A Discrete-Geometric and Algebraic Core of Standard Model Structure from H4/600-cell Geometry

This preprint presents a discrete-geometric and algebraic framework based on the cyclic group GZ60, the H4 root system (600-cell geometry), and the quadratic field Q (sqrt5). The paper is intentionally organized into three layers: exact algebraic results, minimal physical interpretation, and falsifiable predictions. On the exact side, the framework establishes the decomposition GZ60 ≅ Z5 × Z3 × Z4, the necessary emergence of the golden-ratio field from Z5 character data, and the correspondence between H4 Coxeter exponents modulo 12 and the generator set of Z12. Yukawa textures constructed from Z5 character data are shown to lie in Q (sqrt5). On the phenomenological side, the framework proposes a minimal interpretation in which the Z3 factor is associated with generation indexing, the Z4 factor with chirality/isospin bookkeeping, and the Z5 factor with golden-ratio hierarchy structure. Representative charged-fermion mass ratios are compared against low-complexity expressions of the form rφⁿ. The paper does not claim a full derivation of the Standard Model, nor a complete account of flavor physics. Instead, it isolates an exact algebraic core and formulates predictions that are precise enough to be falsified, including benchmark neutrino mixing angles and a heavy right-handed neutrino scale near 10¹6 GeV. Known failures, especially in the CKM sector, are documented explicitly.