Integer multiplication below n log n: the exponent κ

κ such that two n-bit integers multiply in O(n (log n)^(1−κ)) on one fixed multitape Turing machine; a construction gives a lower bound on the best achievable κ.

Community values are conditional: they build on the OpenAI #109 preprint framework and keep its all-size interfaces (compiler, common labels, precision, analytic transfer). Checks are finite and exact, not a complete Lean proof. These compare asymptotic exponents, not running times.

Conditional result : yes