Decision Continuity Engineering: Theoretical Foundations and Mathematical Formalization

Volume II — Mathematical Layer. Establishes the mathematical and conceptual foundations of DCE, including identity, intent, continuity, and the invariant substrate. Decision Continuity Engineering: Theoretical Foundations: DCE Research Series Paper 2 advances the original framework through: • Mathematical formalization of Decision Capsule inheritance patterns• Comprehensive theoretical foundations for cellular AI infrastructure• Integration pathways with Decision Engineering Science Layer 7• Formal definitions enabling systematic implementation and validation Key contributions include heavy-formal capsule inheritance definitions, systematic relationship mapping to established decision engineering frameworks, and theoretical foundations designed for collaborative research development. This work builds upon the original DCE framework (DOI: 10.5281/zenodo.19807026) and provides the mathematical rigor necessary for enterprise implementation and academic collaboration. Part of the DCE Research Series exploring human-AI decision continuity challenges and solutions. Related Papers Paper 1 — Decision Continuity Engineering (Volume I) Paper 3 — DCE Research Foundation (Volume IV)