Meaning
The finite Yang–Mills physical package collects the realized geometry, operators, sectors, ground, local algebras, constraints, and comparison data.
It keeps a localization carrier for regional observables and a possibly smaller detector carrier for selected sector measurements and coercive tests. An isometry J embeds the detector carrier into the localization carrier. The package also retains the electric and magnetic data, full Hamiltonian, exact ground, Gauss–Ward data, seams, and fillings.
Example (illustrative)
A toy localization space may be C⁴ while the detector uses a two-dimensional subspace embedded by J. Operators can act on all four coordinates even though the readout retains only two. Those two spaces have different jobs.
Scope and limits
A small detector matrix is not the complete regional physical package. In particular, its algebraic behavior cannot silently replace the locality audit on the larger carrier.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 7.1.