Let d_ρ = Var (ρₐb, W) be the relational channel variance of two scalar observers over a rolling window of length W. Three results are established. First, the Rank-Collapse Theorem: under weak stationarity and ergodicity, d_ρ 0. 45) with finite-sample bias under 4%; bias enters a monotonic negative third-order regime for σₚost > 0. 30, and both boundaries coincide with the operating limit of the AND gate. Third, non-stationarity is self-detectable: empirical d_ρ > (1−ρ*²) ²/W flags structural drift without external ground truth. The N-observer extension yields a corrected rₑff estimator with MAE < 0. 04 (N = 2–10) and an empirically characterized band structure with analytic motivation deferred to subsequent work. The framework applies to stochastic relational systems including sensor synchronization, coupled oscillators, and correlated financial or biological signals.
Jesus David Calderas Cervantes (Wed,) studied this question.