Spread-out Furstenberg sets II: general configurations and fractal restricted projections

We prove optimal dual Furstenberg estimates for Frostman and Katz–Tao configurations for which the shadings are not locally concentrated near pencils. The starting point is the sticky estimate of Orponen and Shmerkin in a companion paper. We deduce restricted projection theorems in the plane and in higher dimensions. In particular, Ahlfors-regular measures on the circle satisfy a Marstrand-type projection theorem. Applications include restricted projections to surfaces in the $\mathbb{G}(4,2)$ Grassmannian, pinned distances, discretized sum-product, and a new proof of the dimension formula for planar self-affine sets.