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 + 𝑚)-tuple: for 𝑘 partitioning rules and 𝑚 non-partition constraints, cohesion reports 𝑘 (purity, completeness) pairs (2𝑘 scalar components) plus 𝑚 per-constraint scores. This paper addresses the 𝑘 = 1 case — a single modularizing principle — with 𝑚 left unspecified as the general parameter for all other system constraints (regulatory requirements, business rules, security classifications, deployment plans, platform requirements, protocol disciplines, and any other conditions on module membership that do not partition 𝐸). Causal cohesion is therefore one component 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 + 𝑚)-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.