Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 293-01. Invariant-projection counterexamples for every irrational rotation
Manuscript map · lines 8265–8274
OpenAI@2026-10-07#rem:oai-p-293-01
Authors: OpenAI. Family 293.
Title: Invariant-projection counterexamples for every irrational rotation.
Abstract: For every irrational angle, we construct a continuous nonnegative circle weight with exactly one zero and logarithmic integral $-{}infty$ whose weighted rotation has no nontrivial invariant projection in the associated hyperfinite type II1 factor. This answers negatively the question of Zhu, Fang, and Shi, with the angle prescribed in advance. The resulting operator is nonzero and norm-quasinilpotent.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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