This GitHub release contains an OpenAI Math preprint titled "Integer multiplication below n log n" (September 23, 2026). The repository includes a README, a linked paper.pdf, and a build directory, and supplies a formal citation for the work. The entry indexes the downloadable manuscript and the minimal project structure needed to view the full write-up and supporting materials.
The work announces an algorithmic result that achieves asymptotic integer multiplication cost below n log n and presents the associated algorithmic construction, complexity analysis, and proofs that establish the stated bound. That claimed improvement over previous asymptotic bounds constitutes a major advance in the complexity of high-precision arithmetic, with direct implications for algorithmic number theory and cryptographic computation. The manuscript contains the precise theorems, assumptions, proof sketches, and technical innovations required to evaluate the validity and impact of the result; readers should consult the provided PDF for the detailed algorithms, rigorous proofs, and any empirical or theoretical assessments supplied.
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