What was already known
Naimark’s question dates to 1951. Earlier counterexamples used Jensen’s diamond principle; the ZFC status remained the stated obstacle.
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
Answers Naimark’s problem negatively without any additional set-theoretic assumption.
Limitations
The claim is existence in ZFC; it does not assert separability of the algebra.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note constructs the stated ZFC counterexample and excludes isomorphism to compact operators on any Hilbert space.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- In ZFC there exists a unital infinite-dimensional simple complex C∗-algebra with a faithful tracial state whose nonzero irreducible representations are all unitarily equivalent, yet it is not an algebra of compact operators.
- 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