CMP.13:10 - Architectural Rationale

The construction combines two methods of thinking: choose a mathematical account of possible states, then build an effective algorithm on that account. MATH.2’s quotient preserves specified operations independently of representative. Here a summary may deliberately combine different successors, so its justification is inclusion of possibilities rather than equality of returned classes. MATH.18 supplies the direction-sensitive comparison between accounts.

The examples expose three distinct causes of lost information: incompatible representatives in a path, extrapolation across iteration, and discarded correlation. Their repairs act on the abstraction and its algorithm. The physical or organizational interpretation of the original state system remains a separate subject correspondence.