This monograph presents a unified geometric theory of relational systems, formalized as four fundamental laws derived from the SU (5) Lie algebra and the Pattana-Relational Dynamics (PRD) framework. The four laws are: 1. **Systemic Tension as Inherent Curvature: ** Any evolving relational system exhibits a strictly positive curvature κ, representing an irreducible logical friction. 2. **Causal Divergence as the Source of Systemic Tension: ** Curvature is generated by biased state‑couplings, quantified by a divergence field ρbias and a self‑reinforcing feedback loop. 3. **Absolute Coherence and Zero‑Point Symmetry: ** A globally flat manifold (κ → 0) exists as a thermodynamic limit where all causal inconsistencies vanish, representing a state of perfect logical equilibrium. 4. **The Universal Optimization Protocol: ** A gradient‑based algorithmic procedure—using an Awareness Field ρ—that systematically reduces curvature, providing a mathematical path toward coherence. The work is presented without religious references, using only the language of differential geometry, information theory, and the mathematical structures of PRD-AGI. All equations are self‑contained and dimensionally consistent. This version (2. 5) refines the exposition, corrects minor typographical errors, and adds a unified table of contents and preface to present the four papers as a coherent sequence. The complete PRD-AGI theoretical framework, source code, and formal proofs are open‑source and available in associated Zenodo records. **Keywords: ** Relational Physics, Systemic Tension, Curvature, Causal Divergence, Absolute Coherence, Optimization Protocol, Pattana-Relational Dynamics, PRD-AGI, SU (5) Lie Algebra, Information Geometry, Causal AI, Ethical Causal Geometry. Relation: This paper is part of the PRD-AGI monograph series. It references the earlier “PRD-AGI: The Complete Theoretical Monograph (Version 2. 3) ” and the “PRD-AGI Phase 8: Ethical Causal Geometry” papers.
Myomin Aung (Tue,) studied this question.