Non-perturbative finite connectivities in supercritical Bernoulli percolation on $\mathbb{Z}^d$ with $d\geq 3$

We solve a longstanding problem in Bernoulli percolation: we derive sharp Ornstein--Zernike asymptotics for the probability that two distant points are connected by a finite cluster in the whole supercritical regime. Our proof has two main ingredients. First, the renewal structure from Fridbergh and