The modular bounded-witness record is a different theorem

The supplied Family 290-02 record concerns a von Neumann algebra, a faithful normal state with scalar modular centralizer, a fixed Hilbert-space operator, and an invariant modular average on shrinking spectral bands OpenAI290. Its stated conclusion supplies bounded algebra witnesses with a controlled spectral widening.

Our labels live on a finite branching tree. No standard-form representation, modular generator, invariant mean, or correspondence between its $T$ and our channels is supplied. The path theorem therefore neither proves nor instantiates the modular theorem. The reported Lean-note identifier 290-02 is provenance information from the supplied dossier, not proof-assistant verification Dossier.