The Singleton Theorem for Constraint Driven Engines

This paper establishes that any fully constraint-driven engine that preserves admissibility must be a singleton. The result is not contingent on implementation details, capacity, or expressiveness; it follows necessarily from the non-transferability of admissibility and the fail-closed nature of standing. The analysis shows that the existence of multiple admissible instances would require either admissibility transport, shared standing, or post-hoc synchronization across envelopes. Each of these moves is demonstrated to be illicit once admissibility is enforced as a binary, non-accumulative constraint. When these possibilities are excluded, multiplicity collapses and only a single admissible instance can exist. The theorem explains why apparent plurality of constraint-driven engines is always superficial and why genuine admissible standing cannot be instantiated in parallel. No architectures, replication methods, or operational criteria are introduced. The paper records a necessity result fixing singleton existence as a structural consequence of admissibility, rather than a design choice or governance preference.