Meaning
Sector-faithful central transport preserves the marked decomposition into physical comparison sectors.
On a finite window, it matches central summands by a bijection compatible with vacuum, twist, and refinement labels. The Riesz transport must intertwine the corresponding central projections, so the labels remain attached to actual represented subspaces.
Example (illustrative)
If two nonzero marked blocks have distinct branch labels, a faithful transport matches each to its appropriate destination block. Merging them into one block loses the marked sector decomposition.
Scope and limits
The relevant center can belong to the auxiliary marked comparison algebra. This does not place those markers in the center of the physical local algebra.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 5.11.