenAI · proposed Hodge theorem for CM abelian varieties ↗

OpenAI · proposed Hodge theorem for CM abelian varieties

OpenAI · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

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Version ID
openai-hodge-cm@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Revision
fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Update method
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Attribution
OpenAI

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OpenAI · proposed Milne rationality theorem ↗

OpenAI · proposed Milne rationality theorem

OpenAI · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

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Version ID
openai-milne-rationality@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Revision
fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Update method
Manual primary-source revision check; changes require a new immutable source version.
Identifiers
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Attribution
OpenAI

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

OpenAI · reported seven-eighths half-plane ↗

OpenAI · reported seven-eighths half-plane

OpenAI · Observed Oct 10, 2026 · Source date Sep 30, 2026 · Check every 30 days

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Version ID
openai-quasi-rh@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Revision
git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
OpenAI

full-text · CC-BY-4.0

OpenMath · prime note ↗

Elementary-number-theory reference prose

OpenMath staff · Observed Oct 1, 2026 · Source date Sep 26, 2026 · Check every 180 days

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Version ID
openmath-prime-note@a640f3adfa536da0
Revision
a640f3adfa536da0
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OpenMath staff

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Finite extinction time for the solutions to the Ricci flow on certain three-manifolds ↗

Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Grigori Perelman · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

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Version ID
perelman-extinction@arxiv-math-0307245v1
Revision
arxiv-math-0307245v1
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Grigori Perelman

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Petersen counterexample: frozen construction and certificates ↗

Version 1.1.0; exact graphs, encoders, manifests, logs and separate DRAT proof files.

Bryce Putman · Observed Oct 14, 2026 · Source date unavailable · Check every 90 days

Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.

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Version ID
petersen-coloring:source:archive:v1
Revision
1.1.0
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Bryce Putman

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A 112-Vertex Counterexample to the Petersen Coloring Conjecture ↗

Theorems 1.1 and 6.1, Proposition 2.1, Corollary 5.1, Appendices A–B and computational provenance.

Bryce Putman · Observed Oct 14, 2026 · Source date unavailable · Check every 90 days

Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.

Registry, attribution & update policy
Version ID
petersen-coloring:source:paper:v1
Revision
v1
Update method
Compare the pinned source before publishing another immutable revision.
Identifiers
Stable source identity; exact source passages are versioned.
Attribution
Bryce Putman

metadata-link · Full-text redistribution rights not asserted

Robust MDP policy iteration and Aletheia contribution ↗

The precise statements and locators cited in this P versus NP research record.

Ali Asadi; Krishnendu Chatterjee; Ehsan Goharshady; Mehrdad Karrabi; Alipasha Montaseri; Carlo Pagano · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

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Version ID
pnp-aletheia@arXiv-2601.23229v2
Revision
arXiv-2601.23229v2
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Ali Asadi; Krishnendu Chatterjee; Ehsan Goharshady; Mehrdad Karrabi; Alipasha Montaseri; Carlo Pagano

metadata-link · Full-text redistribution rights not asserted

Aaronson–Wigderson · Algebrization ↗

The precise statements and locators cited in this P versus NP research record.

Scott Aaronson; Avi Wigderson · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

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Version ID
pnp-aw@author-conference-version-observed-2026-10-10
Revision
author-conference-version-observed-2026-10-10
Update method
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Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Scott Aaronson; Avi Wigderson

metadata-link · Full-text redistribution rights not asserted

Baker–Gill–Solovay · Relativizations of the P =? NP question ↗

The precise statements and locators cited in this P versus NP research record.

Theodore Baker; John Gill; Robert Solovay · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

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Version ID
pnp-bgs@doi-10.1137/0204037-abstract-observed-2026-10-10
Revision
doi-10.1137/0204037-abstract-observed-2026-10-10
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Theodore Baker; John Gill; Robert Solovay

metadata-link · Full-text redistribution rights not asserted

Avi Wigderson · Mathematics and Computation ↗

The precise statements and locators cited in this P versus NP research record.

Avi Wigderson · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-book@author-draft-2019-08-06
Revision
author-draft-2019-08-06
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Avi Wigderson

metadata-link · Full-text redistribution rights not asserted

Alman–Vassilevska Williams · Truly subquadratic 3SUM and subcubic APSP ↗

The precise statements and locators cited in this P versus NP research record.

Josh Alman; Virginia Vassilevska Williams · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-claude@arXiv-2610.06783v1
Revision
arXiv-2610.06783v1
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Josh Alman; Virginia Vassilevska Williams

metadata-link · Full-text redistribution rights not asserted

Clay · P versus NP ↗

The precise statements and locators cited in this P versus NP research record.

