❯ OpenAI and Anthropic publish claimed ETH refutations, prompting a broad scientific review

Two independent claimsOpenAI and Anthropic have released claimed refutations of the Exponential Time Hypothesis, or ETH, produced by internal AI models. In its October 26 announcement, OpenAI dated the discovery to October 16 and Lean formalization to the following day. Anthropic’s repository also contains a paper and Lean 4 code credited to an internal Claude research model.

A longstanding complexity assumptionETH asserts an exponential worst-case time requirement for 3-SAT, a logical satisfiability problem. Researchers have used it to derive hardness results for many other problems. The proposed algorithms achieve subexponential growth. They have not delivered a practical solver or settled whether P equals NP.

Checking and understanding the resultLean checks logical deductions within a formal statement. Researchers must still examine how the statements, computational models and written arguments correspond. Russell Impagliazzo, Ramamohan Paturi and Ryan Williams have organized an open examination, stressing that their involvement does not certify the claim.

Consequences for existing researchIf independently upheld, the refutations would remove the premise behind many ETH-based hardness results. Whether those problems become easier remains a separate question. Practical consequences for cryptography likewise require algorithms that work against particular systems at realistic scales.

▮ SIGNALAs AI produces proofs faster, independent checking, explanation and the search for usable algorithms take on more of the scientific workload.