A Forcing Theorem for Sufficient Regime Specification Under Bounded Verdict Agreement

Abstract The Identity–Persistence Program establishes forcing theorems for coherent identity and admissibility claims, each beginning from the assumption of a declared regime. This paper addresses the remaining foundational question: what makes a regime specification sufficient for bounded independent evaluators to compute the same persistence or admissibility verdict under the same assumptions? The paper proves that any regime specification sufficient for bounded verdict agreement must instantiate a structural sufficiency floor consisting of fifteen roles. Eleven roles are forced by the persistence/admissibility problem itself, while four additional roles—authority, evaluator access, verification, and conflict resolution—are forced only within the bounded-verdict-agreement class. The proof proceeds by systematic failure-removal, establishing role necessity rather than role independence. The result is structural rather than ontological. It does not identify a unique regime, invariant basis, or admissibility rule, nor does it characterize a canonical minimal specification. Instead, it establishes the minimum structural roles that any sufficient regime specification must contain, explicitly or by unique recovery, for stable, repeatable, independently reproducible verdicts. The paper further separates proven necessity from open questions concerning algebraic independence, minimality, equivalence, refinement, and machine-checkable specification structure, defining a disciplined frontier for future work.