The Verification Boundary: Exact Limits of Verification by Bounded Systems: Identification, Generation, Computation, Implementation, Correspondence — and the Forced Routing at Each Limit

Abstract What can a bounded verifier establish from the evidence and resources available to it? This paper organizes verification limits around declared evidence, tasks, interfaces and computational budgets. Exact verification requires that the available evidence distinguish cases demanding different answers. Further generation or computation from unchanged evidence cannot remove an informational obstruction. Separate results address computational undecidability, adaptive observation, self-verification, probabilistic continuation and the possible absence of a greatest budget-bounded evaluator. Within the stated models, the paper gives attainment conditions and converse results, distinguishing information insufficiency from computational and resource limitations. It develops a routing framework that keeps certification, abstention, additional evidence, restricted scope, probabilistic premises and inconsistency explicitly separate. Probability enters through declared assumptions rather than as a logically compulsory response to deterministic failure. The contribution is a structured account of these boundaries and their relationships, with conditional extensions for certificate transport and continuation-sensitive verification. The results apply under their specified evidence and strategy contracts; correspondence to a concrete human or AI system requires an additional argument. This edition includes the binding correction withdrawing reliance on an unavailable enumeration while preserving the separately supported theorem and witness.