Quark Mod 1710 -

[ M_i = 1710 \ \textMeV \times (1 + k_i \mod 3) ]

A 2024 paper in Physical Review D (titled "Modular Symmetry and Glueball–Quark Mixing" ) demonstrated that if the superpotential respects a modular group (\Gamma(3)), then the mass eigenvalues satisfy: quark mod 1710

where ( |G\rangle ) is the glueball, ( |N\rangle = u\baru+d\bard ) and ( |S\rangle = s\bars ). The "mod" term appears when one imposes on the effective Lagrangian—specifically, requiring that the mixing angles be periodic under shifts of 1710 in a certain scalar potential. [ M_i = 1710 \ \textMeV \times (1