metadata-link · Not established; links and OpenMath paraphrases only
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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.
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.
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
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
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
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
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
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.
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 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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
- Stable source identity with exact versioned passages.
- Attribution
- Weibo Fu, Yanjun Han, Guanyang Wang, Jun Yan, Peng Zhang, Zhengqing Zhou
metadata-link · Original source license and document rights apply.
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.
Registry, attribution & update policy
- Version ID
- feige-conjecture:source:lean:v1
- Revision
- 19c61d6cb556d1e967dbb0ada9f293c290837867
- Update method
- Compare the exact source and publish a new immutable curation revision.
- Identifiers
- Stable source identity with exact versioned passages.
- Attribution
- Guanyang Wang, Peng Zhang
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Registry, attribution & update policy
- Version ID
- feige-conjecture:source:ling:v1
- Revision
- 2026-08-18
- Update method
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- Zhi Ling
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- feige-conjecture:source:nie:v1
- Revision
- 2026-07-27
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- Zipei Nie, Jiaye Wei
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- fluid-regularity:source:announcement:v1
- Revision
- 2026-09-08
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- OpenAI
metadata-link · Original source license and document rights apply.
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
- Revision
- f9e8bc5b38b6e212696e8a30e3e91517af887bbd
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metadata-link · Metadata, links and original OpenMath paraphrases only
Poincaré comparator integration verification
FrenzyMath contributors · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days
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- Version ID
- frenzymath-poincare-verification@432c38f2aa5a30efb13871292d17b4a3309a496a
- Revision
- 432c38f2aa5a30efb13871292d17b4a3309a496a
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- FrenzyMath contributors
metadata-link · Metadata, links and original OpenMath paraphrases only
Poincaré comparator integration verification
FrenzyMath contributors · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days
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- Version ID
- frenzymath-poincare-verification@432c38f2aa5a30efb13871292d17b4a3309a496a-metadata-v2
- Revision
- 432c38f2aa5a30efb13871292d17b4a3309a496a; bibliographic metadata corrected 2026-10-12
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metadata-link · Metadata, links and original OpenMath paraphrases only
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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- Version ID
- frenzymath-poincare@arxiv-2610.08329v1
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- 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
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- gaussian-moments:source:long:v1
- Revision
- 2026-07-20
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- Christopher D. Long
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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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- gaussian-moments:source:original:v1
- Revision
- 2015-06-17
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- Harm Derksen, Arno van den Essen, Wenhua Zhao
metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.
Gomila · proposed improved Newman bound
Jude Gomila · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days
No upstream full text or code is republished by this record.
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- Version ID
- gomila-newman-candidate@git-a74738deb6d5e0f76887cb36901da08b68dca705
- Revision
- git-a74738deb6d5e0f76887cb36901da08b68dca705
- 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
- Jude Gomila
metadata-link · Metadata, links and original OpenMath paraphrases only
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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- Version ID
- hkn-triangle-bound@arxiv-0908.2791v4
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- arxiv-0908.2791v4
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- Jan Hladký; Daniel Král’; Sergey Norin
metadata-link · Metadata, links and original OpenMath paraphrases only
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
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- arxiv-2212.05697v4
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- Patrick Hompe; Tony Huynh
metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.
ICARM · individual high-rank curve record
ICARM leaderboard; submitter ranksunbounded · Observed Oct 10, 2026 · Source date Aug 20, 2026 · Check every 90 days
No upstream full text or code is republished by this record.
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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
metadata-link · Original document rights remain with its authors.
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
- Update method
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- Shuhong Gao
metadata-link · Original document rights remain with its authors.
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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- Source comparison followed by a new immutable curation revision.
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- alerad/alpoge-lean project
metadata-link · Original document rights remain with its authors.
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
OpenMath supplies original paraphrases and links; no proof text is republished.
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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)
metadata-link · Source document rights apply; OpenMath publishes original paraphrases.
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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- Attribution
- Dominik Peters
metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.
Kent · AI-augmented BSD research substrate
Owen P. Kent (repository owner) · Observed Oct 10, 2026 · Source date Jun 14, 2026 · Check every 90 days
No upstream full text or code is republished by this record.
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- Version ID
- kent-bsd-project@0e9519aaeb5c8b8c524f95925eecb970d86bc5b1-metadata-2026-10-10
- Revision
- 0e9519aaeb5c8b8c524f95925eecb970d86bc5b1
- 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
- Owen P. Kent (repository owner)
metadata-link · Original source license and document rights apply.
