A Generalization of Boppana's Entropy Inequality

Precise 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.

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.

What AI did

GPT-5.2 Pro, Harmonic Aristotle, Gemini 3 Pro

"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.

Provider: OpenAI, Harmonic, Google DeepMind · Prompt public: unknown · Independence: unknown

Verification boundary

lean checked statement unaudited

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.

Correctness: supported · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-01-27

   arXiv

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.