Jaba Tkemaladze
The Ze framework represents spacetime as a statistical partitioning of a binary event stream into T-events (state repetitions) and S-events (state transitions), from which proper time tau = sqrt(T^2 - X^2) and velocity v = N_S / N are derived in direct analogy with the Minkowski interval. This paper investigates a new phenomenon: a Ze system Ze1 can generate a daughter Ze system Ze2 by re-encoding the run-length parities of its S-events. We derive the analytical formula v2 = 2(1-v1)/(2-v1)^2 and verify it against simulation data (N = 5 x 10^6, nine velocity values) with residuals below 5 x 10^-4. The map f(v) = 2(1-v)/(2-v)^2 has a unique stable fixed point v* = 0.45631 governed by the cubic equation u^3 - 2u^2 + 2u - 2 = 0 (u = 2 - v*). The Ze cascade Ze1 -> Ze2 -> Ze3 -> ... converges numerically to v*, confirming the fixed-point prediction. An exact algebraic conservation law holds for any partition of Ze1: tau1^2 = tau2^2 + tau3^2 + 2 T2 T3 (1 - v2 v3), verified with relative error < 10^-6. The paper presents four falsifiable predictions of the cascade theory.