The cohesion paper series is now published in full — five papers that build a chain from the concept of cohesion to the Independent Variation Principle (IVP).
The chain:
On the Nature of Cohesion — defines cohesion as a $2k$-tuple: for $k$ partitioning rules, $k$ (purity, completeness) pairs. Proves the knowledge-embodiment theorem: maximal cohesion under a rule coincides with exact knowledge embodiment under that rule. Shows that every published algorithmic cohesion metric measures a structural proxy (method-call overlap, shared-field density), not cohesion as defined by a principle. DOI: 10.5281/zenodo.20785752
Causal Cohesion — instantiates the schema under one concrete rule — change-driver-assignment identity: elements belong together iff $\Gamma(e_1) = \Gamma(e_2)$. Develops the metric $H_\text{causal}(M) = (\text{purity}(M), \text{completeness}(M))$, a two-dimensional score that fills one slot of the $2k$-tuple. DOI: 10.5281/zenodo.20785881
Four Necessary Conditions for Optimal Modularization — from the schema plus the objective of minimizing change propagation, proves four conditions — Admissibility, Element Form, Separation, Unification — are necessary and jointly exhaustive, uniquely pinning the $\Gamma$-equality partition $E / \tilde{\Gamma}$. DOI: 10.5281/zenodo.21362420
Why Minimizing Change Propagation Minimizes Maintenance Cost — decomposes total maintenance cost into access, alignment, cognitive, and domain-fixed components. Proves that minimizing change propagation cost is equivalent to minimizing total maintenance cost under an explicit coefficient condition, justifying the objective paper 5 assumed. DOI: 10.5281/zenodo.21362542
The Independent Variation Principle — synthesizes the chain into a single structural principle and examines the premises (change drivers, functional model, change isolation), preconditions (driver independence, decisional autonomy), and scope boundary. DOI: 10.5281/zenodo.21362618
Two derivations
Last month's preprint — Deriving Optimal Module Boundaries from the Element–Change-Driver Graph — proved that the $\Gamma$-equality partition is the unique cost-minimizing modularization through a self-contained graph-theoretic counting argument: two lemmas on the element–change-driver incidence graph show that scattering same-driver elements or mixing different-driver elements strictly increases cost.
The cohesion series derives the same conclusion through a different route: define cohesion as a schema parameterized by partitioning rules, instantiate a metric, prove optimality under change-isolation, and justify that objective against a richer maintenance-cost model.
The apparatus differs, the route differs, the endpoint is the same.
How the series builds a cohesion schema
The "Nature of Cohesion" paper argues that cohesion is correctness relative to a partitioning rule — an equivalence relation on elements anchored in domain artifacts (regulations, contracts, protocols). Under $k$ rules, it is a $2k$-tuple — $k$ (purity, completeness) pairs, one per rule — because each coupling concern, modeled by its governing change driver, resolves into a partitioning rule over the one element set. Cohesion-4 fills one slot with a concrete metric. Cohesion-5 proves which partition is optimal. Cohesion-6 justifies the cost objective. Cohesion-7 states the principle and examines its assumptions.
All papers free on Zenodo. Also referenced: the graph proof (June 2026).
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