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