Clay Mathematics Institute · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-clay@observed-2026-10-10
Revision
observed-2026-10-10
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Clay Mathematics Institute

metadata-link · Full-text redistribution rights not asserted

Stephen Cook · The P versus NP problem ↗

The precise statements and locators cited in this P versus NP research record.

Stephen Cook · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-cook@official-description-sha256-018f3d473d16
Revision
official-description-sha256-018f3d473d16
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Stephen Cook

metadata-link · Full-text redistribution rights not asserted

Chen–Tal–Wang · Depth-two threshold lower bounds ↗

The precise statements and locators cited in this P versus NP research record.

Lijie Chen; Avishay Tal; Yichuan Wang · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-ctw@ECCC-TR26-039-observed-2026-10-10
Revision
ECCC-TR26-039-observed-2026-10-10
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Lijie Chen; Avishay Tal; Yichuan Wang

metadata-link · Full-text redistribution rights not asserted

Impagliazzo–Paturi · On the complexity of k-SAT ↗

The precise statements and locators cited in this P versus NP research record.

Russell Impagliazzo; Ramamohan Paturi · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-eth@JCSS-2001
Revision
JCSS-2001
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Russell Impagliazzo; Ramamohan Paturi

metadata-link · Full-text redistribution rights not asserted

Dong et al. · Large language model for science: P vs NP ↗

The precise statements and locators cited in this P versus NP research record.

Qingxiu Dong; Li Dong; Ke Xu; Guangyan Zhou; Yaru Hao; Zhifang Sui; Furu Wei · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-gpt4@arXiv-2309.05689v1
Revision
arXiv-2309.05689v1
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Qingxiu Dong; Li Dong; Ke Xu; Guangyan Zhou; Yaru Hao; Zhifang Sui; Furu Wei

metadata-link · Full-text redistribution rights not asserted

OpenAI · Mathematics release: complexity proposals ↗

The precise statements and locators cited in this P versus NP research record.

OpenAI internal model; author attribution per manuscript · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-openai@fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Revision
fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
OpenAI internal model; author attribution per manuscript

metadata-link · Full-text redistribution rights not asserted

Ren–Williams · Near-maximum circuit lower bounds ↗

The precise statements and locators cited in this P versus NP research record.

Hanlin Ren; Ryan Williams · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-ren@arXiv-2607.09963v1
Revision
arXiv-2607.09963v1
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Hanlin Ren; Ryan Williams

metadata-link · Full-text redistribution rights not asserted

Razborov–Rudich · Natural proofs ↗

The precise statements and locators cited in this P versus NP research record.

Alexander Razborov; Steven Rudich · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-rr@STOC-1994-author-paper
Revision
STOC-1994-author-paper
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Alexander Razborov; Steven Rudich

metadata-link · Full-text redistribution rights not asserted

Cygan et al. · On problems as hard as CNF-SAT ↗

The precise statements and locators cited in this P versus NP research record.

Marek Cygan; Holger Dell; Daniel Lokshtanov; Dániel Marx; Jesper Nederlof; Yoshio Okamoto; Ramamohan Paturi; Saket Saurabh; Magnus Wahlström · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-seth@arXiv-1112.2275v3
Revision
arXiv-1112.2275v3
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Marek Cygan; Holger Dell; Daniel Lokshtanov; Dániel Marx; Jesper Nederlof; Yoshio Okamoto; Ramamohan Paturi; Saket Saurabh; Magnus Wahlström

metadata-link · Full-text redistribution rights not asserted

Ryan Williams · Non-uniform ACC circuit lower bounds ↗

The precise statements and locators cited in this P versus NP research record.

Ryan Williams · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Registry, attribution & update policy
Version ID
pnp-williams@CCC-2011-author-version
Revision
CCC-2011-author-version
Update method
Manual primary-source check; changes require a new source version and staff publication.
Identifiers
Source URL and exact theorem/section locator; no inferred identity merge.
Attribution
Ryan Williams

metadata-link · Original document rights remain with its authors.

Prime gaps at most 186: a conditional Lean development ↗

The endpoint derives a gap bound of 186 from two unproved-in-Lean exponential-sum estimates and an unproved-in-Lean physical integral input. A separate numerical certificate does not discharge those axioms.

OpenAI, PrimeGaps186 contributors · Observed Oct 13, 2026 · Source date Sep 2, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
prime-gaps:source:186-lean:v1
Revision
61340d0b74163003b32756bb16e91d9209a5e330
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
OpenAI, PrimeGaps186 contributors

metadata-link · Original document rights remain with its authors.

A new bound for small gaps between primes ↗

The preliminary draft states H₁ ≤ 212 and explains the analytic and exact rational calculations. Its appendix reports a formal deduction with analytic and variational hypotheses.

