A number-theoretic framework in which all fundamental particle masses arise from a single geometric progression governed by the congruence subgroup Γ₀(6). The modular level N=6 is uniquely selected by cusp-width matching to Standard Model representations. The framework predicts 13 masses at 1–5% accuracy (p < 10⁻²⁶), the fine structure constant to 0.001 ppb, and the solar mixing angle sin²θ₁₂ = 4/13 — confirmed by the first JUNO measurement at +0.17σ. Zero continuous free parameters. Nine falsifiable predictions testable within 2–5 years.
Denis Zinchenko (Tue,) studied this question.