MATH.18:10 - Architectural Rationale

Organizing the method around a consequence keeps interpretation connected to mathematical work. Comparing objects, assertions and transformations prevents an object-level match from silently becoming a claim about every use.

The operation-and-order case reconstructs different primitives on the same carrier. The natural-number case exposes domain-sensitive assertion transport. The matrix case compares families of objects through compatible isomorphisms. Together they show different uses of one method without making any one mathematical branch its scope.

MATH.5 and MATH.7 remain direct construction methods for generator extension and bijective transport. This pattern supplies the wider comparison in which those methods may solve one part. MATH.17 supplies operations on operations when the interpretation itself must be constructed or transformed that way.