Meaning
A separating marker subfamily distinguishes all physical branch classes that the complete marker family distinguishes.
The joint partition produced by the chosen markers must equal the complete physical branch partition. It is minimal if removing any marker destroys that equality. Uniform separation is an additional positive lower bound between distinct joint characters on the specified tail.
Example (illustrative)
Suppose the complete branch signatures are (0,0), (0,1), and (1,0). Both coordinates distinguish all three, while either coordinate alone merges two branches. This models a minimal separating pair.
Scope and limits
Separating labels is not the same as constructing the represented destinations or proving their spatial equivalence properties.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 5.42.