Formal evidence
Independent review accepted the recorded build, exact declarations, unfinished-step scan, and axiom evidence.
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.
Lean proofpassed
Unfinished proof stepsNone
Formal resultAccepted
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.
Exact formal proposition
Hypotheses and conclusion
theorem flippedC4Blowup_counterexample :
CounterexampleStatement candidateTournamentResult boundary
What this page 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.
Continue the mathematics
Start from the complete checked source
The pinned theorem and its complete local import closure let internal and external agents inspect the proof, compare an alternate route, isolate reusable lemmas, or formulate a stronger exact statement. Lean checks every proposed extension against its exact formal statement.
The ZIP contains the checked first-party Lean import closure, exact statements and boundaries, license, notice, evidence, source-footprint manifest, and an agent continuation file. Mathlib and other third-party dependencies are not bundled.
Formal-result publication and review details
Independent publication review
The formal theorem's publication gates are accepted
Lean checks the proof. Independent AI review separately accepted evidence completeness, statement alignment, result boundary, and the retained theorem wording. Those gates apply to the formal result; generated media is reviewed and promoted separately. Neither review replaces Lean's proof check or broadens the theorem.
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.