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Abstract We use the recently developed methods of arXiv:2108.07810 to analyze vertical flux backgrounds and associated chiral matter spectra in the 4D universal (SU(3) × SU(2) × U(1))/ℤ 6 model introduced in arXiv:1912.10991, which is believed to describe the most generic family of F-theory vacua with tuned (SU(3) × SU(2) × U(1))/ℤ 6 gauge symmetry. Our analysis focuses on a resolution of a particular presentation of the (SU(3) × SU(2) × U(1))/ℤ 6 model in which the elliptic fiber is realized as a cubic in ℙ 2 fibered over an arbitrary smooth threefold base. We show that vertical fluxes can produce nonzero multiplicities for all chiral matter families that satisfy 4D anomaly cancellation, which include as a special case the chiral matter families of the Minimal Supersymmetric Standard Model.