  We study the maximally-helicity-violating (MHV) six-gluon scattering
amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory at finite
coupling when all three cross ratios are small. It exhibits a double
logarithmic scaling in the cross ratios, controlled by a handful of "anomalous
dimensions" that are functions of the coupling constant alone. Inspired by
known seven-loop results at weak coupling and the integrability-based pentagon
OPE, we present conjectures for the all-order resummation of these anomalous
dimensions. At strong coupling, our predictions agree perfectly with the string
theory analysis. Intriguingly, the simplest of these anomalous dimensions
coincides with one describing the light-like limit of the octagon, namely the
four-point function of large-charge BPS operators.
