Rank Geometry of the Relational Channel: Finite-Sample Calibration, Operating Envelope, and Cross-Domain Validation as an Observability Layer

Let dρ = Var(ρ_ab, 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, dρ 0.45) with finite-sample bias under 4%. Bias enters a monotonic negative third-order regime for σ_post > 0.30, and both boundaries coincide with the operating limit of the AND gate. Third, non-stationarity is self-detectable: empirical dρ > (1 − ρ²)² / W flags structural drift without external ground truth. The N-observer extension yields a corrected r_eff estimator with MAE