An explicit Jacobian counterexample ↗
Explicit three-variable counterexample · observed Oct 13, 2026
Source status date unavailable · observed Oct 13, 2026
The all-dimensions complex Jacobian conjecture.
Publication v2
Record details
Jacobian conjecture →Coverage & review
Coverage of this curation
The canonical statement, selected results and public proof evidence, with historical and contribution context.
Formal proofs: Formal polynomial determinant, fiber collision and no-inverse results have public pinned Lean sources. Analytic derivative correspondence is outside their stated scope; no local proof build is recorded.
AI-assisted work: Discovery: Levent Alpöge with Claude Fable 5. Separate analysis: Shuhong Gao. Formalization: the alerad/alpoge-lean project’s reported AI-assisted workflow.
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
An explicit Jacobian counterexample ↗
Levent Alpöge · 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
- jacobian-conjecture:source:witness:v1
- Revision
- 2026-07
- Content SHA-256
- fcc91582150fa5ed7914bce443080c926771378b8e9bea7b9c2b866ddc6419b2
- Source update
- Unavailable
- Observed
- 2026-10-13
- Check cadence
- 90 days
- Explicit map and verification of determinant and fiber ↗
jacobian-conjecture:entry:witness:v1
Counterexamples to the Jacobian conjecture in dimensions greater than two ↗
Shuhong Gao · 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
- jacobian-conjecture:source:analysis:v2
- Revision
- 2026-07-31
- Content SHA-256
- No upstream byte snapshot retained; linked metadata only
- Source update
- 2026-07-31
- Observed
- 2026-10-13
- Check cadence
- 90 days
- Introduction and analysis of the counterexample ↗
jacobian-conjecture:entry:analysis:v2
Alpöge counterexample in Lean ↗
alerad/alpoge-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
- jacobian-conjecture:source:lean:v1
- Revision
- b8eec94711a9b73151929b78cbd7cb999a008590
- Content SHA-256
- 2cdfa772891c7b7f815c23039de71b971e02beada5fa4fad63350d3b2887a372
- Source update
- 2026-07-23
- Observed
- 2026-10-13
- Check cadence
- 90 days
- README trust boundary; Alpoge/Basic.lean and Alpoge/FormalConjectures.lean ↗
jacobian-conjecture:entry:lean:v1
Publication history
- Problem ID
- problem-jacobian-conjecture
- Publication checksum
- 6f6bb8855dcafe2638192e38f8d784721033245f6c1749867966e7da797411ae
- Published
- 2026-10-13T11:55:41.814069+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 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 5 · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 6 · Oct 14, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 7 · Oct 15, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- Version 8 · Oct 20, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.