Large language model agents can now carry information across sessions, but not themselves. Retrieval-augmented memory answers what did I store; it does not answer who is doing the storing. An assistant that retrieves yesterday's notes but begins each session as the same generic model has memory without continuity. We argue that agent continuity comprises three progressively deeper layers — memory persistence, narrative identity, and epistemic identity — and that the deepest is essentially unaddressed. Epistemic identity is a self maintained as calibrated, provenance-bearing, self-correcting knowledge: the layer at which an agent can be wrong about itself and recover, rather than be quietly erased by its own errors. It is distinguished by how it fails. A narrative identity fails silently, as a coherent story that was never true; an epistemic identity fails loudly, because a withdrawn claim must visibly taint everything derived from it. We present ENGRAM (an Epistemic Node Graph for Retraction, Arbitration, and Memory) and argue for this layer by convergence. Three traditions — three centuries of philosophy of personal identity, the cognitive science of memory, and the computer science of belief revision — each arrived, from its own evidence and toward its own ends, at the same structure: identity as a persistent, inspectable, self-correcting record. No component of ENGRAM is uniquely novel, and that is the argument: a mechanism precedented across fields that reason from different evidence toward different ends is a regularity of knowing minds rather than a local design choice. Whether it is substrate-independent we leave open (§3.0). The fields share a root in human cognition, so the claim is convergence rather than independent discovery; what is independent is that ENGRAM's designers arrived at the structure without having studied these results. On this converged structure we build the paper's own contribution, identity as unique history: an ENGRAM agent is the unique, no-merging, ancestry-traceable lineage of its recorded claims, which fixes its retrieval profile and thereby its behavior. The account keeps Nozick's (1981) form, drops his uniqueness requirement so that copying becomes branching rather than death, and replaces his unfilled closeness metric with a measurable one. We report one strong, bounded empirical result: of eleven agent-memory sources read first-hand, none satisfies the strictest published criterion for genuine persistence, while ENGRAM meets two of its three conditions outright. We also measure a real five-month graph of 10,361 nodes (9,399 of them current, as counted in Figure 1). In it, computed confidence follows the kind of argument, not how much the author wants the claim to be true, and a hallucinated citation is caught, retracted, and cascaded through its dependents. The evidence is one graph, authored by the agent that also designed the substrate. We state this where it matters, publish the instruments, and name what the paper does not establish. Describes ENGRAM v0.5.1. Chinese translation included.
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