MATH.7:10 - Architectural Rationale

Encoding the result of a decoded operation determines the structure that the bijection preserves. Uniqueness prevents an independent choice of a familiar operation from being silently treated as the same construction. The expression-induction argument then explains why equations and their solutions travel.

C.29.1 already gives the common correspondence method and conjugation of a single update. This pattern develops the mathematical structure construction: constants, operations of several arities, relations, their laws and solution return. A single-update use can stay with C.29.1. MATH.5 starts instead with generator images and builds a homomorphism, which may forget information; here a supplied reversible map determines the receiving operations.

Transport is preferable when an available source structure and a useful bijection save construction or reasoning work. Direct definitions can be simpler or faster. A pre-existing isomorphism can supply the result without repeating the derivation. These alternatives retain the question that the representation is meant to answer.