Meaning
The admissible realization fiber is the collection of all certified physical realizations of one formal proposal.
Let π_D forget a physical realization’s extra structure and retain its formal proposal. For a proposal R_D, the fiber is AdmFib_D(R_D)=π_D⁻¹(R_D). Membership means that the realization has this formal input and passes the physical predicate.
Example (illustrative)
If x₁ and x₂ both pass the required physical tests and both have formal shadow R_D, they belong to the same fiber. A third candidate with that shadow but a failed Gauss constraint does not.
Scope and limits
The fiber can be empty. Calling it a fiber supplies neither a lift of a refinement arrow nor a fibration structure.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 4.2.