What question did this study set out to answer?

This research aims to derive the masses of charged fermions using geometric and topological principles.

March 26, 2026Open Access

Ab Initio Derivation of the Charged Fermion Mass Spectrum from Density Field Dynamics

Key Points

This research aims to derive the masses of charged fermions using geometric and topological principles.
Utilized a master formula for fermion mass based on density field dynamics.
Computed prefactors from A₅ icosahedral geometry on CP² × S³.
Derived the fine-structure constant from topological considerations.
Utilized one global normalization value from the Fermi constant.
Predicted masses achieve a mean absolute error of 1.42% against PDG 2024 values.
Maximum error observed was 3.32% for the electron.
Best predictions were for strange and charm quarks with errors of 0.03% and 0.04% respectively.
Determined six mass ratios with no free parameters.

Abstract

We derive the masses of all nine charged fermions from the master formula mf = Af α^nf v/√2, where the prefactors Af are computed from A₅ icosahedral class geometry on the DFD microsector CP² × S³, and the exponents nf arise from Spinᶜ line-bundle degrees on CP². The fine-structure constant α = 1/137. 036 is itself derived from topology (companion paper, doi: 10. 5281/zenodo. 18045109). One global normalization (v/√2 from the Fermi constant) is used; no per-fermion fitting exists. The nine predictions achieve 1. 42% mean absolute error against PDG 2024 values, with maximum error 3. 32% (electron) and best predictions for strange (0. 03%) and charm (0. 04%). Six structural mass ratios are determined with zero free parameters. The derivation transforms nine arbitrary Standard Model parameters into consequences of CP² × S³ topology and A₅ representation theory.

Ab Initio Derivation of the Charged Fermion Mass Spectrum from Density Field Dynamics

Key Points

Abstract

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