What question did this study set out to answer?

This work aims to derive fundamental constants and parameters of the Standard Model using the W(3,3) strongly regular graph.

May 21, 2026Open Access

A Strongly Regular Graph Derivation of Standard Model Parameters: The W(3,3) Geometric Framework

Key Points

This work aims to derive fundamental constants and parameters of the Standard Model using the W(3,3) strongly regular graph.
Utilized spectral data from the W(3,3) strongly regular graph SRG(40,12,2,4).
Derived parameters including fine-structure constant, Weinberg angle, and neutrino mass from eigenvalues.
Provided experimental predictions for testing at facilities like JUNO and DUNE.
Fine-structure constant α−1 = 137 (experimental: 137.036, error 0.026%).
Weinberg angle sin²θW = 0.2308 (error 0.18%) determined from the graph.
Neutrino mass sum Σmν = 30.7 meV and CP phase δCP = 80.1°, with eight predictions testable in upcoming experiments.

Abstract

The W (3, 3) theory derives all fundamental constants, particle quantum numbers, and mixing parameters of the Standard Model from the spectral data of the W (3, 3) strongly regular graph SRG (40, 12, 2, 4). From the three eigenvalues 12, 2, -4 with multiplicities 1, 24, 15 we recover: Fine-structure constant α−1 = 137 (experiment: 137. 036, error 0. 026%) Weinberg angle sin²θW = 3/13 ≈ 0. 2308 at the Z-pole (error 0. 18%) SM gauge group U (1) × SU (2) × SU (3) from the spectral triple automorphism Master energy scale E = 480 = |Φ (E8) | linking graph spectrum to the E8 root system Neutrino mass sum Σmν = 30. 7 meV (normal hierarchy, Majorana) Atmospheric mixing angle θ23 = 45° (maximal mixing) CP phase δCP = 80. 1° Eight falsifiable experimental predictions testable at JUNO, KATRIN, DUNE, Hyper-Kamiokande, LEGEND-1000, and LISA The uniqueness of SRG (40, 12, 2, 4) up to isomorphism eliminates all tunable moduli. This repository contains the full LaTeX paper, PRL letter, Python computation scripts, SVG figures, and arXiv submission bundle.

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