The generator problem for finite factors

What OpenAI claims

Proves that every type II1 factor with separable predual is generated by a single operator, equivalently by two self-adjoint operators, resolving the generator problem. More strongly, for every irreducible inclusion P ⊂ M of such factors, the unitaries u with M=W^*(P,u) form a dense Gδ subset in the trace 2-norm topology. (Lean)

Paper

1. Relative generation and the generator problem for finite factors

   23 September 2026 · Preprint, not peer reviewed · PDF

   We prove that every type II1 factor with separable predual is generated by one operator, equivalently by two self-adjoint operators. Combined with the established direct-integral reduction to this case, this gives an affirmative solution of the generator problem for von Neumann algebras with separable predual.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.