Stopping as a Database Property: Reason-Bearing Termination for Long-Running LLM Agents

Loop termination should be a property of the data layer: when the substrate owns resource and intent state, stopping becomes a reason-bearing, auditable predicate rather than an arbitrary step cap or an unreliable model decision. We document this in a self-built agent research testbed. The substrate's signal ledger holds 48,061 self-monitoring events over 45 days; loop-related entries reference round counts up to 212 (208 distinct values). A mutual-critique relay loop emerged on its own and converged naturally at 29 rounds, seven weeks before any predicate formalized that behavior. A self-narration layer grew to 12,102 entries. On the official ARC-AGI-3 benchmark: 28.57 (3/6 levels, 31 steps) and 0.15 on Kaggle, operating under a self-imposed 82-step budget. We crystallize the mechanisms into four data-computable termination predicates, and document a recurring dissociation: convergence control and converged-to content are separable—a relay loop faithfully amplifies upstream wiring faults. Contributions: placement taxonomy, predicate family, two audit protocols (Drift Probe, Loop Budget Test), and a failure record. No cross-system superiority is claimed. Includes both English and Chinese versions.