Ze Impedance and the Emergence of the Minkowski Metric

We propose a derivation of the Minkowski spacetime metric that proceeds entirely from the combinatorial structure of a dual-channel binary event counter—the Ze system. A Ze system partitions any binary observation stream into T-events (stasis) and S-events (change), defining a Ze impedance Z_Ze ≡ N_S/N_T and the Ze proper time τ = √(N_T² − N_S²). The resource constraint N_T + N_S = N − 1 forces N_T and N_S into anti-phase: any increase in N_S must reduce N_T, generating the quadratic invariant τ² = N_T² − N_S². In the continuous limit, assigning coordinate differentials dN_T → dt and dN_S → dx/Z_Ze and imposing Z_Ze = const yields the line element ds² = Z_Ze²dt² − dx², which coincides with the Minkowski metric upon the identification Z_Ze ≡ c. The speed of light thus emerges as a structural impedance limit of the counting process, not as an independently postulated constant. Numerical simulations with N up to 5 × 10⁶ confirm the invariant τ² = N_T² − N_S² with relative error below 0.01% for N > 10⁵. Extension to variable Z_Ze(x) reproduces the Schwarzschild metric form, suggesting that curved spacetime corresponds to spatially modulated Ze impedance. Five falsifiable predictions are provided.