The Modal Triplet Theory Program C: Realizing the Modal Triplet Core

We construct explicit realizations of the Modal Triplet Theory core and encoding classes using geometric, bundle-theoretic, spectral, and extended-carrier models. The purpose of this paper is to demonstrate existence and non-uniqueness of realizations without altering the structural conclusions of the theory. Geometry, bundles, operators, and Hilbert-like structures are shown to arise as realization-level bookkeeping frameworks rather than as axioms. The paper provides a realization dictionary connecting the abstract encoding responses to familiar formalisms while preserving strict separation between structural necessity and instantiation.