We establish a biconditional theorem characterizing when a finite physical system can continue to improve its predictions about its environment. A finite physical learner remains adaptive if and only if its minimal predictive state is not yet a sufficient statistic for the predictive structure of its causally accessible environment, and the remaining predictive residual is physically encodable. The theorem synthesizes Shannon information theory, Landauer's principle, and the Bekenstein bound into a single result with two collapse modes (informational closure and physical closure), companion structural and compression forms, and resolutions to three classical objections (predictive selectivity, boundary determination, and self-referential closure). All components draw on established physics; the contribution is the specific synthesis.
Taylor Prather (Sun,) studied this question.