ONE AXIOM : FUNDAMENTAL FORCES

ONE AXIOM: Fundamental Forces — Geometric Derivation of Couplings and Constants (Version 4.6) Abstract: This document (1A) is the second part of the ONE AXIOM series, providing a rigorous derivation of the fundamental constants of nature from the primordial symmetry $G = S_4 \times \mathbb{Z}_2^3$ and the principle of Informational Coherence ($\heartsuit > 0$). While the preceding Document 0A established the geometric foundation, this work translates those results into the domain of fundamental interactions: Electromagnetism, Strong and Weak forces, and Gravitation. Key Highlights of Version 4.6: The G-Exact Theorem: A three-step geometric derivation of the Gravitational Constant ($G$) with a precision of 0.0023% relative to CODATA 2022, effectively resolving the long-standing difficulty of linking gravity to quantum scales. GAC Rigidity Theorem: A mathematical proof demonstrating that the Gauge-Algebra Correspondence is "rigid"—the mapping between the symmetry group and physical gauge sectors is unique and breaks if the spatial dimension $D \neq 3$. Structural Identities: Discovery of the identity $\sin^2\theta_W = \Lambda_{QCD}/m_p = 3/13$, providing a deep geometric link between electroweak mixing and the strong interaction scale. RG-Attractor Theory: An innovative approach to the Renormalization Group, interpreting geometric constants not as UV inputs, but as IR fixed points (attractors) towards which physical couplings naturally evolve. Falsifiability: The document defines four strict, quantifiable criteria (F1-F4) for experimental falsification, ensuring the framework adheres to the highest standards of scientific methodology. Scientific Significance: By replacing "free parameters" with geometric necessities derived from the Fisher Information Metric and Category Theory (OCR/OER Duality), this framework offers a complete, self-consistent, and highly precise alternative to the traditional empirical adjustment of the Standard Model constants.