Algorithmic universality in F-theory compactifications

We study universality of geometric gauge sectors in the string landscape in the context of F-theory compactifications. A finite time construction algorithm is presented for 4/3×2.96×10⁷⁵⁵ F-theory geometries that are connected by a network of topological transitions in a connected moduli space. High probability geometric assumptions uncover universal structures in the ensemble without explicitly constructing it. For example, non-Higgsable clusters of seven-branes with intricate gauge sectors occur with a probability above 1--1.01×10^-755, and the geometric gauge group rank is above 160 with probability 0.999995. In the latter case there are at least 10 E₈ factors, the structure of which fixes the gauge groups on certain nearby seven-branes. Visible sectors may arise from E₆ or $SU(3)$ seven-branes, which occur in certain random samples with probability 1/200.