Deterministic Factoring in Sublinear Space from Boolean Tensor Contraction

This preprint is conditional on an external result that has not been independently certified. OpenAI's manuscript "The Exponential Time Hypothesis is False" (25 October 2026, pinned at commit 42907c9e999cc00d6abe7a50bfc1023250edd1b9) states a deterministic Boolean tensor-contraction theorem, Theorem D.1: a bipartite network with s Boolean edges, polynomially many vertices, maximum degree at most ceil(s^(9/10)) and efficiently computable entries can be contracted in 2^(O(s/sqrt(log s))) time and polynomial space. Its Lean formalization covers a weaker k-SAT bound, not Theorem D.1. Nothing in this record certifies that theorem or the manuscript's main claim. Taking Theorem D.1 as given, this paper shows that every positive n-bit integer can be completely factored, with all prime factors and multiplicities, by a deterministic algorithm in 2^(O(n/sqrt(log n))) time and polynomial space. Taking also the recursive identities and estimates of Section D.4 of the same source, the working space drops to O(n/sqrt(log n)) bits, with read-only input and write-only output. For comparison, the best unconditional deterministic bound is exponential in n (Harvey 2021; Harvey and Hittmeir 2022), and rigorous randomized factoring runs in expected time 2^(O(sqrt(n log n))) (Lenstra and Pomerance 1992), which is smaller. The result concerns worst-case deterministic complexity and gives no practical algorithm. The local contributions are three. A parsimonious multiplication network, built from grouped bivariate evaluation and interpolation, encodes pq = N with O(n) Boolean edges and maximum degree O(n^(4/5)), so that the contraction bound is exponential in n rather than in a circuit size of order n log n. A bit-at-a-time implementation of the source's scalar contraction recomputes individual bits of large residues and stores mode tuples by rank, which gives the sublinear workspace bound. A short modulus of O(n/log n) bits separates all divisors, so that each factor is recovered, tested for primality and multiplicity, and streamed to the output through bit queries without ever being stored. The arithmetic, fingerprinting and small-space primitives are classical and are credited. Anthropic's same-day manuscript "A 2^(o(n)) time algorithm for 3-SAT" (26 October 2026, pinned at commit 16a5ce41304fcdaea4e0be7c132e1c361dc26da5) is cited and compared; the polynomial-space time bound may also follow from its clique-contraction theorem, which the paper does not verify. All results are derived from the OpenAI source alone. This record contains the 12-page manuscript and its self-contained TeX source, which rebuilds to identical text. Local Lean lemmas cover grid uniqueness, carry telescoping and coordinate-product identities; exact finite checks cover the arithmetic networks and selected contraction interfaces. They do not formalize the whole algorithm or the external theorem. AI models (OpenAI GPT-6 via Codex, Anthropic Claude Opus 5.5, Claude Fable 5.1, Google Gemini 4 Argon) assisted with proof development, review, drafting and test code, as stated in the manuscript; model-generated reviews are not independent certification. The author takes responsibility for all claims. No priority claim is made, and the work is not peer-reviewed.