  We develop new tools for isolating CFTs using the numerical bootstrap. A
"cutting surface" algorithm for scanning OPE coefficients makes it possible to
find islands in high-dimensional spaces. Together with recent progress in
large-scale semidefinite programming, this enables bootstrap studies of much
larger systems of correlation functions than was previously practical. We apply
these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d
$O(2)$ model, computing new precise values for scaling dimensions and OPE
coefficients in this theory. Our new determinations of scaling dimensions are
consistent with and improve upon existing Monte Carlo simulations, sharpening
the existing decades-old $8\sigma$ discrepancy between theory and experiment.
