Remark: Family 142. Deterministic polynomial factorization over prime fields

Gives a uniform deterministic algorithm that completely factors every nonzero dense degree-$n$ polynomial over a prime field ${\mathbb{F}}_p$, including multiplicities, in bit complexity polynomial in $(n+1)\log p$. The prime is supplied in binary. No randomness, integer-factorization or primitive-root oracle, or GRH assumption is required.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.