A Toy Model from the Z₁₀×Z₁₂ Discrete Network: Three-Generation Fermion Mass Spectrum

We report a toy model that attempts to provide a compact parameterization of the three-generation mass spectrum of charged leptons and quarks, starting from the algebraic structure of a single discrete group Z₁₀×Z₁₂. After fixing all parameters with a single free scale (the electron mass, 0.511 MeV), the model reproduces nine experimental mass points with deviations not exceeding 1% and mostly below 0.5%. The parameters themselves exhibit four non-trivial algebraic constraints——base numbers sum to 6, base numbers are symmetric about 2.5, deformation masses are generation-independent, and first-generation sinking masses follow a 3 : 2 : 1 ratio with electric charge——all of which can be traced back to the discrete symmetries of the Z₁₀×Z₁₂ group. More intriguingly, the exponents and base numbers in the model appear to emerge naturally from the geometric parameters of the group structure (this Brief Communication reports only the phenomena; a detailed derivation is deferred to forthcoming work [4]). We categorize every claim according to its epistemic status: group-theoretic necessity, formal motivation, or open question. This paper is positioned as a toy-model report and makes no claim of "new physics."