What was already known
Kirchberg–Rørdam’s comparison question had been settled under structural assumptions such as simplicity, real rank zero, approximate divisibility or Hausdorff primitive ideal space. The unrestricted implication remained open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the ordinary-to-strong implication without exactness, nuclearity, unitality or simplicity assumptions.
Limitations
The selected implication concerns individual proper infiniteness of every positive element. A separate finite-amplification result in the manuscript requires exactness.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves the full positive-element diagonalization property from individual proper infiniteness without extra structural hypotheses.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Every complex C∗-algebra in which each positive element is properly infinite is strongly purely infinite, satisfying the full positive-element diagonalization property.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision