Arun’s latest conditional integer multiplication submission raised the exponent saving parameter κ to about 0.00075115, from OpenAI’s original 2⁻¹⁸². The parameter appears in the theoretical running time bound T(n) = O(n(log n)^(1−κ)); its increase is not a corresponding increase in practical multiplication speed. Arun said adding agents did not accelerate progress linearly and that human researchers were needed to guide independent fleets.
Separately, a mathematician writing on MathOverflow alleged that OpenAI omitted credit in two manuscripts generalizing his earlier work. He wrote that one paper’s “proof strategy and specific choices of notation are identical” to a preliminary version he uploaded to ChatGPT on Sept. 8. Verification concerns also emerged around OpenAI’s earlier Navier–Stokes claim: Valerio Capraro described a paper identifying two differences between the written argument and its Lean formalization, including an estimate requiring five additional input derivatives rather than four. Whether those differences invalidate the entire proof remains unclear.