The Cohesion Series and IVP - Five Papers Published

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).

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).