Rel–$C^\infty$ structures on Gromov–Witten moduli spaces

We show that moduli spaces of transversely cut-out (perturbed) pseudo-holomorphic curves in an almost complex manifold carry canonical relative smooth structures (relative to the space domain curves). The main point is these can be characterized by a universal property. tools required are ordinary gluing analysis combined with some fundamental results from polyfold theory Hofer--Wysocki--Zehnder.