{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:monical-snp-conjecture",
  "title": "Monical's Saturated Newton Polytope Conjecture",
  "canonical_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 $(7,4,1)$.",
  "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",
  "solution_events": [
    {
      "id": "vibemathed:monical-snp-conjecture:event",
      "problem_id": "vibemathed:monical-snp-conjecture",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-07-23T00:00:00.000Z",
      "title": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
      "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.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:monical-snp-conjecture:attempt"
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      "method_family_ids": [
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      "source_assertion_ids": [
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      "id": "vibemathed:monical-snp-conjecture:attempt",
      "problem_id": "vibemathed:monical-snp-conjecture",
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      "attempted_at": "2026-07-23T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The finite witness was found with ChatGPT-5.6 Sol Pro and verified by direct computation.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
          "url": "https://arxiv.org/abs/2607.21508",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Monical's Saturated Newton Polytope Conjecture",
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          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
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      "cost_usd": null,
      "independence": "unknown"
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      "solution_event_id": "vibemathed:monical-snp-conjecture:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Author-checked finite witness with a combinatorial proof, in the same preprint that resolves the claw-free Schur-positivity conjecture. Not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Monical's Saturated Newton Polytope Conjecture",
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          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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        {
          "label": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
          "url": "https://arxiv.org/abs/2607.21508",
          "kind": "primary-mathematical-source",
          "license": null
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  "sources": [
    {
      "label": "arXiv:2607.21508 - Chromatic symmetric functions of claw-free graphs are not Schur positive",
      "url": "https://arxiv.org/abs/2607.21508",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Monical's Saturated Newton Polytope Conjecture",
      "url": "https://vibemathed.com/problem/monical-snp-conjecture",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:monical-snp-conjecture:signal:watch_only",
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      "kind": "watch_only",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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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."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}