Theoretical computer science · Oct 6, 2026
Unique Games conjecture
Proves Khot's Unique Games Conjecture. Independent direct reductions also establish NP-hardness, on unweighted graphs, of approximation beyond the Goemans–Williamson ratio for Max-Cut, below factor two for Vertex Cover, and within any fixed constant factor for Min-UnCut and directed feedback vertex set. These direct proofs use established PCP and Label Cover hardness results.
Scope and what remains
Retain fixed parameter quantifiers and promised-input model. NP-hardness does not establish P≠NP.
Contributors
OpenAI source publisher and an unnamed unreleased internal model. Exact paper-level human roles are not disclosed by the family summary.
AI systems: Unreleased OpenAI model