The Root of the Demand: Two Limitative Theorems and a Conditional Forcing Result for Answerable Inquiry

This paper asks what forces the demand for bounded verdict agreement in the Identity–Persistence Program. It first proves a limitative result: boundedness alone cannot force answerability or verdict agreement, since a bounded system may emit non-claim states. It then argues that answerability—the capacity of an output to be false relative to a production-independent standard—forces re-identifiable content and evaluator-relative admissibility. The remaining evaluator-elimination problem is quotiented: unbound, it is refuted by countermodel; bound by a shared declared regime, it closes by derivation. The residue is co-declaration, the holding of a standard in common, which is shown to be exempt from the program’s own closure operations while remaining a necessary unit for shared formal reason. The resulting conditional root is: bounded inquiry, answerable under a co-declared standard, forces the verdict demand. The paper distinguishes PROVEN, DERIVED, OPEN, and REFUTED claims throughout.