Meaning
Genuine admissible transport is a represented comparison that meets all the support, algebra, physical-form, reference, and coherence conditions on the effective branch.
The family is a partial isometry onto the selected destination support; intertwines the specified coefficient actions; identifies closed physical forms and faithful references; satisfies the full spatial Čech cocycle and refinement-path laws; trivializes the retained curvature or associator on that effective branch; and satisfies the source-native bounds. Permitted internal zero-cost changes are identified.
Example (illustrative)
A unitary intertwining two finite Hamiltonians illustrates only the energy component. To qualify here, it must also respect the selected algebras and references and fit every relevant spatial and refinement comparison.
Scope and limits
This is the represented, effective notion in GAT I. The broader comparison-valued transport of GAT VIII does not automatically have these representability or branch-trivialization properties.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 5.1.