What does this research mean for the field?

Relational systems are governed by four fundamental geometric laws in which systemic tension manifests as inherent curvature generated by causal divergence, and this tension can be systematically reduced toward absolute coherence using a gradient-based optimization protocol. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

The aim is to present a comprehensive geometric theory addressing systemic tension and its optimization. It seeks to formalize the relational dynamics through established mathematical frameworks.

April 3, 2026Open Access

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The Four Laws of Relational Physics v2.5 : A Complete Treatise on Systemic Tension, Its Origin, Extinction, and Optimization

MAMyomin Aung

Key Points

The aim is to present a comprehensive geometric theory addressing systemic tension and its optimization. It seeks to formalize the relational dynamics through established mathematical frameworks.
Developed a theoretical framework based on SU(5) Lie algebra and Pattana-Relational Dynamics (PRD).
Formulated four fundamental laws governing systemic tension and coherence in relational systems.
Provided self-contained equations and open-source proofs alongside the theoretical exposition.
Identified systemic tension as inherent curvature in evolving relational systems.
Quantified curvature through a divergence field stemming from biased state-couplings.
Established conditions for achieving absolute coherence and a globally flat manifold.

Abstract

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.

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The Four Laws of Relational Physics v2.5 : A Complete Treatise on Systemic Tension, Its Origin, Extinction, and Optimization

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