Meaning
Pre-spectral branch retention means that every marked source packet reaches exactly one allowed represented destination without losing rank.
It is stated using marked Riesz packets, their transported auxiliary central supports, and selected refinement arrows. Each packet must retain its prescribed branch character, and no unresolved component may remain outside the represented marked family. The condition is checked before the later spectral trichotomy is used.
Example (illustrative)
A rank-two marked source packet transported into a rank-one destination loses information and fails retention. A rank-two image in its uniquely prescribed destination illustrates the rank and label requirements, with the other comparison conditions still to be checked.
Scope and limits
Retention cannot be justified by assuming the later transport–migration–escape theorem. It is an input expressed in source-native packet data.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 5.13.