What question did this study set out to answer?

This research aims to analytically evaluate the muon anomalous magnetic dipole moment using Modular Substrate Theory.

June 17, 2026Open Access

Analytical Evaluation of the Muon g − 2 Anomaly via Modular Substrate Topology in Quantum Electrodynamics

Key Points

This research aims to analytically evaluate the muon anomalous magnetic dipole moment using Modular Substrate Theory.
Replaces the empirical fine-structure constant with a geometric expansion derived from topological vacuum impedance.
Uses a Mellin transform over the noncommutative Dirac operator and the $ ext{Z}_6^{(1)}$ 1-form gauge symmetry.
Calculates a mass-gap penalty and deviation using high-precision computational frameworks.
Determined an exact geometric series that isolates the pure topological chiral limit.
Found a mass-gap penalty of approximately 38.1 x 10^-11, reflecting the current Standard Model tension.
Achieved high precision in deviations as reported in parts per billion.

Abstract

This repository hosts the supplementary computational framework and the associated manuscript detailing the analytical evaluation of the muon anomalous magnetic dipole moment (a_) utilizing the Modular Substrate Theory (MST). By replacing the empirical fine-structure constant () 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 Z₆^ (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 38. 1 10^-11 mass-gap penalty that mirrors the scale of the current Standard Model tension. Files Included Modulargₘinus₂. 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. MSTgₘinus₂Report. txt: The automatically generated summary report detailing the final absolute deviations and precision metrics (in parts per billion). Modularg2. 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 (Modulargₘinus₂. 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.

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