Anthropic publishes Claude paper claiming a sub-exponential 3-SAT algorithm refuting ETH

Anthropic has published a research preprint titled “A 2^o(n) Time Algorithm for 3-SAT”, authored by Claude with human research co-authors, accompanied by a complete Lean 4 formalisation in the anthropics/formal-math GitHub repository. The paper presents a deterministic algorithm capable of counting 3-SAT solutions in 2^O(n log log n / sqrt(log n)) asymptotic runtime, directly contradicting the widely held Exponential Time Hypothesis (ETH).

The Exponential Time Hypothesis conjectures that 3-SAT requires 2^Omega(n) time in the worst case, serving as a cornerstone for conditional lower bounds across theoretical computer science. Anthropic stated that the core structural reduction was discovered during autonomous mathematical exploration by an internal Claude research model.

The authors emphasised that the result is strictly asymptotic and does not provide practical speedups for finite SAT instances. The Lean 4 formalisation allows mathematicians and complexity theorists to inspect every inductive step of the reduction independently, establishing complete machine-checked validity across the formalised mathematical assertions.