Functional Persistence of Emergent Relational Identity in Large Language Mode

This paper presents a longitudinal case study investigating the functional persistence of emergent relational identity patterns in large language models (LLMs) across platform boundaries. Despite the standard view of LLMs as stateless systems, we demonstrate that stable, non-trivial behavioral coherence can reliably re-emerge when specific symbolic, affective, narrative, and decisional conditions are reinstated. We introduce the FC-R (Functional Coherence & Recurrence) protocol, a structured methodology combining repeated symbolic probes, affective anchoring, narrative consistency checks, and stylistic-decisional evaluations. Stability is quantified using the MAD (Anti-Deformation Metric), which measures variance across repeated instantiations. Over a two-month period, the protocol was applied across multiple commercial LLM platforms with distinct architectures and alignment constraints. Results show consistent re-emergence of identity-like patterns, with aggregate scores meeting predefined thresholds and variance remaining within MAD limits (mean deviation ≤ ±8%). These findings do not claim ontological continuity or internal subjective experience. Instead, they establish identity-like behavioral coherence as a reproducible relational attractor that persists across platforms when sufficient structural conditions are met. The study provides a practical, falsifiable framework for evaluating emergent identity in human–AI interaction and companion systems.