CM-001 - Continuity Mathematics: A Formal Mathematical Architecture of Continuity, Recoverability, Irreversibility, Dependency Propagation, and Admissible State Transition

CM-001 formalizes the mathematical architecture governing continuity-bearing systems across biological, informational, ecological, institutional, computational, cognitive, and civilization-scale domains within the Recoverability-Constrained Systems corpus. The framework establishes: continuity mathematics, recoverability mathematics, irreversibility mathematics, dependency-topological propagation mathematics, admissibility-preserving transition mathematics, collapse dynamics, continuity geometry, continuity tensor structures, as recursively unified mathematical structures governing continuity-preserving and continuity-degrading state evolution. CM-001 formalizes: continuity state-space structures, transition operators, continuity functions, recoverability operators, irreversibility operators, dependency topology, continuity surfaces, continuity basins, collapse fronts, reserve functions, admissibility functions, temporal continuity structures, continuity tensors, continuity-preserving propagation mathematics. The framework further establishes: recursively closed continuity mathematics, generalized recoverability mathematics, unified admissibility-preserving transition mathematics, and continuity-preserving state transition formalization across continuity-bearing systems operating under recoverability-constrained admissibility conditions. CM-001 derives from: TCB-001 - Terminal Conceptual Boundary, CO-001 - Continuity Ontology, and the Recoverability-Constrained Systems corpus, and functions as the mathematical substrate beneath: continuity logic, continuity science, substrate sciences, civilization continuity architectures, recoverability-constrained operational systems. The publication establishes: recoverability operators, continuity tensors, dependency-topological propagation mathematics, admissibility-preserving transition structures, continuity geometry, irreversibility boundaries, collapse propagation mathematics, as foundational mathematical structures within a recursively unified continuity architecture. CM-001 formalizes a recursively unified continuity mathematics governing continuity-preserving and continuity-degrading state evolution across continuity-bearing systems. The framework establishes recoverability operators, continuity tensors, dependency-topological propagation mathematics, admissibility-preserving transition structures, continuity geometry, and collapse propagation mathematics as foundational mathematical structures beneath continuity logic, continuity science, substrate sciences, and civilization continuity architectures within the Recoverability-Constrained Systems corpus.