ψ-Retentive Tail — First Laboratory Detection: AIC/BIC-Based Statistical Identification of a Non-Vanishing Late-Time Offset in a Ring-Down Experiment

This preprint proposes a reproducible statistical protocol for detecting or rejecting a non-vanishing constant offset (“retentive tail”) in laboratory ring-down measurements. The method does not introduce theoretical assumptions about physical mechanisms. It specifies when a constant term must be modeled instead of being dismissed as baseline noise. A ring-down response R(\tau) is evaluated under two nested models: M_0 = A e^{-\gamma\tau}, \qquad M_1 = A e^{-\gamma\tau} + C_{\mathrm{ret}}. Detection requires three independent acceptance criteria: (1) late-time decomposition of transient and plateau components; (2) variance stability on a late-time interval compared to a noise estimate \sigma_{\mathrm{noise}}; (3) model-selection advantage \Delta\mathrm{AIC}\ge10 or \Delta\mathrm{BIC}\ge10 together with Gaussian significance Z\ge3 for C_{\mathrm{ret}}. Failure of any single requirement rejects the claim. The protocol includes recommendations for data acquisition, environmental stabilization, calibration, negative controls, and open-data reproducibility (raw time-series, analysis scripts, and software versions). The purpose is strictly methodological: a decision boundary for statistical evaluation of ring-down data. Failure of the criterion eliminates the claim; success enables further laboratory testing.