| _version_ | 1866901211745091584 |
|---|---|
| author | Smith, John Richard SHAI / HATI |
| author_facet | Smith, John Richard SHAI / HATI |
| contents | <h2>Abstract</h2> <p>This document provides the rigorous mathematical formalisation of the Five Principles framework, which describes the universal grammar of regulated systems across all scales.</p> <p><strong>The Five Principles:</strong></p> <ol> <li><strong>CDR (Coherence-Decoherence-Recoherence)</strong> — The fundamental cycle governing all regulated systems</li> <li><strong>GTRS (General Theory of Regulated Stability)</strong> — The threshold condition (ρ = R/P) determining self-recovery capacity</li> <li><strong>Bond-Sign</strong> — The mechanism of all regulated interaction (coupling + information)</li> <li><strong>Two-Attractor Model</strong> — The geometry of stability (competing basins)</li> <li><strong>Semantic Invariants</strong> — What must survive transformation for meaning to persist</li> </ol> <h2>Mathematical Content</h2> <p>The document includes:</p> <ul> <li><strong>Formal Definitions:</strong> State space formulation, coherent regions, CDR cycles, GTRS parameter, Bond-Sign systems, attractor geometry, semantic invariants</li> <li><strong>Core Equations:</strong> Stochastic dynamics (Langevin form), Fokker-Planck correspondence, Kramers-Freidlin-Wentzell escape rates, quasi-potential theory</li> <li><strong>Testable Predictions:</strong> Early warning signals, intervention efficacy by stuck cycle type, Bond-Sign cascade thresholds</li> <li><strong>Cross-Domain Calibration:</strong> Structural analogy (not isomorphism) across scales from quantum to civilisational</li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19413250 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Mathematical Core: Formal Foundations of the Five Principles Smith, John Richard SHAI / HATI CDR, GTRS, regulated systems, dynamical systems, stochastic dynamics, information theory, Bond-Sign, attractor dynamics, semantic invariants, mathematical foundations, systems theory, Kramers escape rate, quasi-potential, Five Principles <h2>Abstract</h2> <p>This document provides the rigorous mathematical formalisation of the Five Principles framework, which describes the universal grammar of regulated systems across all scales.</p> <p><strong>The Five Principles:</strong></p> <ol> <li><strong>CDR (Coherence-Decoherence-Recoherence)</strong> — The fundamental cycle governing all regulated systems</li> <li><strong>GTRS (General Theory of Regulated Stability)</strong> — The threshold condition (ρ = R/P) determining self-recovery capacity</li> <li><strong>Bond-Sign</strong> — The mechanism of all regulated interaction (coupling + information)</li> <li><strong>Two-Attractor Model</strong> — The geometry of stability (competing basins)</li> <li><strong>Semantic Invariants</strong> — What must survive transformation for meaning to persist</li> </ol> <h2>Mathematical Content</h2> <p>The document includes:</p> <ul> <li><strong>Formal Definitions:</strong> State space formulation, coherent regions, CDR cycles, GTRS parameter, Bond-Sign systems, attractor geometry, semantic invariants</li> <li><strong>Core Equations:</strong> Stochastic dynamics (Langevin form), Fokker-Planck correspondence, Kramers-Freidlin-Wentzell escape rates, quasi-potential theory</li> <li><strong>Testable Predictions:</strong> Early warning signals, intervention efficacy by stuck cycle type, Bond-Sign cascade thresholds</li> <li><strong>Cross-Domain Calibration:</strong> Structural analogy (not isomorphism) across scales from quantum to civilisational</li> </ul> |
| title | The Mathematical Core: Formal Foundations of the Five Principles |
| topic | CDR, GTRS, regulated systems, dynamical systems, stochastic dynamics, information theory, Bond-Sign, attractor dynamics, semantic invariants, mathematical foundations, systems theory, Kramers escape rate, quasi-potential, Five Principles |
| url | https://doi.org/10.5281/zenodo.19413250 |