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A Generalization of Boppana's Entropy Inequality

Combinatorics · solved

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Statement

A generalization of Boppana's entropy inequality, of the kind used in union-closed-sets arguments, proved and formalized: the sharp form with the extremal constant characterized via the unique positive solution of an explicit equation.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    Boon Suan Ho, using GPT-5.2 Pro, Harmonic Aristotle, Gemini 3 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    "Key steps in some proofs were generated with the assistance of GPT-5.2 pro. The result has also been formalized in Lean 4 using Harmonic Aristotle and Gemini 3 Pro Preview" - with the formalization public.

  2. Machine-checked by Lean on #1 · not a person

    lean: partially checkedLean

    scope Lean formalization of the core argument; statement correspondence not independently audited

    Formalized in Lean 4 (Aristotle plus Gemini); code public on GitHub. No independent review. Tier: the formalization was produced by the assisting systems and checked by the author; no independent statement audit.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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