Monical's Saturated Newton Polytope Conjecture

Precise statement

If a chromatic symmetric function is Schur positive, must every finite-variable specialization $X_G(x_1, \dots, x_k)$ have a saturated Newton polytope? A $12$-vertex bipartite graph realizes weights $(6,6,0)$ and $(8,2,2)$ but omits their midpoint $(7,4,1)$.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT-5.6 Sol Pro

The finite witness was found with ChatGPT-5.6 Sol Pro and verified by direct computation.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Author-checked finite witness with a combinatorial proof, in the same preprint that resolves the claw-free Schur-positivity conjecture. Not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-23

   arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.