Geometric Origin of Fermion Mass Hierarchy Exponents

This work presents an explicit F-theory compactification on a CKPT-class Calabi–Yau fourfold and derives, from this construction, two complementary structures relevant to fermion mass hierarchies in the Standard Model. The witness geometry has gauge algebra su (5) u (1) ² with Mordell–Weil rank 2, GUT divisor W dP₂ supporting an explicit matter spectrum, three-generation chirality (10) = (5) = +3 from a specified G₄-flux, and thirteen SO (12) Yukawa enhancement points realizing the down-type coupling. The construction satisfies Freed–Witten quantization, primitivity, D3-tadpole cancellation, and SO (12) Yukawa neutrality, all verified explicitly. From this geometry, the paper derives (i) a generation-overlap structure with exponents (₁, ₂) = (7/6, -4/5) via the spectral cover and BHV factorization, and (ii) a charge-weighted hierarchy kernel with parameters (, ) (8/7, 2. 23) via a modular fixed-point analysis on the elliptic-fiber moduli space. The combined four-parameter mass-ratio law matches empirical fermion mass data within the published spread of mass-only fits. Companion software for the geometric and modular computations is archived separately and linked under "Related identifiers, " URL: https: //zenodo. org/records/19022834