Atomic Trust Systems: A Closed Algebraic Framework for Normative Interpretation, Propagation, and Verifiable Governance

We introduce the Atomic Trust System (ATS), a closed algebraic structure for modeling governance, interpretation, and verification over normative semantic spaces. The system formalizes how weighted votes on clause interpretations propagate through equivalence and similarity structures, subject to conflict constraints, producing cryptographically verifiable state snapshots. We provide complete definitions, establish fundamental properties, and give a simple illustrative instantiation demonstrating the framework's applicability to distributed governance scenarios. This paper presents only the abstract framework; concrete optimized implementations are described in separate work.