The documentary complexity claim

The OpenAI catalogue records 283-01, Polynomial-Time Unitary Synthesis from a Boolean Oracle, dated 5 October 2026. Its stated target has the quantifier order

where $\mathsf{Gen}(1^n)$ produces the circuit structure from $n$ alone, polynomial bounds apply to its oracle-model resources, and the target-dependent Boolean truth table is unrestricted OpenAI283,OpenAIOverview.

The existence of $\mathsf{Gen}$, its polynomial bounds, and the universal approximation statement are not proved here. Selected proof excerpts supplied with the question do not constitute an independent verification of their recursive construction.

The underlying unitary-synthesis question belongs to the Aaronson–Kuperberg programme AaronsonKuperberg. A published one-query lower bound concerns a different, restricted query regime LombardiMaWright. In particular, “one Boolean oracle” means one supplied function, not necessarily one query.