Meaning
A derived certificate package assembles new certified conclusions from compatible primitive certificates and explicit theorem implications.
GAT I records which combinations certify branch retention, sector effectivity, a physical Hilbert realization, kernel identification, destinations, compactness, and stability. Composition includes passage to a common cofinal tail and retention of the witnesses needed by the consuming theorem.
Example (illustrative)
A compactness certificate can combine a certified destination family with heat bounds and the additional compactness inputs. If the destination-effectivity hypothesis is absent, placing the other certificates in one folder does not complete the implication.
Scope and limits
Derived certification does not create missing hypotheses. The theorem and the concrete witnesses for its application must remain distinguishable.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 13.4.