Meaning
Formal equivalence means that two proposals specify the same finite problem after permitted changes of presentation.
The identifications must preserve the global form, detector and sector labels, geometric incidence, coefficient systems, requested fillings, seams, markings, and validity metadata. This comparison takes place before using a successful filling, physical Hamiltonian, or coercive estimate.
Example (illustrative)
Renaming two region indices while carrying their incidence, orientations, detector labels, and all comparison requirements with them can be a formal equivalence. Changing which regions overlap changes the proposal.
Scope and limits
Formal equivalence does not assert that physical realizations exist or that two resulting physical systems are equivalent.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 3.3.