Meaning
The finite physical realization predicate is the full test a candidate must pass to count as physically realized.
GAT 0 separates ten requirements: genuine global-form realization; nonzero physical rank in required sectors; realized carriers; the complete physical operator on a controlled domain; the exact complete ground; realized coefficients and fillings; Gauss–Ward compatibility; seams and markings; algebraic closure; and every analytic estimate used at this stage. Each requirement applies to the same declared finite package.
Example (illustrative)
A candidate whose proposed ground vector is correct for the electric block can still fail if a magnetic or seam term changes the ground of the complete Hamiltonian. The complete-ground clause tests the full operator.
Scope and limits
Passing one clause does not certify the package. Failure of one candidate does not prove that every candidate for that proposal fails.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 4.1.