What a grammar of records fixes: a modular flavour triplet, its couplings, and the boundary of what it leaves free

This preprint investigates a grammar of two integer records acted on by unit shear transformations and their inverses. Primitive hyperbolic paths on the modular surface are considered collectively, and the resulting structures are studied through parity lines, modular representations, theta-function multipliers and coupling identities. The manuscript identifies a three-component representation and examines its relationship to a weight-one theta triplet. It develops algebraic constraints on coupling matrices in specified frames, including null-vector and determinant identities, and reports bounded computational investigations. The work explicitly separates consequences of its mathematical inputs from additional postulates and physical identifications. Its index calculation of ±3 is conditional on stated assumptions; it is not an unconditional derivation of three physical fermion generations. The manuscript also discusses conditional anomaly constraints and the remaining freedom in physical interpretation. No Standard Model parameter is derived. Assumptions, correction history, verification procedures and unresolved selection problems are documented. The manuscript is presented as a mathematical investigation with conditional connections to particle physics, not as a completed Standard Model or theory of everything. The verification reported is internal to the project.