Google-led team proves Courtade–Kumar conjecture in full, with AI and Lean
RexDouglass · x · 2026-09-22
A Google group with CUHK collaborators announced a complete, computer-assisted proof of the Most Informative Boolean Function (Courtade–Kumar) conjecture, posted to arXiv (2609.24931). The proof uses the differential-equation method, reduces entropy production to an unrestricted Bellman inequality with mean and entropy constraints, and shows I(g(X);Y) ≤ 1 − H₂(p) with dictator functions as equality. Analytic parts were verified in Lean, emerging from extensive human–AI collaboration with multiple Gemini models via the Stellar Colosseum harness.
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