The Quadratic Parabolic Relation for Standard Model Charged Fermion Masses

First in a Twinity with The Quadratic Parabolic Relation for Stellar Occultation fringes at the Lunar Limb

This paper reports the discovery of a high-precision quadratic parabolic relation that unifies the masses of all nine charged fermions in the Standard Model: the electron, muon, tau, and the six quarks (up, down, strange, charm, bottom, top). Using a logarithmic coordinate transformation, a dimensionless scalar coordinate S (the Splat coordinate) is introduced with the electron fixed at S = 1.0000. In this frame, the base-10 logarithm of the fermion masses satisfies a simple quadratic equation with three free parameters. The relation achieves an R² value greater than 0.9999999998, reproducing experimental masses spanning more than five orders of magnitude to within current measurement uncertainties. All Splat coordinate values are rational fractions expressed to exactly four decimal places. The result replaces eighteen independent Yukawa couplings with three universal parameters, offering a striking phenomenological constraint on mass-generation mechanisms. The deeper geometric origin of the Splat coordinate is derived from Annihilation Cosmology (AC Math V2.4), which is referenced and linked in the paper.

**Second in a Twinity:** [The Quadratic Parabolic Relation for Stellar Occultation Fringes at the Lunar Limb] https://doi.org/10.5281/zenodo.19748672

Philosophical preamble to this paper: 10.5281/zenodo.20837896

Mathemathical Preamble to this paper: 10.5281/zenodo.20838411

The Bridge between the preambles and the Phenomenological Additions is the AC Particle table here: https://zenodo.org/records/20975973

Contact the Author regarding the Annihilation Cosmology framework at: [DavidMcClean@protonmail.com] or David McClean - Splat Cosmology