Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Monical, Tokcan and Yong conjectured that every fixed positive power of the Vandermonde determinant fails to have saturated Newton polytope in sufficiently many variables. For every even power $k \ge 4$ there is an explicit lattice point of the Newton polytope of $a_{\delta_k}^k$ with vanishing coefficient, obtained from a Dyson constant-term identity; the odd case follows by alternation, proving the conjecture.
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.
The key even-power construction and the proof strategy arose from prompting OpenAI Codex; the complete transcript appears in the paper's appendix. The authors subsequently checked and organized the argument.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint with the prompting transcript in an appendix and an accompanying Lean formalization (coverage per its repository); not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.