Formal evidence
Independent review accepted the recorded build, exact declarations, unfinished-step scan, and axiom evidence.
ProofAtlas research case study
Starting frontierJackson's unrestricted conjecture→AI-developed checked counterexampleExplicit order-12 Lean-checked counterexample
Evidence and status →Graph theory · formal theorem
12-Vertex Hamilton Counterexample
Kernel-checked Lean proof that an explicit 12-vertex regular bipartite tournament has no Hamilton decomposition. The statement matches the unrestricted formulation recorded by Granet and Liebenau–Pehova.
Scope: The explicitly encoded 12-vertex orientation of K₆,₆ is a bipartite tournament, has indegree and outdegree three at every vertex, and has no Hamilton decomposition.
Lean checkedBuild passed
Unfinished proof stepsNone
PublicationAccepted formal theorem
Exact formal proposition
Hypotheses and conclusion
theorem flippedC4Blowup_counterexample :
CounterexampleStatement candidateTournamentResult boundary
What this theorem does—and does not—establish
The explicitly encoded 12-vertex orientation of K₆,₆ is a bipartite tournament, has indegree and outdegree three at every vertex, and has no Hamilton decomposition.
- Granet already described the flipped-C₄ construction and its opposite-pair structure; no novelty claim is made for the construction.
- Historical novelty of the class-size-three parity obstruction remains under specialist review; no first, resolves, or priority claim is made.
- The result does not conflict with Granet’s theorem for all sufficiently large orders.
- Computational minimum order is independent corroboration and is not Lean-verified.
- The independent finite verifier and corroborating AI review are not theorem evidence or specialist novelty review.
Line counts exclude blank lines; comments and documentation count. The total is the commit-pinned first-party Lean import closure; Mathlib and other third-party dependencies are excluded.
Continue the mathematics
Open questions and extensions
The pinned theorem and its complete local import closure let people and AI agents inspect the proof, compare another route, isolate reusable lemmas, or formulate a stronger exact statement. Lean checks each proposed extension against its own exact statement.
What the source ZIP contains
The ZIP contains the checked first-party Lean import closure, exact statements and boundaries, license, notice, evidence, source-footprint manifest, and continuation data. Mathlib and other third-party dependencies are not bundled.
Independent review
Review record
Independent review accepted
Lean checks the exact proof. Independent reviewers accepted evidence completeness, statement alignment, scope, and public wording; the visual review covers explanation only.
Statement alignment
The formal declaration was accepted against the named theorem and its exact variant.
Result boundary
The accepted boundary keeps nearby stronger or commonly confused claims out of scope.
Public wording
Independent review accepted the retained theorem explanation and source presentation. Generated media follows a separate review and promotion gate.
Canonical source
The first-party source link is pinned to the checked package commit and exact Lean file.
Accepted result
A validated accepted-result record binds the four reviews to the checked formalization.
Credit for this release
Contributors and roles
Authorship and other contributions are recorded separately for this version.
Contributions
- Upstream attributionBertille Granet
Bertille Granet is credited for the prior flipped-C4 construction, opposite-pair structure, unrestricted formulation, and sufficiently-large theorem.
- Problem framing
- Proof strategy
- Direct contributionLech Mazur
Lech Mazur contributed the explicit class-size-three obstruction, matching-parity proof, and checked Lean formalization.
- Counterexample
- Formalization
- Proof strategy
- Source maintenance
Selected reviews
Review record
Each entry names the question reviewed, its exact scope, and the reviewer provenance recorded for this release.
Download exact review bindings
Formal-evidence review of the exact checked counterexample package.
- Reviewer
- OpenAI Codex / GPT-5
- Independence
- Independence not asserted
Limits of this review
- The heavy Lean build was not rerun; the reviewer audited the retained transcript and exact evidence bindings.
Public-wording review of the retained narrow counterexample presentation.
- Reviewer
- Claude Fable 5
- Independence
- Independence not asserted
Limits of this review
- The wording review did not establish historical novelty, priority, or specialist approval.
Result-boundary review of the exact twelve-vertex counterexample.
- Reviewer
- Claude Fable 5
- Independence
- Independence not asserted
Limits of this review
- The review did not establish historical novelty or priority, inspect the full Jackson 1981 paper, or convert computation into theorem evidence.
Statement-alignment review of the exact counterexample declaration.
- Reviewer
- Claude Fable 5
- Independence
- Independence not asserted
Limits of this review
- Primary-paper comparison used retained source quotations rather than a fresh paper fetch.
Citation
Cite this release
Use the version-specific citation so the authorship, scope, and public record remain attached.
Release history
Versions and public record
- Release
- Counterexample release
- Version
- v001
- Published
- Canonical page
- Open canonical page
Release chronology
This version is part of the release history. No independent external timestamp is claimed.
Scope of this release
- Computational minimum order is corroborating evidence and is not Lean-verified.
- Granet's sufficiently-large theorem is unaffected.
- Historical novelty of the class-size-three obstruction remains under specialist review.
- No independent external priority anchor is recorded.
- The flipped-C4 construction and opposite-pair structure are upstream work due to Bertille Granet.