  Using 1-twist rim surgery, we construct infinitely many smoothly embedded,
orientable surfaces in the 4-ball bounding a knot in the 3-sphere that are
pairwise topologically isotopic, but not ambient diffeomorphic. We distinguish
the surfaces using the maps they induce on perturbed sutured Floer homology.
Along the way, we show that the cobordism map induced by an ascending surface
in a Weinstein cobordism preserves the transverse invariant in knot Floer
homology.
