  We propose an integrability setup for the computation of correlation
functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric
Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion
and at any order in the 't Hooft coupling $g_{\text{YM}}^2N_{\text{c}}$. In
this multi-step proposal, one polygonizes the string worldsheet in all possible
ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over
all hexagon junctions to obtain the full correlator. We test our
integrability-based conjecture against a non-planar four-point correlator of
large half-BPS operators at one and two loops.
