{
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  "problem_id": "vibemathed:vandermonde-powers-non-snp",
  "title": "Powers of the Vandermonde Determinant Are Eventually Non-SNP",
  "canonical_statement": "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.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
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      "type": "proved",
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      "occurred_at": "2026-07-26T00:00:00.000Z",
      "title": "arXiv:2607.23828 - Powers of the Vandermonde determinant are eventually non-SNP",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "provider": "OpenAI",
      "attempted_at": "2026-07-26T00:00:00.000Z",
      "human_collaborators": [
        "Thien Le",
        "Melanie Weber"
      ],
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      "outcome": "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.",
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      "verifier": "VibeMathed (source-reported label)",
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      "note": "arXiv preprint with the prompting transcript in an appendix and an accompanying Lean formalization (coverage per its repository); not yet peer-reviewed.",
      "sources": [
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  "sources": [
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      "label": "arXiv:2607.23828 - Powers of the Vandermonde determinant are eventually non-SNP",
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      "kind": "primary-mathematical-source",
      "license": null
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    {
      "label": "VibeMathed: Powers of the Vandermonde Determinant Are Eventually Non-SNP",
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  "uncertainties": [
    "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."
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  "generated_at": "2026-09-13T16:28:40.178Z"
}