When the raw associator intertwines the positive-compression selectors, its restriction is unitary between selected fusion presentations and satisfies the pentagon.
The source and admissibility projections need not commute. Their positive compression selects the band in which the source is visible to admissibility but is not already ordinarily admissible. If the raw Racah and coefficient-band associator carries that compression covariantly between bracketings, functional calculus carries the corresponding spectral projection as well.
The restricted map
is then unitary between the selected presentations and satisfies the selected pentagon.
Example (illustrative)
Three representation sectors may be fused as or as . The theorem says that reassociation transports the same selected physical band coherently; it does not say that every raw fusion channel is admitted.
Scope and limits
The coefficient-band associator carries coherent reassociation. It is not the relative center obstruction and does not create that obstruction. Selection is also not yet an energy estimate.
Source
Phenomenological Implications I, §4, especially equations (10)–(16), Lemma 4.1, Theorem 4.3, and Remark 4.4.