Admissibility–Execution–Witness Coupling: Necessary Requirements for Accountable Viability under Finite Horizons

This preprint formalises a minimal architectural necessity for finite-horizon viability under finite capacity. The core claim is that accountable admissibility-preservation cannot be realised by a constraint specification alone (which does not execute) nor by an execution system alone (which does not define the constraint) without collapsing one role into the other. We introduce the coupled AEW unit—Admissibility, Execution, and Witness—as the minimal unit of responsibility for auditable viability regimes. The paper proves a role-separation and structural necessity result (AEW Necessity): without valid coupling and a boundary-legible witness, at least one predictable structural failure mode must occur on some admissible workload family: Specification erasure (admissibility is absorbed into local performance trade-offs and ceases to function as a boundary), System erasure (admissibility remains inert and cannot act on an execution surface), or Silent degradation (boundary violations occur without explicit refusal/holding witness, becoming non-auditable). The note is architectural rather than algorithmic: it does not propose a controller, learning method, or optimisation scheme. Instead, it clarifies what must be structurally present for “safe / viable” behaviour to be accountable under finite horizons: (i) a specification-level admissibility boundary, (ii) a cost-bearing execution surface with first-class outcomes (ACCEPT / REFUSE / HOLD), and (iii) a witness interface enabling verification without full internal disclosure. An illustrative failure example (silent degradation under boundary-blind logging) is provided in Appendix A. Relation to adjacent literatures. The result is complementary to constructive approaches such as Control Barrier Functions, constrained decision-making (e.g., CMDPs / safe RL), and monitoring in runtime verification: these can be understood as providing mechanisms that, when present, instantiate parts of the AEW architecture (invariance mechanisms, constrained formalisms, and witness/monitor surfaces, respectively). The present manuscript focuses on the necessity of coupling and witness for auditable viability under finite horizons. Version 1.1 revises the framing of the paper by identifying the main result as a structural necessity result for accountable viability under finite horizons. It also clarifies that the theorem is architectural rather than algorithmic, and expands the role-level relation between the AEW unit and adjacent approaches such as control barrier functions, constrained Markov decision processes, and runtime verification.