ZQCM V1.4: First‑Principles Derivation of Standard Model Parameters from S³ Spectral Geometry and Spin(9) Root Systems

Abstract

The Standard Model has been verified to high precision. This work addresses the question of whether its parameters can be derived from a smaller set of geometric axioms.Falsifiable Predictions: Starting from S3×Cl(9) first principles with no free fitting parameters, the framework yields: Higgs mass mH=128.11±0.20 GeV; CKM mixing angle sin⁡θ13=3.56×10−3 (discrepancy −2.4 from experiment); PMNS angle sin⁡θ13PMNS=0.148; neutrino mass sum ∑mν≈0.092,eV. Gauge couplings emerge from the spectral decomposition of S3 Laplacian combined with Spin(9) root‑system branching rules. Fermion mass hierarchies are obtained via Clifford‑algebra projection onto the S3 harmonic modes. No ad‑hoc Yukawa couplings are manually tuned. The theory is purely geometric: all SM constants become observables of a compact internal spectral geometry.