Modal Triplet Theory and Calabi–Yau Compactification: A Conditional Realization Map and Its Selection Boundary

A Calabi–Yau compactification is not specified by a six-dimensional metric alone. It also requires topology, complex and Kähler data, gauge bundles and connections, anomaly cancellation, a supersymmetry convention, and a declared worldsheet or effective-field-theory approximation. This paper asks what Modal Triplet Theory (MTT) presently establishes about that complete object. We define a typed realization map from an upper MTT configuration to a lower Calabi–Yau compactification record and prove the corresponding conditional realization theorem: if one MTT source emits every required row and its reduction factors through the standard compactification functional, then both descriptions give the same declared lower data. This is an exact embedding statement, not a derivation or selection of a unique Calabi–Yau vacuum. We also isolate the analytic conditions under which spectral gaps, harmonic projectors, and commuting modal operators are available. A positive gap and bounded harmonic projector hold for each fixed compact elliptic problem; uniformity over moduli and operator commutation require additional non-collapsing or product hypotheses. A flat six-torus gives an elementary compatibility witness but not realistic four-dimensional phenomenology. The selected q=79 Fu–Yau program is a distinct non-Kähler torsional branch and cannot serve as a proof of a strict Calabi–Yau corner. The outcome is a precise and reusable realization contract, with unique-vacuum selection, moduli stabilization, and phenomenological prediction retained as independent open problems.