{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:hamaker-reiner-asm-weak-order-topology",
  "title": "The Hamaker-Reiner Conjecture on ASM Weak Order Intervals",
  "canonical_statement": "Hamaker and Reiner conjectured that the order complex of an open interval $(u,w)$ in the ASM weak order is contractible unless $w$ is the long element of a standard parabolic subgroup, in which case it is homotopy equivalent to a sphere. False: there is an interval in the ASM weak order on $S_n$ whose order complex is not contractible even though $w$ has no such form, detected by a nonzero Mobius function value.",
  "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:hamaker-reiner-asm-weak-order-topology:event",
      "problem_id": "vibemathed:hamaker-reiner-asm-weak-order-topology",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-05-08T00:00:00.000Z",
      "title": "arXiv:2605.08033 - Weak Order on the MacNeille Completion of Bruhat Order",
      "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:hamaker-reiner-asm-weak-order-topology:attempt"
      ],
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      "source_assertion_ids": [
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  "attempts": [
    {
      "id": "vibemathed:hamaker-reiner-asm-weak-order-topology:attempt",
      "problem_id": "vibemathed:hamaker-reiner-asm-weak-order-topology",
      "model": "ChatGPT 5.4 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-05-08T00:00:00.000Z",
      "human_collaborators": [
        "Colin Defant"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Arrived as a refusal to do what it was asked. Having polished the author's notes, the model was asked what else was worth exploring around weak order on MacNeille completions and suggested proving the Hamaker-Reiner conjecture. The author asked it to prove that conjecture; instead it returned the counterexample that appears as Figure 1 of the paper. The author describes both this and the Escobar-Klein-Weigandt proof as obtained autonomously.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2605.08033 - Weak Order on the MacNeille Completion of Bruhat Order",
          "url": "https://arxiv.org/abs/2605.08033",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Hamaker-Reiner Conjecture on ASM Weak Order Intervals",
          "url": "https://vibemathed.com/problem/hamaker-reiner-asm-weak-order-topology",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
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    {
      "id": "vibemathed:hamaker-reiner-asm-weak-order-topology:verification",
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      "solution_event_id": "vibemathed:hamaker-reiner-asm-weak-order-topology:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint, not peer-reviewed. The refutation is a single explicit interval whose order complex has nonzero Mobius function, printed in full in the paper, so it is checkable by finite computation.",
      "sources": [
        {
          "label": "VibeMathed: The Hamaker-Reiner Conjecture on ASM Weak Order Intervals",
          "url": "https://vibemathed.com/problem/hamaker-reiner-asm-weak-order-topology",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2605.08033 - Weak Order on the MacNeille Completion of Bruhat Order",
          "url": "https://arxiv.org/abs/2605.08033",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2605.08033 - Weak Order on the MacNeille Completion of Bruhat Order",
      "url": "https://arxiv.org/abs/2605.08033",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Hamaker-Reiner Conjecture on ASM Weak Order Intervals",
      "url": "https://vibemathed.com/problem/hamaker-reiner-asm-weak-order-topology",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
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    {
      "id": "vibemathed:hamaker-reiner-asm-weak-order-topology:signal:watch_only",
      "problem_id": "vibemathed:hamaker-reiner-asm-weak-order-topology",
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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"
}