Quadrillion $F$-Theory Compactifications with the Exact Chiral Spectrum of the Standard Model

We present $\mathcal{O}({10}^{15})$ string compactifications with the exact chiral spectrum of the standard model of particle physics. This ensemble of globally consistent $F$-theory compactifications automatically realizes gauge coupling unification. Utilizing the power of algebraic geometry, all global consistency conditions can be reduced to a single criterion on the base of the underlying elliptically fibered Calabi-Yau fourfolds. For toric bases, this criterion only depends on an associated polytope and is satisfied for at least $\mathcal{O}({10}^{15})$ bases, each of which defines a distinct compactification.