ProofAtlas

Lean evidence record

12-Vertex Hamilton Counterexample: Lean evidence

This technical record binds the exact theorem statement to its commit-pinned Lean source, checker results, assumptions, and publication-review status.

Read theorem page
Lean buildpassed
Unfinished proof stepsNone
Publication reviewsAccepted

Exact recorded Lean statement

The declaration this evidence supports

theorem flippedC4Blowup_counterexample :
    CounterexampleStatement candidateTournament

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.

Technical evidence record

Source identity, checker results, and assumptions

Main Lean declaration
flippedC4Blowup_counterexample
Source commit
52ae1c0b7cff

Mechanical evidence

Lean verification

These fields support the exact Lean declaration, not a broader informal claim.

Artifact ID
artifact.jackson.flipped-c4-blowup-counterexample.lean-package.v001
Declarations covered by recorded evidence
JacksonHamiltonDecomposition.flippedC4Blowup_counterexample
Lean build
passed
Recorded build time
134.5 s one machine-dependent evidence run, not a benchmark
Evidence collected
· clean-source provenance recorded
Unfinished proof check
passed
Lean toolchain
leanprover/lean4:v4.29.1
Recorded source commit
52ae1c0b7cffe499aa0427ea08bed6e85eff6df3
Source SHA-256
sha256:0d8b1274eb8ff1581e77b1bb6d905243e3d29d5af714fa14fa76fb7ca046982e
Statement alignment
accepted

Lean foundations

Standard foundations used by the proof

Lean reports the logical foundations below through Mathlib. They are standard proof-system foundations, not conjectural mathematical assumptions about this theorem. The recorded closure stays within the approved classical_mathlib_standard profile, with no unexpected axiom or unfinished-proof placeholder.

  • Classical.choice
  • Quot.sound
  • propext

Files and machine-readable evidence

Reproduce or inspect the recorded check

Use the complete first-party source bundle for reconstruction, or inspect the exact main file and checker evidence separately. Mathlib and other third-party dependencies are identified but not rebundled.

Complete checked Lean source · 6 Lean files · 1 evidence record · Download ZIPBrowse counted source onlineDownload main Lean fileDownload checker evidence (JSON)Download Apache-2.0 license

Review results

Publication reviews accepted

All four required publication-review gates are accepted for the reviewed presentation of this exact theorem. The review results are separate from the Lean build and do not broaden the formal statement.

Read the publication-review details

Credit for this release

Contributors and roles

Authorship and other contributions are recorded separately for this version.

Authorship

Lean formalization
Lech Mazur
Mathematical proof
Lech Mazur

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

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

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

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

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.