The Innovation Floor-Lock Theorem; Observation Limits in a Self-Field-Following Agent under Optimal Kalman Filtering

We present a structural analysis of detection failure in a self-referential adaptive perception architecture. An SFE agent tracks a one-dimensional stochastic field via a matched Kalman filter and monitors prediction surprise through a self-regulating windowed gate. We prove that once the filter reaches steady state, the predictable component of state evolution is absorbed by the estimator, leaving a whitened residual that carries no information about the field's confinement regime k. The normalized residual magnitude locks at a universal value: "E[ε̃] = sqrt(2/π) · (σₘ / V_field) ≈ 0.714 (for all k ≥ 0 under matched filtering)", independent of field-confinement strength. This is a structural detection-impossibility result: a gate downstream of a matched adaptive estimator cannot detect the regime that the estimator was built to track. The mathematical result (Kalman innovation whitening) is classical; the contribution is the detection-impossibility framing and the architectural diagnosis of why the detection channel must fail. Scope: the impossibility holds for linear Gaussian processes with correct model parameters at steady state. It breaks under model mismatch, time-varying k, or when the detection observable bypasses the estimator's residual channel. Section 9 presents the architectural resolution confirmed in SFE-05.13b: decoupling the detection channel from the adaptive estimator (null predictor with fixed reference x̂ = 0) restores geometric separability at 3.02σ, confirming that the information erased from the residual channel was never lost from position space.