Mass, Proper Time, and Gravity — Part II: Proper Time as Causal Counting, a pre-geometric realization of the rhythm of processes

Part I (Zenodo, DOI 10.5281/zenodo.20708661) proposed reading proper time not as an external flow, but as the physical rhythm of each process. This Part II makes the claim concrete and verifiable: in a pre-geometric structure (a causal set, defined only by a causal order and a counting measure, with no distances or metric) the proper time between two events is reproduced by the number of steps in the longest causal chain that links them. We demonstrate this numerically and show that the counting reproduces time dilation (the twin paradox) and is invariant under Lorentz changes of coordinates, because the causal order relation is invariant; statistically, the Poisson sprinkling introduces no preferred direction, unlike a regular lattice. The demonstration is extended to a curved spacetime, and reinforced by three additional checks: convergence to the continuum, recovery of the spacetime dimension (Myrheim-Meyer), and the contrast between a regular lattice and a random sprinkling. The paper introduces no new equations and changes no prediction; the counting result is a known fact of causal set theory, used here to anchor the thesis of Part I (proper time is the intrinsic counting/rhythm of a process). The dynamical origin of the causal structure itself remains, explicitly, outside the scope of this work.