The generator problem: is every von Neumann algebra with separable predual singly generated?

Lineage and corrections

A second route via the generator problem (OpenAI math release) evidence for this event

Theorem 1.2: every type $\mathrm{II}_1$ factor with separable predual is $W^*(x)$ for one $x$ (two self-adjoint generators). Theorem 1.1: for an irreducible inclusion $P\subset M$ of $\mathrm{II}_1$ factors, $M$ separable, the unitaries $u$ with $W^*(P,u)=M$ are a dense $G_\delta$ in the 2-norm topology. With Willig's reduction this gives single generation of every von Neumann algebra with separable predual. Consequences: the generator invariants $G$ and $G_{sa}$ vanish, and Voiculescu's $\delta,\delta_0$ are not $W^*$-invariants on $L(\mathbb F_n)$, $n\ge3$. No explicit generator is constructed. parent of this event

This event attributed to Unreleased internal OpenAI model

Sherman 2012, Canad. J. Math. 64 (history of the problem) evidence for this event

Lean Comparator statement FactorGeneration evidence for this event

Lean Comparator statement RelativeGeneration (not in formalization.yaml main results) evidence for this event

Lean scope note for family 296 evidence for this event

VibeMathed record: The generator problem: is every von Neumann algebra with separable predual singly generated? evidence for this event

The generator problem: is every von Neumann algebra with separable predual singly generated? parent of this event