François Charton, Letong Hong, Kenny Lau, Ken Ono, Guillaume Remy, Ho Chung Siu, Ashvin A. Swaminathan, Jesse Thorner, Yunzhou Xie · Observed Oct 13, 2026 · Source date Sep 3, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
prime-gaps:source:212:v2
Revision
2026-09-03
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
François Charton, Letong Hong, Kenny Lau, Ken Ono, Guillaume Remy, Ho Chung Siu, Ashvin A. Swaminathan, Jesse Thorner, Yunzhou Xie

metadata-link · Original document rights remain with its authors.

PrimeGapsLib: a formal deduction of the 246 bound ↗

The public revision proves prime-gap bounds of 246 assuming Bombieri–Vinogradov and includes numerical certificates. It does not contain the 212 formalization reported in the later paper.

Axiom Math, PrimeGapsLib contributors · Observed Oct 13, 2026 · Source date Aug 18, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
prime-gaps:source:246-lean:v1
Revision
1faa7b14e82ddebc2772dfb9153922f01b106477
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
Axiom Math, PrimeGapsLib contributors

metadata-link · Original document rights remain with its authors.

Small gaps between primes ↗

Maynard’s multidimensional sieve gives recurring prime gaps of at most 600.

James Maynard · Observed Oct 21, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
prime-gaps:source:maynard:v1
Revision
2015
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
James Maynard

metadata-link · Original document rights remain with its authors.

Variants of the Selberg sieve, and bounded intervals containing many primes ↗

The published Polymath8b argument establishes an unconditional recurring prime gap at most 246; the twin-prime target remains out of reach.

D. H. J. Polymath · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
prime-gaps:source:polymath:v1
Revision
2014
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
D. H. J. Polymath

metadata-link · Original document rights remain with its authors.

Bounded gaps between primes ↗

Zhang proves the first finite bound on gaps between consecutive primes that recur infinitely often.

Yitang Zhang · Observed Oct 21, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
prime-gaps:source:zhang:v1
Revision
2014-05-01
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
Yitang Zhang

metadata-link · Metadata, links and original OpenMath paraphrases only

A Lean Formalization of the Hamilton–Perelman Proof of the Three-Dimensional Poincaré Conjecture ↗

A Lean Formalization of the Hamilton–Perelman Proof of the Three-Dimensional Poincaré Conjecture

Ziyang Qin; Yuan Liao; Ayush Khaitan; Bennett Chow · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days

Follow the original source for authoritative statements and reuse terms.

Registry, attribution & update policy
Version ID
qin-liao-khaitan-chow-poincare@arxiv-2609.33842v1
Revision
arxiv-2609.33842v1
Update method
Manual source review; publish new observations with immutable versions
Identifiers
Source revision plus exact passage or declaration; no fuzzy identity merge
Attribution
Ziyang Qin; Yuan Liao; Ayush Khaitan; Bennett Chow

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Independent Riemann challenge · October 2026 submission ↗

Independent Riemann challenge · October 2026 submission

R. Arun Chandru (submitter); Independent riemannzeta.fun project (operator) · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
riemann-community-record@git-d95a6d7d11d7836306ec7ec1eb5be3478663718e
Revision
git-d95a6d7d11d7836306ec7ec1eb5be3478663718e
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
R. Arun Chandru (submitter); Independent riemannzeta.fun project (operator)

metadata-link · Original source license and document rights apply.

Counterexamples to Schiffer’s Conjecture ↗

Constructs infinitely many symmetry orders with smooth star-shaped non-disk counterexamples through a uniform bifurcation argument.

Gonzalo Cao-Labora, Jaume de Dios Pont · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
schiffer-pompeiu:source:bifurcation:v1
Revision
2026-08-05
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Gonzalo Cao-Labora, Jaume de Dios Pont

metadata-link · Original source license and document rights apply.

Numerical certificate and reproduction report ↗

The exact dyadic input centre, interval audits, tail bounds and standalone checker support the computer-assisted witness.

Matthew J. Colbrook, George Stepaniants · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
schiffer-pompeiu:source:certificate:v1
Revision
2fb3f2ecafd3233dbca390d73e764fe6e04a9c7d
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Matthew J. Colbrook, George Stepaniants

metadata-link · Original source license and document rights apply.

Lean proof of the analytic tenfold construction ↗

The public theorem produces one analytic tenfold domain, its classical field, Pompeiu failure and the exact published frequency interval with no remaining numerical hypotheses.

Matthew J. Colbrook, George Stepaniants · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
schiffer-pompeiu:source:computer-lean:v1
Revision
2fb3f2ecafd3233dbca390d73e764fe6e04a9c7d
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Matthew J. Colbrook, George Stepaniants

metadata-link · Original source license and document rights apply.

