Modal Triplet Theory and Perturbative String Theory: A Conditional Encoding Contract and the q=79 Worldsheet Boundary

This paper asks when Modal Triplet Theory (MTT) realizes a perturbative string background. A target metric, two-form, dilaton, and gauge connection are not yet a string theory: one must also supply a two-dimensional quantum field theory, its ghost and BRST systems, criticality, spin structures and GSO projection, modular amplitudes, sewing and factorization, anomaly and global B-field data, and an infrared prescription. We package these ingredients as a typed perturbative-string record and define a partial map from an upper MTT state to that record. The main theorem is conditional: if one selected MTT state emits every required row, the lower record is string-consistent at the declared order and genus, and the MTT observable map factors through the standard worldsheet amplitude map, then MTT realizes that perturbative string sector on the stated domain. The theorem is an exact encoding statement, not a derivation of string theory from saturation or projection alone. We also separate target-space beta-function equations from exact conformal invariance, cohomological anomaly cancellation from the differential Bianchi identity, central-charge arithmetic from model selection, and circle-spectrum symmetry from full quantum T-duality. The current selected q=79 heterotic program supplies five of twelve worldsheet rows and partially constructs two more. The physical non-pullback visible-hidden bundle, exact infrared (0,2) SCFT, analytic GSO and modular characters, quantum BV data, tadpole control, and all-genus or nonperturbative completion remain open.