Nuclear dimension and Jiang–Su stability without elementary subquotients

OpenAI

For separable nuclear complex C*-algebras with no nonzero elementary ideal subquotients, the manuscript claims finite nuclear dimension, Jiang–Su stability and nuclear dimension at most one are equivalent. It separately claims dim_nuc(A₀⊗Z)≤1 for every separable nuclear A₀.

Sources for this record

What was already known

The finite-dimension-to-absorption implication was known for simple unital algebras and restricted nonsimple classes. Elementary subquotients obstruct the unrestricted statement.

AI involvement AI-led

OpenAI is credited as author, and its release identifies model-produced manuscripts. It names no human checker or explainer for this result.

OpenAI institutional authorship and release provenance support AI-led work; the exact prompting and human guidance are undisclosed.

Importance Major

The equivalence resolves Robert–Tikuisis Conjecture C1 in its stated nonsimple scope.

Limitations

No completed human check or Lean target for the C1 proof was identified; the ideal-structure argument and dimension-one construction need specialist review.

Technical verification Reported

The source contains a written proof, but the repository's formalization catalogue does not identify a Lean check of the C1 equivalence and no explicit completed human check was found.

Human understanding Few

No named human explanation of the new nonsimple proof is documented; this is an evidence default, not a finding of incomprehensibility.

Correction and publication history

2026-10-18 · publication

If correct, the equivalence resolves Robert–Tikuisis Conjecture C1 in its stated nonsimple scope.

Read this published revision