Perfect completeness for 2-to-1 games
We prove the 2-to-1 Games Conjecture with perfect completeness. For every fixed rational $\delta\in(0,1)$, it is NP-hard to distinguish satisfiable 2-to-1 games from games of value at most δ , with a fixed alphabet and an explicitly listed unweighted multiset of constraints.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
announces a proof of the Unique Games Conjecture and, separately, the 2-to-1 Games Conjecture with perfect completeness . Matrix multiplication. My post Cap Sets, Sunflowers, and Matrix Multiplication explored the connections between these problems. The new bound is over the complex numbers , a…