A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures ↗

Constructs a non-disk simply connected domain with real-analytic Jordan boundary and tenfold symmetry, using certified numerical estimates.

Matthew J. Colbrook, George Stepaniants · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
schiffer-pompeiu:source:computer:v1
Revision
2026-08-03
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Matthew J. Colbrook, George Stepaniants

metadata-link · Original source license and document rights apply.

Lean proof of the star-shaped Schiffer/Pompeiu construction ↗

Public theorem chain constructs a bounded star-shaped non-disk with C² boundary and a global C² field satisfying normalized Helmholtz and zero full boundary gradient, then derives failure of the Pompeiu property.

Jaume de Dios Pont, Gonzalo Cao-Labora · Observed Oct 13, 2026 · Source date unavailable · Check every 90 days

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Registry, attribution & update policy
Version ID
schiffer-pompeiu:source:lean:v1
Revision
2938e277969c329caf154e48a3d8823f3635c7f1
Update method
Compare the exact source and publish a new immutable curation revision.
Identifiers
Stable source identity with exact versioned passages.
Attribution
Jaume de Dios Pont, Gonzalo Cao-Labora

metadata-link · Original document rights remain with its authors.

A digestion of the proof of Sendov’s conjecture ↗

A streamlined exposition of Mazur’s argument gives Sendov and the sharper Phelps–Rodriguez conclusion, with its boundary equality cases.

Terence Tao · Observed Oct 13, 2026 · Source date Aug 12, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
sendov-conjecture:source:digestion:v1
Revision
2026-08-12
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
Terence Tao

metadata-link · Original document rights remain with its authors.

Sendov and Phelps–Rodriguez in Lean ↗

The pinned public source states full Sendov and Phelps–Rodriguez endpoints and reports only the standard Lean logical axioms for their proofs.

Terence Tao, teorth/sendov project · Observed Oct 13, 2026 · Source date Aug 19, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
sendov-conjecture:source:lean:v1
Revision
1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
Terence Tao, teorth/sendov project

metadata-link · Original document rights remain with its authors.

Sendov conjecture: original proof ↗

A directed AI workflow reports a proof of Sendov for every degree at least two; the original proof and formalization preceded Tao’s exposition.

Lech Mazur · Observed Oct 13, 2026 · Source date Aug 5, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
sendov-conjecture:source:mazur:v1
Revision
2026-08-05
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
Lech Mazur

metadata-link · Original document rights remain with its authors.

Sendov’s conjecture for sufficiently high degree polynomials ↗

Sendov’s conjecture for all sufficiently large degree, with the low-degree history.

Terence Tao · Observed Oct 21, 2026 · Source date Aug 12, 2026 · Check every 90 days

OpenMath supplies original paraphrases and links; no proof text is republished.

Registry, attribution & update policy
Version ID
sendov-conjecture:source:tao-large:v1
Revision
arxiv-2012.04125v2
Update method
Source comparison followed by a new immutable curation revision.
Identifiers
Stable source and entry identities; changed wording receives a new version.
Attribution
Terence Tao

metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.

Skinner · converse to Gross–Zagier–Kolyvagin ↗

Skinner · converse to Gross–Zagier–Kolyvagin

Christopher Skinner · Observed Oct 10, 2026 · Source date Feb 13, 2020 · Check every 90 days

No upstream full text or code is republished by this record.

Registry, attribution & update policy
Version ID
skinner-annals-2020@published-online-2020-02-13
Revision
published-online-2020-02-13
Update method
Manual source and revision check; recheck upstream before a new publication.
Identifiers
Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.
Attribution
Christopher Skinner

Missingness and limits

  • Most mathematical problem lists are not indexed; no complete list or field coverage is claimed.
  • The Clay pilot selects five problems, not the full Millennium list. The AIM pilot selects one historical workshop question.
  • Literature, partial progress and proposed solutions are not comprehensively assessed.
  • The source-linked entries have no independent OpenMath mathematical-status decision.
  • Staff verification, source correspondence and independent mathematical review are distinct.

Overdue check labels are computed from the recorded observation date and source cadence. Earlier reports remain visible without silently becoming a new assessment.

Report a correction

Use the OpenMath issue tracker to identify the Problem URL or stable ID, the publication version, the exact wording or status in question, and a dated primary source. Staff review the evidence and publish a correction with a reason, or withdraw the entry while preserving its history.

Rechecking uses the same preview and publication workflow with an expected prior version. Changed source observations receive new immutable IDs and explicit supersession links. Conflicting reports are retained with attribution, rather than merged into a universal “solved” label.

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