Late synchronization and the geometry of Collatz families

We determine the geometry of Collatz trajectories conditioned on late synchronization. Their absolute odd-count separation converges, in the physical shortcut clock, to a Brownian meander continued to its first zero. One excursion carries asymptotically all the duration and height. For every fixed finite family of integer shifts under one 2-adic Haar root, the entire separation matrix converges to one random two-block cut multiplied by that same arch. The cut is independent of the arch, and its weights are recovered from the family absorption coefficients. A weighted chronological path lemma handles dependent excursions and random positive-level entrances using only expected total weight. We transfer the joint path and lifetime law to actual integer logarithmic separations at sublogarithmic horizons. We also prove relative absorption tails uniformly over every subexponential offset envelope and show that every positive linear exponential envelope fails uniformity. The exact scalar laws and arithmetic occupation estimates are imported from the rates companion; the additional path and uniformity arguments are proved here. Companion papers: Exact rates in Collatz synchronization; The stochastic 3x+1 model is a theorem: Brownian structure of Collatz orbits.