The Closure Accounting Structure (CAS): A Formal Framework for Observability, Adjacency, and Ledger Closure

This paper introduces the Closure Accounting Structure (CAS), a formal and polymorphic framework for the accounting of observable configurations under admissibility, adjacency, and closure constraints. CAS is defined axiomatically and independently of physical interpretation, dynamics, or ontology. Observable records are represented as ordered ledgers of admissible configurations, while structural adjacency and conservation are enforced through realization-dependent adjacency constraints and a closure functional. Within CAS, conservation is reinterpreted as a closure condition on observable records rather than as a dynamical law.CAS is intentionally realization-independent and serves as reusable mathematical infrastructure rather than a physical theory. It separates observability from underlying transformation and permits discrete observable records to coexist with continuous or unobservable structure. The framework is formally closed at the axiomatic level and admits multiple polymorphic realizations, including discrete, continuous, and causally constrained settings. CAS provides a structural criterion—CAS-invariance—for consistent observable accounting and is intended to undergird, rather than compete with, domain-specific theoretical frameworks.