Sweet Trims are made of Threes: A càdlàg erasure of the Brownian tree

We present a simple trimming algorithm that generates nested uniform binary plane trees by removing leaves one-by-one using a best-of-three-match procedure. While its one-step transition specializes to the Luczak-Winkler & Caraceni-Stauffer coupling, its scaling limit provides a suprising càdlàg erasure of Brownian trees, reminiscent of SLE theory.