Causal Cohesion

This paper instantiates the cohesion schema developed in [1] under change-driver-assignment identity — the principle that elements belong together iff they share the same change-driver set (Γ(𝑒1) = Γ(𝑒2)). The general cohesion definition is a 2𝑘-tuple: for 𝑘 partitioning rules, cohesion reports 𝑘 (purity, completeness) pairs. This paper addresses the 𝑘 = 1 case — a single modularizing principle — yielding one (purity, completeness) pair from the full 2𝑘-tuple. Causal cohesion is therefore one slot of the full cohesion profile, not the complete profile. We develop the full formal apparatus: the system tuple, change drivers, driver assignments, equivalence classes, and the normative decomposition. The result is causal cohesion: a two-dimensional metric 𝐻causal(𝑀) = (purity(𝑀), completeness(𝑀)) in ]0, 1] ×]0, 1], a (purity, completeness) pair that occupies one partitioning-rule slot in the 2𝑘-tuple, with both axes directly interpretable and mapped to design actions (separate elements of impure modules into distinct modules for low purity, merge for low completeness). The metric satisfies all six necessary conditions, and we provide an operational computation procedure. The metric depends on element-level change-driver assignments Γ(𝑒); the prerequisite of identifying these from domain artifacts is addressed separately.