Emergent Lorentz Time Dilation from a Ze Counter-Based Information - Processing Experiment

I present the Ze experiment — a minimal counter-based information-processing framework in which the Lorentz time-dilation factor emerges without invoking spacetime geometry, a metric tensor, or any relativistic postulate. A binary event stream of N elements is partitioned into temporal updates (sequential correlations, x_k = x_{k−1}) and spatial updates (inverse correlations, x_k ≠ x_{k−1}). Coordinate time is defined as the total event count T = N; spatial displacement as X = N_S; and proper time as the Minkowski interval τ = √(T² − X²). The velocity parameter v = X/T then satisfies τ(v)/τ₀ = √(1 − v²) — the Lorentz time-dilation factor — with residuals below 10⁻⁵ across 21 velocity values and N = 10⁷ events per point. Three independent falsifiability tests (stream independence, monotonicity, Lorentz-factor consistency) are all passed within their pre-specified thresholds. This constitutes the experimental arm of the Ze System theoretical programme (Tkemaladze, 2026a, 2026b) and provides a direct informational derivation of the relativistic time-dilation structure from pure counting dynamics.