Meaning
Finite admissible decoupling means that the actual mixed comparison factors through independently certified marginal comparisons with the required relative higher comparison.
The gauge and regional–refinement marginals must be certified separately. The actual mixed surface must factor in the marked sense, and an admissible relative 3-cell must connect it to the independent calibration. This is a statement about the full comparison geometry.
Example (illustrative)
The direct factorized case, with actual surface equal to the certified independent surface and the identity relative 3-cell, illustrates decoupling. Observing only the scalar phase Π□=1 leaves the factorization and 3-cell to be established.
Scope and limits
Trivial calibrated phase is necessary under the stated theorem, but is not a complete test for decoupling.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 20.5.