Unified Fermion Mass Ratios from Orbifold Conformal Field Theory

Motivated by simple-current orbifolds, where twisted sectors come with characteristic chiral and left–right “degrees,” we construct the minimal modular-covariant, permutation-symmetric, degree-zero functional of charged-fermion masses, Formula: see text This CFT-motivated ansatz reproduces Formula: see text for charged leptons (the known Koide relation) and yields a quark-sector ratio numerically consistent with Formula: see text when evaluated on current Formula: see text quark masses. The ratio is approximately invariant at one loop; full two-loop running causes only few-Formula: see text-level variations in Formula: see text over the range Formula: see text–Formula: see text. Under SM running, this predicts Formula: see text a precision target within reach of forthcoming lattice step-scaling calculations. The construction is numerically verified, RG-stable, and falsifiable through improved mass determinations. This framework offers a CFT-motivated route to linking low-energy flavor phenomenology and high-scale orbifold dynamics.