  We prove weighted analytic regularity of solutions to the Dirichlet problem
for the integral fractional Laplacian in polygons with analytic right-hand
side. We localize the problem through the Caffarelli-Silvestre extension and
study the tangential differentiability of the extended solutions, followed by
bootstrapping based on Caccioppoli inequalities on dyadic decompositions of
vertex, edge, and edge-vertex neighborhoods.
