This bridge manuscript formalizes the transition from verifier-governed admissibility to projection-aware envelope cost within the Coh framework. Layer 1 establishes that proposed state transitions execute only when accepted by a deterministic verifier and when they satisfy an admissibility inequality involving valuation, spend, and defect. The bridge result shows that when a verifier observes only a coarse record of an execution rather than the full hidden realization, any sound declared defect must dominate the supremum of hidden costs over the projection fiber. The central theorem states that if Π maps hidden executions to observable verifier records, FR is the fiber of hidden realizations compatible with a record R, and W is hidden execution cost, then any sound defect declaration D must satisfy D (R) ≥ sup⏝ ∈ ₅ₑ W (ξ). Thus projection-aware envelope defect is not optional; it is the minimal conservative structure required for sound admissibility under partial observability. This release provides the Layer 1 → Layer 2 bridge for the Coh program: it closes verifier-native admissible execution and motivates the projection-induced oplax envelope structure developed in later Coh framework releases.
Micheal Ellington (Sun,) studied this question.