A Low-Rank Ternary Structure of Fermion Masses and Hidden Flavor Coordinates

Abstract

We investigate an empirical low-rank structure underlying the fermion mass spectrum. The construction is based on an integer exponent matrix L=QG+Be, where Q labels shell type, G labels generation, and Be introduces a correction affecting only the first generation. The resulting matrix reproduces the observed hierarchy of fermion masses using a small number of integer parameters. The construction naturally introduces hidden coordinates X=(Q,G,C) associated with each fermion species. We show that fermion masses depend primarily on the projected quantity L, while flavor information appears to require the full hidden-state coordinates. Possible implications for the observed structure of the CKM and PMNS mixing matrices are briefly discussed.

Comments: Results are incomplete or premature