What was already known
Earlier real-rank-zero results gave tracial divisibility without central coefficient identities; other uniform-Gamma routes imposed additional hypotheses.
AI involvement
OpenAI is credited as author of this model-produced result. No individual human checker or explanation of the construction was identified.
The institutional AI authorship and release provenance document central model mathematical work.
Importance
The claimed implication answers Schafhauser–Tikuisis–White Problem XXI in this scope.
Limitations
The Lean endpoint and statement comparison cover the stated central-splitting implication. No named human mathematical review of the proof was identified.
Technical verification
OpenAI reports a Lean proof of the exact real-rank-zero-to-uniform-Gamma statement; Challenge.lean proves that its packaged statement is equivalent to the original formulation. The comparator target's sorry is a challenge placeholder, not the cited proof endpoint.
Formal checking
OAI.ComparatorModel.CurrentMain.main via main_iff_original and OAI.CurrentMain.real_rank_zero_uniform_gamma; ComparatorChallenges/UniformGamma.lean states the target
- Checker
- Lean 4 development in the OpenAI release
- Scope
- Real rank zero of B^ω implies a coefficient-halving central projection and uniform Gamma for the stated simple unital nuclear stably finite algebra and fixed free ultrafilter
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human account explaining the model's central-splitting proof was found; Few is the documentation default.
Correction and publication history
The claimed implication answers Schafhauser–Tikuisis–White Problem XXI in this scope.
Read this published revision