When Is Test-Time Adaptation Identifiable from Unlabeled Evidence?

Test-time adaptation (TTA) offers many ways to update a deployed model without labels, but choosing the wrong update can make a strong source model worse. Recent methods therefore try to predict which adaptation will work from unlabeled test data. Yet the difficulty is not merely that different deployments can prefer different TTA actions: two deployments can be indistinguishable under the selector's allowed pre-action evidence while requiring opposite actions. We therefore ask a prior question: does the evidence given to the selector contain enough information to determine the best action at all? We show that this is not guaranteed, even with a perfect selector. If an observation channel makes two deployments look the same while their TTA rankings differ, reliable selection is impossible from that channel; richer evidence can restore the decision only when it resolves the relevant ambiguity. TTA selection failure can therefore reflect an information-channel failure, not only a selector-capacity failure. We make this boundary explicit in a finite-batch Gaussian TTA model, where doing nothing beats mean recentering for small shifts, recentering wins beyond a unique critical shift, and the boundary shrinks with batch size $n$ as $1/\sqrt{n}$. Controlled experiments on CIFAR-100-C and DomainNet-126 instantiate the same obstruction with modern TTA methods: across both synthetic corruptions and natural domain shifts, changing only deployment stream structure can reverse the oracle action while global order-blind evidence remains essentially invariant. Graded correlation sweeps show these reversals emerging progressively as temporal structure increases, while order-blind evidence barely changes. This separates two failure modes that are usually mixed together—a weak selector and an information channel that cannot support the desired decision—and suggests a simple question before building a stronger selector: can its inputs support the decision at all?