The Cohesion Series and IVP — Five Papers Published

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:

1. On the Nature of Cohesion — defines cohesion as a 2k2k -tuple: for kk partitioning rules, kk (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

2. Causal Cohesion — instantiates the schema under change-driver-assignment identity: elements belong together iff Γ(e1)=Γ(e2)\Gamma(e_1) = \Gamma(e_2) . Develops the metric Hcausal(M)=(purity(M),completeness(M))H_\text{causal}(M) = (\text{purity}(M), \text{completeness}(M)) , a two-dimensional score that fills one slot of the 2k2k -tuple. DOI: 10.5281/zenodo.20785881

3. 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 Γ\Gamma -equality partition E/Γ~E / \tilde{\Gamma} . DOI: 10.5281/zenodo.21362420

4. 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

5. 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

Additional paper: the historical survey of 24 cohesion metrics — DOI: 10.5281/zenodo.20584161.

Two derivations

Last month’s preprint — Deriving Optimal Module Boundaries from the Element–Change-Driver Graph — proved that the Γ\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. Different apparatus, same endpoint.

How the series builds a cohesion schema

The cohesion-2 paper argues that cohesion is correctness relative to a partitioning rule — an equivalence relation on elements anchored in domain artifacts (regulations, contracts, protocols). Under kk rules, it is a 2k2k -tuple — kk (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).