Retention Without Activation: A Minimal Relational System of Failure Under Persistence

This paper defines a minimal relational system in which failure persists without resolution. The system does not describe generation, causality, or transition. It does not explain how structures emerge or how states evolve. Instead, it fixes the condition under which application occurs without completion and relation is retained without activation. Retention is defined as persistence without guarantee. Activation is defined as the condition under which relation becomes operative. The system isolates the case in which retention remains while activation fails. Failure is not treated as absence, error, or termination. It is defined as the condition in which application does not close. No state is completed, and no transition is secured. Within this configuration, structure is not produced. It is fixed as the persistence of non-completion. This paper establishes a non-modal, non-causal framework that repositions relation, operation, and persistence as conditions without resolution.