A proof of the cycle double cover conjecture ↗
Full cycle double cover proof reported · observed Oct 13, 2026
Source status date unavailable · observed Oct 13, 2026
Universal finite loopless bridgeless multigraph formulation.
Publication v5
Record details
Cycle double cover conjecture →Coverage & review
Coverage of this curation
The canonical statement, selected results and public proof evidence, with historical and contribution context.
Formal proofs: A pinned Lean source reports a complete unconditional endpoint for the ordinary conjecture. OpenMath has not built it; source-reported completion does not replace independent mathematical review.
AI-assisted work: OpenAI reports GPT-5.6 Sol Ultra discovery and formal work. Shiva Kintali’s Codex-assisted manuscript is a separate contribution.
Search scope & review
Selected primary manuscripts, theorem declarations and project provenance reviewed on 13 October 2026; this is not an exhaustive literature survey.
Checked Oct 13, 2026 · independent review pending.
- Independent mathematical review and local execution of the cited formal proofs are pending.
General status observations
Source identities & rights
A proof of the cycle double cover conjecture ↗
OpenAI · metadata-link · Original document rights remain with its authors.
OpenMath supplies original paraphrases and links; no proof text is republished. Rights / source terms
1 cited entry · exact source identity
- Version
- cycle-double-cover:source:proof:v1
- Revision
- 2026-07-10
- Content SHA-256
- b4797f5053d9067329b3dcfcbf913f8bb40d13467453b1300f6d78d08460fc13
- Source update
- 2026-07-10
- Observed
- 2026-10-13
- Check cadence
- 90 days
- Main theorem and flow-to-cover construction ↗
cycle-double-cover:entry:proof:v1
Cycle double cover in Lean ↗
OpenAI, openai/cdc-lean project · metadata-link · Original document rights remain with its authors.
OpenMath supplies original paraphrases and links; no proof text is republished. Rights / source terms
1 cited entry · exact source identity
- Version
- cycle-double-cover:source:lean:v1
- Revision
- 577e9d9ea326d520f80672ee69b830bf1d513df5
- Content SHA-256
- ffe1a481bcfa67c49b25830a67cb338a6c7fdda3eb29e4dcffcd63e795f0c963
- Source update
- 2026-07-09
- Observed
- 2026-10-13
- Check cadence
- 90 days
- CDCLean/Main.lean; README verification and exact endpoint ↗
cycle-double-cover:entry:lean:v1
Three-Bit Flows and Cycle Covers. Part I ↗
Shiva Kintali · metadata-link · Original document rights remain with its authors.
OpenMath supplies original paraphrases and links; no proof text is republished. Rights / source terms
1 cited entry · exact source identity
- Version
- cycle-double-cover:source:separate:v2
- Revision
- 2026-07-13
- Content SHA-256
- No upstream byte snapshot retained; linked metadata only
- Source update
- 2026-07-13
- Observed
- 2026-10-13
- Check cadence
- 90 days
- Abstract and theorem statement ↗
cycle-double-cover:entry:separate:v2
Publication history
- Problem ID
- problem-cycle-double-cover
- Publication checksum
- 4e137c731e4d28b63626662664290817ecef1e6c01cc33698c286cc1243a63d8
- Published
- 2026-10-21T12:38:41.571989+00:00
- Publication reason
- Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 1 · Oct 13, 2026
Initial checked pilot publication; source attribution, rights, wording and coverage reviewed by OpenMath staff.
- Version 2 · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 3 · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 4 · Oct 14, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 5 · Oct 21, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.