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  "problem_id": "vibemathed:ternary-maximum-entropy-sums",
  "title": "Maximum Entropy of Sums of Independent Ternary Random Variables",
  "canonical_statement": "The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet, settled in the ternary case. For independent $X_1, \\ldots, X_n$ taking values in $\\{0,1,2\\}$, the entropy of $S_n = X_1 + \\cdots + X_n$ is maximized when $X_1, \\ldots, X_{n-1}$ are uniform on $\\{0,2\\}$ and $X_n$ has an explicitly described three-point distribution. This extends the Shepp-Olkin-Mateev theorem to ternary alphabets.",
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      "type": "proved",
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      "occurred_at": "2026-05-12T00:00:00.000Z",
      "title": "arXiv:2605.11831 - Maximum Entropy of Sums of Independent Ternary Random Variables",
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      "model": "ChatGPT",
      "provider": "OpenAI",
      "attempted_at": "2026-05-12T00:00:00.000Z",
      "human_collaborators": [
        "Mladen Kovačević"
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      "verifier": "VibeMathed (source-reported label)",
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      "note": "arXiv preprint, not peer-reviewed. The proof runs through the Hermite-Biehler theorem, Newton's inequalities and Yu's maximum-entropy theorem for ultra-log-concave distributions, all standard tools, so it is checkable by a specialist.",
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      "label": "VibeMathed: Maximum Entropy of Sums of Independent Ternary Random Variables",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}