What was already known
Kaplansky’s quasitrace conjecture predicted that every 2-quasitrace on a C∗-algebra is additive and hence a trace; the general question was unresolved.
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
Refutes Kaplansky’s quasitrace conjecture and overturns a proposed general identification of quasitraces with traces.
Limitations
This selected contribution is the quasitrace counterexample. The same Lean note separately records tensor-product failures of stable finiteness.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note constructs the algebra and fixed positive contractions, with a quantified failure of additivity for every normalized 2-quasitrace.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- There is a separable unital complex C∗-algebra with normalized 2-quasitraces but no tracial state; its quasitraces fail additivity on a fixed pair of positive contractions.
- 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