Tier-Bundle Algebra in Inter-Organizational Resource Transfer: A Fork-Operation Formalism Over the Six-Tier Acquisition-Target Ontology

Abstract

An acquisition is not a monolithic transfer of a firm but a bundle of tier-level transfers, and integration risk arises when the bundle severs a dependency that day-to-day operation requires. This paper develops a compositional grammar for that structure over the six-tier acquisition-target ontology: a fork operator that transfers one tier across an ownership boundary, the tier-bundle as the central algebraic object, a bundle signature that classifies a transaction by its per-tier transfer content, a directional cascade rule stating which forks structurally require adjacent forks along the service hierarchy, and an admissibility predicate derived from tier-collapse states that identifies which going-concern transfers are structurally impossible. Fourteen named deal types are recovered as bundle signatures, and a hybrid deal that no named type covers is constructed to demonstrate the algebra's generative reach. The empirical anchor is a pre-registered, blindly-coded corpus of thirty documented transactions; that anchor is preliminary, and its correctly-scoped necessary-condition reading is developed in a companion large-N study. Full closure – identity, inverse, and the resulting category-theoretic structure – is reserved for future work; the paper establishes the partial-algebra structure adequate for typing named and hybrid deal forms. Includes zharnikov-2026bj-tier-bundle-algebra.yaml (Paper Spec v0.1.0) – a machine-readable specification of the paper's claims, assumptions, and dependencies. The paper's full machine-first bundle (the SPINE claim/dependency graph and the ONTOLOGY term module) lives in the public repository; see https://github.com/spectralbranding/paper-spec for the standard. This PDF is generated programmatically from that machine-first source under a research-as-repository model.