The Physical Limits of Finite Observation: Seven Bounds on Sensing, Inference, and Control

Engineering practice often treats the error of a sensing-and-control system as a quantity that may, in principle, be driven to zero. We argue that this target is unreachable under finite resources, and we make the obstruction precise. We assemble seven established bounds—from information theory, statistical estimation, thermodynamics, the relativistic limits of computation, computability, and learning theory—and show how they constrain any finite observer that senses, infers, and acts. The bounds are of three kinds, which we name for downstream citation: physical and information-theoretic (_phys), statistical and inductive (_stat), and logical (_logic); they are assembled, not derived from a single principle, and later papers in this series inherit them by slice, not as one object. Taken together they imply that no finite observer can at once represent a continuous environment without loss, estimate a continuous quantity exactly, retain its full history, be optimal across all environments, and certify its own consistency. We then add one further premise—a modest criterion of correctness, bounded error on every input the system acts upon—and we are explicit that it is a premise chosen, not a consequence of the bounds. Under it, the bounds compel a definite operating discipline: a declared error budget, an explicit representation of the boundary of competence, and the capacity to abstain on inputs that fall outside it. We state the modality of each: the error budget and the abstention are necessary under the criterion where the task's geometry engages them—a positive error floor where one attaches, refusal where the input universe exceeds the demonstrated domain; the explicit boundary is necessary for correctness to be demonstrated—it is what an auditor requires, since no finite observer can certify itself. The result is substrate-independent, applying alike to a structural monitor, a quantum estimator, and an autonomous agent. We give the necessary properties of such a system, not a construction, and we close with an assumption ledger recording what each claim rests on. The bounds are established results; their assembly, and the conditional architecture they imply, are the contribution.