{
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  "source": "vibemath",
  "problem_id": "vibemathed:reciprocal-fermat-constant-is-nonnormal",
  "title": "Reciprocal Fermat Constant is Nonnormal",
  "canonical_statement": "Statement not supplied by the source.",
  "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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      "occurred_at": "2026-09-08T00:00:00.000Z",
      "title": "GitHub repository with Lean proof",
      "summary": "The paper proves that the reciprocal Fermat constant is disjunctive but nonnormal in binary, explicitly locates every finite word, and establishes positive lower word frequencies. It extends these properties to a broad family of arithmetic series. Behavior in unrelated bases remains open.",
      "ai_contribution": "ai_discovered",
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      "attempted_at": "2026-09-08T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Astra developed several techniques in a previous work we did together. I asked it to find problems where the techniques could be of use, it chose the constant, proved it was disjunctive in base 2, proved it was nonnormal in base 2, then generalized the result.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "GitHub repository with Lean proof",
          "url": "https://github.com/CaptainSude/reciprocal-Fermat-constant-Nonnormal/releases/tag/v1.0.0",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Reciprocal Fermat Constant is Nonnormal",
          "url": "https://vibemathed.com/problem/reciprocal-fermat-constant-is-nonnormal",
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      "note": "Full Lean verification is here: https://github.com/CaptainSude/reciprocal-Fermat-constant-Nonnormal/releases/tag/v1.0.0",
      "sources": [
        {
          "label": "VibeMathed: Reciprocal Fermat Constant is Nonnormal",
          "url": "https://vibemathed.com/problem/reciprocal-fermat-constant-is-nonnormal",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Reciprocal Fermat Constant is Nonnormal",
      "url": "https://vibemathed.com/problem/reciprocal-fermat-constant-is-nonnormal",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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      "problem_id": "vibemathed:reciprocal-fermat-constant-is-nonnormal",
      "kind": "watch_only",
      "reason": "The source statement is missing; retrieve it before constructing a replay task.",
      "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.",
    "The source did not supply a mathematical statement; retrieve it before replay or verification. VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}