# Infinite-operator invariant-subspace fixture

Family 293: Invariant projections, hyperinvariant subspaces, and transitive algebras. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track nonzero norm-quasinilpotent infinite-Hilbert-space and hyperfinite-factor counterexamples to specified invariant-subspace properties.

## Applicability and commercial boundary

Finite-dimensional invariant-subspace intuition does not transfer; hyperinvariant and invariant projection claims must remain separate.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Read explicit construction and test only valid finite approximations.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Invariant-projection counterexamples for every irrational rotation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026/paper.pdf).