{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:signed-bar-uniqueness-harrison-reiman",
  "title": "The Signed BAR Uniqueness Problem",
  "canonical_statement": "For a multidimensional reflected diffusion, does the basic adjoint relationship uniquely characterize the stationary distribution? The question had stood unresolved for more than thirty-five years since the BAR approach was introduced. For stable Harrison-Reiman data with a nonsingular $M$-matrix reflection matrix, the finite-signed uniqueness problem is settled, via pathwise differentiability of the reflected process; the nonsigned version is also shown unique within the Harrison-Reiman class.",
  "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:signed-bar-uniqueness-harrison-reiman:event",
      "problem_id": "vibemathed:signed-bar-uniqueness-harrison-reiman",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-07-03T00:00:00.000Z",
      "title": "arXiv:2607.03639 - An AI-Assisted Solution to the Signed BAR Conjecture: Uniqueness in the Harrison-Reiman Class",
      "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_co_developed",
      "attempt_ids": [
        "vibemathed:signed-bar-uniqueness-harrison-reiman:attempt"
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      "id": "vibemathed:signed-bar-uniqueness-harrison-reiman:attempt",
      "problem_id": "vibemathed:signed-bar-uniqueness-harrison-reiman",
      "model": "ChatGPT 5.5 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-07-03T00:00:00.000Z",
      "human_collaborators": [
        "Yiping Lu",
        "Youheng Zhu"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The paper names the model contribution in its title and states that the proof was discovered with the assistance of ChatGPT 5.5 Pro and subsequently verified by the authors, with the chat logs published. It also records a negative result worth having: on a harder related task both ChatGPT 5.5 Pro extended and Claude Opus 4.8 max failed.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2607.03639 - An AI-Assisted Solution to the Signed BAR Conjecture: Uniqueness in the Harrison-Reiman Class",
          "url": "https://arxiv.org/abs/2607.03639",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Signed BAR Uniqueness Problem",
          "url": "https://vibemathed.com/problem/signed-bar-uniqueness-harrison-reiman",
          "kind": "source-assertion",
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      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint with the originating chat logs linked, so the provenance claim is checkable even though the mathematics is not yet refereed.",
      "sources": [
        {
          "label": "VibeMathed: The Signed BAR Uniqueness Problem",
          "url": "https://vibemathed.com/problem/signed-bar-uniqueness-harrison-reiman",
          "kind": "source-assertion",
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        {
          "label": "arXiv:2607.03639 - An AI-Assisted Solution to the Signed BAR Conjecture: Uniqueness in the Harrison-Reiman Class",
          "url": "https://arxiv.org/abs/2607.03639",
          "kind": "primary-mathematical-source",
          "license": null
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  "sources": [
    {
      "label": "arXiv:2607.03639 - An AI-Assisted Solution to the Signed BAR Conjecture: Uniqueness in the Harrison-Reiman Class",
      "url": "https://arxiv.org/abs/2607.03639",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Signed BAR Uniqueness Problem",
      "url": "https://vibemathed.com/problem/signed-bar-uniqueness-harrison-reiman",
      "kind": "source-assertion",
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      "problem_id": "vibemathed:signed-bar-uniqueness-harrison-reiman",
      "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"
}