Abstract This document provides the rigorous mathematical formalisation of the Five Principles framework, which describes the universal grammar of regulated systems across all scales. The Five Principles: CDR (Coherence-Decoherence-Recoherence) — The fundamental cycle governing all regulated systems GTRS (General Theory of Regulated Stability) — The threshold condition (ρ = R/P) determining self-recovery capacity Bond-Sign — The mechanism of all regulated interaction (coupling + information) Two-Attractor Model — The geometry of stability (competing basins) Semantic Invariants — What must survive transformation for meaning to persist Mathematical Content The document includes: Formal Definitions: State space formulation, coherent regions, CDR cycles, GTRS parameter, Bond-Sign systems, attractor geometry, semantic invariants Core Equations: Stochastic dynamics (Langevin form), Fokker-Planck correspondence, Kramers-Freidlin-Wentzell escape rates, quasi-potential theory Testable Predictions: Early warning signals, intervention efficacy by stuck cycle type, Bond-Sign cascade thresholds Cross-Domain Calibration: Structural analogy (not isomorphism) across scales from quantum to civilisational
Smith et al. (Sat,) studied this question.