OpenAI · 279-01 · 2026-09-25 · Mathematical physics
Exact quantum factoring over a fixed finite gate set
preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026
Family 279. Exact quantum factoring over a fixed finite gate set.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Gives a polynomial-time uniform quantum circuit family that outputs the complete prime factorization of every integer with probability one. Both gate count and qubit count are polynomial in the input length, and one fixed finite gate set suffices.
We give a polynomial-time uniform quantum circuit family that outputs the complete prime factorization of every integer N ≥ 2 with probability one. A fixed finite set of bounded-arity gates suffices, and both the gate count and the number of qubits have polynomial worst-case bounds in the input length.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 279: Exact quantum factoring over a fixed finite gate set. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
ExactQuantumFactoring.lean · ExactQuantumFactoring.lean
Page curve
A finite prime list is not a Page curve
Family 279 records exact quantum factoring over a fixed finite gate set, with probability one, for every integer. Oai279-A records a 175-gate reversible certificate for every integer from 2 through 15 and does not verify 279-01. The circuit is not an extracted Family 279 instance. ExactQuantumFactoring.lean ends in sorry and is not this certificate. A classical prime list is not a Page curve. A finite reversible circuit is not gravity-generated entanglement and not an exclusion of classical gravity. The authors of the external preprint are OpenAI. The companion does not verify those proofs.
Page curveOai279-A finite factoring certificateI destructive readoutEn02-B decoder ledger