OpenAI posted a preprint on GitHub that claims a deterministic algorithm for counting solutions to k-CNF formulas and says that algorithm shows the Exponential Time Hypothesis is false¹.

Techmeme, linking OpenAI, said the company announced three claimed breakthroughs in computer science, mathematics, and physics, including that ETH is false².

The GitHub PDF, dated Oct. 17, 2026, and revised Oct. 25, lists OpenAI as the author¹.

Its abstract says that for every fixed k of at least 2, the algorithm exactly counts satisfying assignments of a k-CNF on n variables and m clauses in polynomial space and in time (n + m) to a k-dependent polynomial times 2 to the n over (log n) to the 1/2 plus o(1)¹.

The paper says that bound refutes ETH, which it states as the postulate that deciding 3-SAT on n variables requires 2 to the Omega(n) time in the worst case¹.

A later theorem in the manuscript restates the runtime as 2 to the O(n log log n over square root of log n) bit operations with polynomial space, and a tighter form when the number of clauses is linear in n¹.

Techmeme did not reproduce those runtime claims; it summarized OpenAI as announcing three results and highlighting ETH as a longstanding conjecture said to be false².

The assigned GitHub file is only the ETH preprint; it does not itself document the math and physics items Techmeme attributed to OpenAI^1,2.

Independent review of the algorithm, Lean formalization if any, and the other two claimed results is not established in these two sources^1,2.