What was already known
Shor’s polynomial-time factoring algorithm has bounded error. Exact transforms or factoring procedures in broader quantum models did not establish worst-case polynomial, probability-one factoring over one fixed finite gate set.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Upgrades quantum factoring to an exact polynomial-time circuit family under a fixed finite gate set.
Limitations
The conclusion is complete factorization with exact probability one, not merely a high-probability factor or expected-time retry procedure.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note covers exact complete factorization, polynomial-time uniformity, fixed finite gate set and polynomial worst-case gate/qubit bounds.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- A polynomial-time uniform family of quantum circuits over one fixed finite bounded-arity gate set outputs the complete prime factorization of every integer N≥2 with probability exactly one, using polynomially many gates and qubits in the input bit length.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision