This paper establishes a system of cross-domain realisation functors within thetheory of structural openness, faithfully mapping the meta-rule skeleton to fivedomains: physical cosmology, non-associative algebra, arithmetic geometry, multiagent governance, and information encoding. Under the axioms of informationconservation and computability established by the underlying self-consistent logic,the meta-rule category M is constructed as a category whose objects are spectraltriples, whose morphisms are structure-preserving maps, and which carries an internal modification endofunctor. Five faithful covariant functors respectively mapthe spectral structure, recursion depth, level generating function, associative algebra, and constraint network in M to the core objects of each target domain: phasetransitions and dark energy parametrisation in effective field theory, the normof associator jumps in the Cayley–Dickson sequence, the level compression ratiolocked by cusp periods of modular forms, the exit-right indicator in distributedconsensus, and the error-correction radius of stabiliser codes. All functors strictlysatisfy the axioms of object faithfulness, morphism surjectivity, and coarse-grainingcompatibility on finite-dimensional subcategories, while their infinite-dimensionallimits are approached asymptotically. The constructive verification of five naturaltransformation commutative diagrams guarantees the structural compatibility ofcross-domain mappings. This paper strictly distinguishes between proven resultsand heuristic conjectures: the subfactor origin of the Standard Model gauge group,the curvature dynamics of recursive recoil, and the unified classification of threetypes of gaps are explicitly marked as open questions.