What was already known
Monical conjectured Schur positivity always implied a saturated Newton polytope for every finite-variable specialization. Prior work placed a counterexample at at least 12 vertices.
AI involvement
ChatGPT-5.6 Sol Pro found G3 in Matherne’s first prompt. Matherne and Morales selected the question, interpreted the graph and supplied the mathematical argument.
The model found the decisive graph G3 in a human-chosen search problem.
Importance
If the reported Schur positivity is confirmed for G3, this explicit graph refutes the universal conjecture.
Limitations
The color-class obstruction is explained, but the displayed Schur expansion is labeled G2 although the surrounding argument concerns G3. The exact positivity certificate needs clarification.
Technical verification
The paper supplies an elementary color-class proof of the missing SNP weight and reports exact SageMath calculation of Schur positivity. The displayed expansion is labeled G2, a graph §2 says is Schur negative, so the exact G3 positivity certificate needs clarification before complete verification. The written proof alone is not a separate documented human check.
Formal checking
Exact symbolic Schur expansion linked from Example 3.1; displayed label conflict
- Checker
- Matherne and Morales using SageMath
- Scope
- Reported Schur positivity of G3
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the G3 graph, coloring obstruction and logical counterexample mechanism.
Correction and publication history
If the reported Schur positivity is confirmed for G3, this explicit graph refutes the universal conjecture.
Read this published revision