We present a tiered methodology for extracting results from Modal Triplet Theory (MTT) without requiring a full internal metric solution. The program is organized into four operational tiers with explicit contracts specifying allowed inputs, mathematical tools, and guaranteed outputs. Tier 1 delivers exact, topology-only results independent of geometry. Tier 2 establishes geometry-light identities and bounds requiring minimal assumptions. Tier 3 treats MTT as a superset framework and calibrates a small set of latent parameters algebraically from overlaps among gauge, gravitational, and auxiliary sectors using one unavoidable normalization input. Tier 4 introduces explicit string-lift realizations to obtain quantitative predictions from algebraic-geometric data. We provide explicit algorithms, uncertainty accounting, validation workflows, and a consolidated test matrix distinguishing proved results from executed computations and planned extensions. This paper defines the computational architecture of the MTT program and serves as the methodological reference for all subsequent calculations.