Stable Loci Addressing: A Shared-State Architecture for Referential Stability in Evolving Long-Term LLM Memory

Long-term memory for large language models (LLMs) is usually treated as a retrieval problem: given a query, find the relevant stored information. But a memory that changes over time faces another problem. Once a computation refers to a record, later updates should not make that reference silently point elsewhere. We call this requirement referential stability and show that exact revisitation requires retained information about the earlier choice. We introduce Stable Loci Addressing (SLA), which unifies persistent indirection, rebinding, and structured locus operations within one shared-state memory interface without a separate per-record reverse-locator layer. Shared writes can therefore affect other references. We derive exact RLS and Delta one-write laws, an exact cumulative native-Delta law, and a necessary-and-sufficient Top-1 certificate. Experiments span semantic conflict, learned cue embeddings, long mutation sequences, LongMemEval content and structural evolution, cross-bank maintenance, and zero-trainable-parameter integration with a frozen DeltaNet. Raw semantic keys can initialize correctly yet fail after relocation. Verified dereference prevents wrong-record returns, and the certificate tracks failure. On 70 LongMemEval-S knowledge-update questions, stale predecessor evidence lowers answer accuracy by 68.6 percentage points, while SLA exactly matches updated-pointer semantics. Together, these results show static retrieval accuracy is insufficient for evolving shared memory and establish referential stability as a distinct, testable correctness criterion.