What was already known
The previous reported universal bound was 186, improving an earlier 199053 bound. Shepherd’s conjecture that every t-perfect graph is 4-colorable remains open.
AI involvement
Oum states that GPT found the proof through multiple rounds of questions from him and generated the Lean proof. Claude drafted the manuscript from GPT research notes under Oum’s detailed direction and revision requests. This documents model-led mathematical work without establishing task-only autonomy.
Importance
Improves a concrete universal coloring bound for a class defined by exact polyhedral constraints.
Limitations
The theorem proves 50-colorability, not the conjectured 4-colorability. The manuscript is undated; 22 October is the registration date. The source does not document a named human explaining the complete new proof.
Technical verification
The versioned registry reports protected statement comparison and acceptance by Lean, NanoDa and con-ron for the finite-graph 50-color theorem, with only the three standard Lean axioms. The pinned challenge uses the stable-set-polytope definition of t-perfection.
Formal checking
The versioned registry reports protected statement comparison and acceptance by Lean, NanoDa and con-ron for the finite-graph 50-color theorem, with only the three standard Lean axioms. The pinned challenge uses the stable-set-polytope definition of t-perfection.
- Checker
- Palomar: Lean, NanoDa and con-ron
- Scope
- Every finite t-perfect graph, defined by its stable-set polytope and nonnegativity, edge and odd-cycle inequalities, is 50-colorable.
- Basis
- Reported by the linked checker
- Check date
- 2026-10-21
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The source credits models with the proof and manuscript draft. Human direction and adoption are documented, but a named human explanation of the central proof is not; Few is the documentation default.
Correction and publication history
Added the sourced contribution with its stated hypotheses, AI role, prior work and checking limits.
Read this published revision