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  "problem_id": "vibemathed:score-determined-induced-tournament-statistics-an-all-orders-classification-and-",
  "title": "Score-Determined Induced Tournament Statistics: an All-Orders Classification",
  "canonical_statement": "A tournament orients every pair in a round-robin (winner → loser). The score sequence is the sorted win-count list. Reversing a directed 3-cycle never changes scores, so score-equivalent tournaments can look structurally different.\n\nQuestion: Which linear combinations of induced k-subtournament type-counts are score-determined — identical across all tournaments sharing a score sequence, at any host size?\n\nAnswer: Exactly the linear combinations of degree-multiplicity counts $m_0,\\dots,m_{k−1}$, where $m_r$ counts how many of the $k$ chosen vertices have exactly $r$ internal wins. These $k$ functions satisfy one linear relation, so score-determined statistics have dimension $k−1$.",
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      "occurred_at": "2026-08-14T00:00:00.000Z",
      "title": "Reproducibility Archive for “Score-Determined Induced Tournament Statistics: An All-Orders Classification and a Square-Zero Defect Algebra”",
      "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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      "outcome": "Absolutely everything, i occasionally steered and redirected.",
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      "note": "Checked by this site on 17 August 2026: the Zenodo reproducibility archive (21959291, Howard-Stanley) is real and carries the manuscript and code. The classification itself was not checked here, no independent review exists, and - flagged plainly - nobody has swept the tournament-theory literature for prior appearances of this question, which for a self-posed problem is the main risk. The disclosure (\"absolutely everything, I occasionally steered\") is the frankest ai-discovered claim in the catalog.",
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          "label": "VibeMathed: Score-Determined Induced Tournament Statistics: an All-Orders Classification",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}