Meaning
A finite spacetime cover organizes the regions on which a candidate’s or realization’s data are supported.
It consists of a finite family of admitted regions. A tuple is compatible when its supported intersection is an admitted region, collar, seam, mediation region, or declared empty intersection. These tuples form the spacetime Čech nerve. The available regions can depend on the chosen physical realization.
Example (illustrative)
Two thick tubes may have disjoint central loops but overlapping collars. Their spacetime compatibility must use the full supports and seam data, not just a picture of the thin loops.
Scope and limits
This cover records physical localization. It does not replace gauge-presentation compatibility or establish locality of the operators by itself.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 5.2.