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…