Analytical Evaluation of the Muon g − 2 Anomaly via Modular Substrate Topology in Quantum Electrodynamics
José Ignacio Peinador Sala · Zenodo (CERN European Organization for Nuclear Research) · 2026
This repository hosts the supplementary computational framework and the associated manuscript detailing the analytical evaluation of the muon anomalous magnetic dipole moment ($a_\mu$) utilizing the Modular Substrate Theory (MST). By replacing the empirical fine-structure constant ($\alpha$) with its exact geometric expansion derived from the topological vacuum impedance, this framework computes the pure Quantum Electrodynamics (QED) 5-loop perturbative sector deterministically. Furthermore, it introduces a first-principles derivation of the Hadronic Vacuum Polarization (HVP) sector. Applying a Mellin transform over the noncommutative Dirac operator and utilizing the $\mathbb{Z}_6^{(1)}$ 1-form gauge symmetry, the model yields an exact geometric series. This series isolates the pure topological chiral limit (massless vacuum), rigorously exposing a $\sim 38.1 \times 10^{-11}$ mass-gap penalty that mirrors the scale of the current Standard Model tension. Files Included Modular_g_minus_2.ipynb: An interactive, high-precision Jupyter Notebook (Python) utilizing the mpmath library. It executes the full theoretical pipeline: the geometric derivation of the QED sector, the dynamic isolation of the hadronic target, and the exact mass-gap deviation calculation. MST_g_minus_2_Report.txt: The automatically generated summary report detailing the final absolute deviations and precision metrics (in parts per billion). Modular_g2.pdf: The full companion article prepared for peer review. Reproducibility The Python notebook is completely self-contained. It requires the mpmath library initialized to an arbitrary precision of 50 decimal places to prevent floating-point truncation. It is ready to be executed in local Jupyter environments or cloud-based platforms such as Google Colab. Licensing and Usage This project is dual-licensed to ensure open academic access while protecting the computational implementation: Theoretical Content, Article, and Text: Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Executable Source Code (Modular_g_minus_2.ipynb): Released under the Polymorph License. When utilizing or referencing these materials, please cite the permanent DOI: 10.5281/zenodo.20704308. Keywords: Quantum Electrodynamics, Muon g-2, Modular Substrate Theory, Hadronic Vacuum Polarization, Fractal Topology, Python, mpmath.