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
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- kls-conjecture:source:song:v1
- Revision
- arXiv:2610.01447v1
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- Zhao Song, Xinzhi Zhang
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- kls-conjecture:source:song:v2
- Revision
- arXiv:2610.01447v2
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- Zhao Song, Xinzhi Zhang
metadata-link · Metadata, links and original OpenMath paraphrases only
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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- Attribution
- Ciprian Manolescu
metadata-link · Metadata, links and original OpenMath paraphrases only
Mathlib · wanted Poincaré statements
Mathlib contributors · Observed Oct 12, 2026 · Source date unavailable · Check every 90 days
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- Version ID
- mathlib-poincare-wanted@9454a4c25a2b923eb55dba3098f2d6ae0484d09b
- Revision
- 9454a4c25a2b923eb55dba3098f2d6ae0484d09b
- Update method
- Manual source review; publish new observations with immutable versions
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- Attribution
- Mathlib contributors
licensed-excerpt · Apache-2.0
Natural-number primality and divisibility
mathlib contributors · Observed Oct 1, 2026 · Source date unavailable · Check every 180 days
Licensed source links and exact source spans; attribution retained.
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- Version ID
- mathlib-prime-defs@32d24245c7a12ded17325299fd41d412022cd3fe
- Revision
- 32d24245c7a12ded17325299fd41d412022cd3fe
- 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
- mathlib contributors
licensed-excerpt · Apache-2.0
Natural-number prime statements
mathlib contributors · Observed Oct 1, 2026 · Source date unavailable · Check every 180 days
Licensed source links and exact source spans; attribution retained.
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- Version ID
- mathlib-prime-infinite@32d24245c7a12ded17325299fd41d412022cd3fe
- Revision
- 32d24245c7a12ded17325299fd41d412022cd3fe
- Update method
- Manual checked import; new observations require staff preview and publication
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- Canonical source URL plus explicit item/declaration locator; no fuzzy identity merge
- Attribution
- mathlib contributors
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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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- Version ID
- milnor-four-centuries@icm-2014-slides-sha256-89cf5c46
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- icm-2014-slides-sha256-89cf5c46
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- John Milnor
metadata-link · Metadata, links and original OpenMath paraphrases only
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
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- clay-description-observed-2026-10-12
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- Attribution
- John Milnor
metadata-link · Metadata, links and original OpenMath paraphrases only
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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- Attribution
- John Morgan; Gang Tian
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- navier-stokes:source:clay-announcement:v1
- Revision
- 2026-09-11
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- Attribution
- Clay Mathematics Institute
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- navier-stokes:source:clay:v1
- Revision
- 2000
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- Attribution
- Charles L. Fefferman
metadata-link · Original source license and document rights apply.
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
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
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- Version ID
- navier-stokes:source:paper:v1
- Revision
- 2026-09-08
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- Attribution
- OpenAI
metadata-link · External full-text redistribution rights not asserted
OpenAI · proposed full BSD from low Selmer corank
OpenAI · 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
- openai-bsd-low-selmer@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
- Revision
- fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
- 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
- OpenAI
metadata-link · External full-text redistribution rights not asserted
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
- Manual primary-source revision check; changes require a new immutable source version.
- Identifiers
- Stable bibliographic identity, explicit revision and exact source-entry locators.
- Attribution
- OpenAI
metadata-link · External full-text redistribution rights not asserted
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
- Manual primary-source revision check; changes require a new immutable source version.
- Identifiers
- Stable bibliographic identity, explicit revision and exact source-entry locators.
- Attribution
- OpenAI
metadata-link · External full-text redistribution rights not asserted
OpenAI · proposed Milne rationality theorem
OpenAI · Observed Oct 10, 2026 · Source date unavailable · Check every 30 days
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Registry, attribution & update policy
- Version ID
- openai-milne-rationality@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
- Revision
- fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
- 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
- OpenAI
metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.
OpenAI · reported seven-eighths half-plane
OpenAI · Observed Oct 10, 2026 · Source date Sep 30, 2026 · Check every 30 days
No upstream full text or code is republished by this record.
Registry, attribution & update policy
- 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
Elementary-number-theory reference prose
OpenMath staff · Observed Oct 1, 2026 · Source date Sep 26, 2026 · Check every 180 days
Licensed source links and exact source spans; attribution retained.
Registry, attribution & update policy
- Version ID
- openmath-prime-note@a640f3adfa536da0
- Revision
- a640f3adfa536da0
- Update method
- Manual checked import; new observations require staff preview and publication
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- Canonical source URL plus explicit item/declaration locator; no fuzzy identity merge
- Attribution
- OpenMath staff
metadata-link · Metadata, links and original OpenMath paraphrases only
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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- Attribution
- Grigori Perelman
metadata-link · Source document rights apply; OpenMath publishes original paraphrases.
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.
Registry, attribution & update policy
- Version ID
- petersen-coloring:source:archive:v1
- Revision
- 1.1.0
- Update method
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- Attribution
- Bryce Putman
metadata-link · Source document rights apply; OpenMath publishes original paraphrases.
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.
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- Stable source identity; exact source passages are versioned.
- Attribution
- Bryce Putman
metadata-link · Full-text redistribution rights not asserted
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
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
- 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
- Scott Aaronson; Avi Wigderson
metadata-link · Full-text redistribution rights not asserted
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.
Registry, attribution & update policy
- 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
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
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
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
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
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
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
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
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
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
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
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
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.
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.
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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.
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 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.
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.
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 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
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