Meaning
A uniformly separated central marking keeps distinct branch labels a definite spectral distance apart along the certified refinement tail.
The commuting normal markers have joint spectral packets. The definition requires a positive separation bound for distinct branch labels, uniform in refinement on the stated tail and with the finite-window quantifiers given in the source. This prevents the marked clusters from becoming indistinguishable in that regime.
Example (illustrative)
Markers with two packet values 0 and 1 keep separation 1. Values 0 and 1/n are distinct at every finite n but have no positive separation uniform in n.
Scope and limits
Pointwise distinction is weaker than uniform separation. Do not extend a bound beyond the source’s declared tail or window quantifiers.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 5.12.