Problem detail · source-aware
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The Courtade-Kumar conjecture (2014) posits that dictatorship functions maximize mutual information between a Boolean function's output and a noisy input. The paper resolves an open question posed by Courtade and Kumar themselves - a sharp bound of $1-H(\alpha)$ on the sum of coordinate-wise mutual informations for arbitrary bias - and extends the proven high-noise range of the main conjecture via optimal entropy bounds.
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"The results in this paper were obtained with significant interaction with a larger version of Google's Deep Think Gemini-based model. The authors verified the entire paper and take full responsibility." The acknowledgments thank the Deep Think team by name.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
No verification note supplied.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Fully resolves the posed coordinate-wise question; the main Courtade-Kumar conjecture itself remains open outside the extended high-noise range.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.