A note on alternative symmetric polynomials in A4 quark-lepton mass relations

Cross-sector mass relations between down-type quarks and charged leptons have been obtained in flavor symmetry models with and without grand unification. These relations typically constrain the product of quark masses through the third elementary symmetric polynomial e3 of the lepton mass square roots. We examine whether alternative symmetric polynomials of the same quantities can constrain individual quark masses. Using e1 and e2 in the combination with no fitted continuous parameters (0.01σ residual, both PDG and FLAG. These observations are documented as empirical input for flavor model building.