Meaning
Certified admissible continuation is a full-package comparison across a specified admitted passage, with an explicit account of each retained coordinate.
It controls the relevant global-form and detector identity, sectors, gauge and spacetime descent, Cauchy markings, physical and ground projections, physical form, Ward structure, higher data, and provenance. Each coordinate is recorded as preserved, a controlled defect, externalized to a named interface, or outside the declared scope. Variance follows the actual comparison slot.
Example (illustrative)
A regional restriction might preserve a sector marking exactly while introducing a bounded Hamiltonian seam residual. The continuation records both facts, including the residual bound and its valid domain.
Scope and limits
“Externalized” and “outside scope” are not synonyms for proved. Composition must propagate the actual comparison defects, and the passage need not be invertible.
Source
GAT III — Admissible Yang–Mills Fibrations and Thin Haag–Kastler Reconstruction. GAT III, Definition 3.3.