Gap-Free Anytime-Valid Computerized Classification Testing under the 2PL Model

Computerized classification tests decide on which side of a cutoff an examinee lies. Classical sequential probability ratio tests calibrate errors at two separated abilities, leaving behavior inside a user-chosen indifference region unresolved. Under a known two-parameter logistic response model, we develop gap-free e-process procedures—requiring no user-chosen separated ability design points—whose finite-sample directional error control permits any predictable item policy. A shrinking-reference rule has local mean order $O({\delta }^{-2}{\log }^2(1/\delta ))$. Our main rule mixes over dyadic discrimination-standardized alternatives and attains the optimal worst-scale order $O({\delta }^{-2}\log \log (1/\delta ))$ in an ideal experiment with independent, identically parameterized cutoff-centered items. Known-truth simulations and logged-response comparisons show that the mixture substantially reduces exposure relative to shrinking. The logged study is observational and does not validate latent truth, item calibration, or counterfactual adaptive policies.