What was already known
Zhu, Fang and Shi asked whether the vanishing-determinant weighted rotations in this setting must admit nontrivial affiliated invariant subspaces. Earlier Brown-measure methods gave projections when the Brown measure was not a point mass, leaving the point-mass case 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
Gives a negative answer for every prescribed irrational rotation angle.
Limitations
The exclusion concerns projections inside the associated factor; it does not rule out arbitrary invariant Hilbert-space subspaces outside that factor.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note constructs the stated weight for every irrational angle and proves no nontrivial invariant projection; it also records quasinilpotence.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every irrational rotation angle θ in (0,1), there is a continuous nonnegative circle weight f with one zero and integral log f equal to negative infinity such that the weighted rotation U f(V) has no nontrivial invariant projection in its associated hyperfinite type II₁ factor.
- 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