ONE AXIOM FUNDAMENTAL FORCES

ONE AXIOM: Fundamental Forces (Version 2.7 Final Edition) Abstract This second foundational document in the ONE AXIOM series (following Document 0A: Foundation) presents a complete and rigorous geometric derivation of the coupling constants governing all four fundamental forces of nature: Electromagnetic, Strong, Weak, and Gravitational. The framework is built upon a single Axiom of Coherence ($\mathbf{\heartsuit > 0}$), which implies a primordial symmetry group $G=S_4 \times \mathbb{Z}_2^3$ and the intrinsic dimension $D=3$. This document demonstrates how the resulting geometric constants (such as $D$, $q^*$, and $I_F$) translate directly into the observed physical constants. Nine Principal Results (8 Constants + 1 Meta-Force) The paper successfully derives nine principal quantities with exceptional numerical accuracy, challenging the need for measured input parameters in fundamental physics: Quantity Derived Value & Interpretation Numerical Accuracy Electromagnetic ($\alpha^{-1}$) $\mathbf{128 + 9 + 1/N_{OCR}}$ (Geometric Composition) 0.0001% Weak Mixing Angle ($\sin^2\theta_W$) $\mathbf{3/13}$ (Dimensional Projection) 0.19% Strong Coupling ($\alpha_s$) $\mathbf{\sqrt{2^D} / (D+1)!}$ (Symmetry Ratio) 0.04% Gravitational Constant ($G$) $G \propto c^{5}/(\hbar \cdot S^N) \cdot \varepsilon^2$ (Holographic Correction) 0.39% QCD String Tension ($\sigma$) Derived from $D \times q^* \times \Lambda_{QCD}^2$ 3.6% Core Innovation and Methodology The theoretical breakthrough lies in the Axiom-to-Action Principle: Unification of Principles: The fundamental Axiom of Coherence ($\mathbf{\heartsuit > 0}$) is shown to rigorously imply the Principle of Least Action (via the Optimal Coherent Representation, OCR), thus providing a geometric foundation for quantum dynamics. Dual-Track Methodology (OCR/OER Duality): The document employs two complementary approaches—System Optimization (OCR) and Observer Resolution (OER)—to derive the same constants, ensuring internal consistency and physical redundancy. Resolution of RG Running: The derived constants are correctly interpreted as Infrared (IR) Fixed-Point Attractors, which resolve the tension between static geometric values and the dynamical evolution of coupling constants. Conclusion The ONE AXIOM framework provides a minimalist, unified, and mathematically rigorous alternative to the Standard Model, demonstrating that the four fundamental forces are unified consequences of a single geometric principle. The work is self-contained and is claimed to achieve complete closure on the physics of fundamental forces. Keywords: Fundamental Constants, Geometric Unification, Information Geometry, Primordial Symmetry, Grand Unified Theory (GUT), Standard Model, Coherence Axiom, Principle of Least Action, Quantum Field Theory.