Problem detail · source-aware
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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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
At the weak end of what the catalog records. The author used ChatGPT to verify some of the derivations and to assist with formatting, reviewed and edited the content, and takes full responsibility for it. Verifying derivations is a mathematical use rather than a purely editorial one, which is why this is listed at all, but no idea in the paper is credited to the model.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint, not peer-reviewed.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.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.