  We construct four-dimensional, globally consistent F-theory models with three
chiral generations, whose gauge group and matter representations coincide with
those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and
the Trinification Model. These models result from compactification on toric
hypersurface fibrations $X$ with the choice of base $\mathbb{P}^3$. We observe
that the F-theory conditions on the $G_4$-flux restrict the number of families
to be at least three. We comment on the phenomenology of the models, and for
Pati-Salam and Trinification models discuss the Higgsing to the Standard Model.
A central point of this work is the construction of globally consistent
$G_4$-flux. For this purpose we compute the vertical cohomology
$H_V^{(2,2)}(X)$ in each case and solve the conditions imposed by matching the
M- and F-theoretical 3D Chern-Simons terms. We explicitly check that the
expressions found for the $G_4$-flux allow for a cancelation of D3-brane
tadpoles. We also use the integrality of 3D Chern-Simons terms to ensure that
our $G_4$-flux solutions are adequately quantized.
