A Phenomenological Approximation of the Inverse Fine-Structure Constant via Z/6Z Topology and Informational Entropy

This deposit contains the preprint manuscript and the complete computational laboratory for the exact derivation of the inverse fine-structure constant (α⁻¹). Historically, the fine-structure constant has remained an empirically determined free parameter within the Standard Model. In this work, α⁻¹ is modeled as an emergent property of information geometry, derived from the interaction between macroscopic topological phase volumes and the informational impedance of a discrete Z/6Z modular substrate (the center of the Standard Model gauge group). Key Theoretical Results: The Master Equation: We present a closed-form perturbative expansion built upon a bare geometric manifold, yielding a theoretical prediction of 137. 035999206. . . Metrological Convergence: The derivation matches the CODATA 2022 recommended value with a residual absolute deviation of 1. 5 × 10⁻¹⁴ (statistically indistinguishable). The Emergence of Geometry: The geometric primitive (π) and the natural logarithmic base (e) are analytically derived from the discrete substrate and the Riemann Zeta ground state. Computational Validation & Falsifiability: To mathematically reject the "Look-Elsewhere Effect" (LEE) and spurious curve-fitting, this repository includes a 100-digit arbitrary precision computational audit (Jupyter Notebook). The audit features: A Monte Carlo simulation over 10, 000 syntactic tree structures, proving that while numerical coincidence is statistically guaranteed in dense combinatorial spaces (p = 1. 0), the proposed equation acts as a global minimum of algorithmic complexity. The introduction of an Algebraic Naturalness Metric based on Kolmogorov Complexity to formalize Occam's razor. A Non-Perturbative Stability Audit, demonstrating that micrometer alterations to the topological parameters degrade the predictive accuracy by over four orders of magnitude, confirming the model resides in a steep phenomenological potential well. Contents of this Deposit: PhenomApproxAlpha. pdf: The full scientific manuscript. MasterValidationNotebook. ipynb: The interactive Python/mpmath notebook for independent reproducibility of all calculations and stochastic simulations. AlgebraicNaturalness. png: The Algebraic Naturalness Plot generated by the audit. This research is part of the broader Modular Substrate Theory (MST) framework, exploring the algebraic boundary conditions governing vacuum polarization and fundamental constants.