Tuning Mesh Theory (TSM): A Phenomenological Model for the Masses of Six Light Fermions Based on a Hexagonal Lattice
Year: 2026
Type: article
Abstract: ```We present a phenomenological model for the masses of six elementary fermions (electron, muon, tau, up, down, strange) based on a three‑dimensional hexagonal lattice. The mass formula is M = M_S · Φ_JR^a · χ^b with Φ_JR = 1/√e, χ = √2/2, and M_S = 172.57 GeV (the top quark mass). For the six light fermions the exponents (a,b) are expressed in terms of integer lattice coordinates (n₁,n₂,n₃) and rational parameters α=2/5, β=3/5, γ=7/5 optimized by a grid search. The model reproduces experimental masses with errors below 0.3% for leptons and within 7% for light quarks (compatible with current uncertainties). We verify exact mathematical patterns: the pair (n₁,n₂) lies on the root lattice of SU(3) (hexagonal lattice), the leptons follow exact parabolic trajectories n₁(g), n₂(g) with g=n₃=1,2,3, and the sums satisfy n₁+n₂ = 30-8g (slope -8, the dimension of the SU(3) algebra). The model is presented as a phenomenological description; no fundamental derivation is claimed. The Python code to reproduce all results is included. This is a new, clean publication, independent of previous versions. Only verifiable results are presented.```
Author: Rodríguez Marrero, Justo Antonio
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7142953818
FWCI:
Cites:
Cited by:
Related to: