Modal Triplet Theory: Parameters, Closure, and Structural Falsifiability

A parameter count is meaningful only relative to a model, a physical tier, a choice of observables, a quotient by redundancies, and a rule separating construction data from held-out tests. This paper rebuilds the parameter and falsifiability account of Modal Triplet Theory (MTT) around that principle. We distinguish structural assumptions, selected discrete data, continuous construction primitives, measured source coordinates, nuisance and metrology inputs, derived outputs, and uncertainty data. We prove that raw symbol counts are not invariant under reparameterization or gauge redundancy, that replay of data used in construction is not a held-out prediction, that loss of a global right inverse is not by itself a falsifier, and that a scalar coherence-capacity diagnostic cannot eliminate the full source ledger. At the current profile-standard Standard Model tier, the auditable ledger contains one shared electroweak construction primitive and fifteen measured common-scheme source coordinates. The transported couplings, charged Yukawa rows, Higgs row, covariance workspace, and finite operators are outputs of that declared construction and are not counted again. This is a coherent embedding and reuse result, not a strict reduction of the Standard Model parameter set. The stronger no-knob program remains two of nine upgrades closed. We give valid falsification capsules for exact algebraic results, numerical certificates, source provenance, and held-out empirical predictions. The result is an honest parameter-identifiability framework: MTT has substantial structural economy, but strict numerical economy must be demonstrated rather than inferred from notation.