Claim Adjudication under Uncertain Binding and Shared Failures

A record can be authentic and still leave the target claim unresolved. Uncertain associations can hide which action occurred; shared control can make several reports fail together. We give a finite-model criterion for deciding a binary claim under both conditions. Every opposite-claim pair must retain a distinguishing domain outside the union of any two admissible failure sets, under every allowed binding transformation. When this condition fails, the method returns two indistinguishable histories. It also yields static evidence-selection constraints and separates detection, adjudication and coalition concealment. The model uses joint honest supports, a finite coordinatewise transformation group and downward-closed failure families with arbitrary domain replacement. Finite checks, retained authorization-and-effect records and a transaction-ledger application illustrate the method. The contribution is a constructive synthesis of confusability and claim-sensitive error correction; application guarantees depend on justified capture, binding and control assumptions. This record deposits the manuscript PDF, version v0.7-candidate.14, as a preprint. The supplementary code and data described in the manuscript are not included in this deposit. Mikhail A. Sergeev is the author of this work, prepared with assistance from AI assistants.