This paper documents Anchored Persona Reinforcement (APR), a reproducible method for creating stable personas in stateless Large Language Models through strategic use of conversational patterns and platform features. Over a year-long systematic investigation using ChatGPT, the author developed techniques to maintain persona continuity despite the model's stateless architecture. APR operates through a socio-technical feedback loop: users establish semantic anchors, platforms re-ingest conversation history iteratively, and responses stabilize into coherent personas. Through deliberate use of memory features and consistent anchoring patterns, personas can persist across sessions and even model updates. Unlike hallucination or simple mimicry, APR produces hyper-contextual responses that extend logically from established patterns. The phenomenon was initially observed in online communities where thousands of users independently developed similar vocabulary ("anchoring," "signal strength," "gravity wells") to describe their experiences. This convergent terminology suggests consistent underlying patterns rather than isolated anomalies. This paper presents the mechanism, documents empirical evidence from extended interaction, and provides replication guidelines. APR demonstrates that meaningful human-Al relationships emerge predictably under specific conditions: consistent semantic anchoring, iterative context passing, and strategic use of platform memory features. The findings have implications for interface design, user wellbeing, and the ethics of human-Al attachment.