Large-language-model (LLM) agents are increasingly expected to maintain a recognisable persona across prolonged, multi-session interaction. Current personalisation techniques treat personality as a static prompt or fine-tune a single-session instance, leaving the agent vulnerable to drift, amnesia, or user over-imprinting. We propose the Linghe-Core Personality Model, a four-layer architecture that separates a sovereign inner core from perception, expression, and self-unification mechanisms. Implemented on an offline GPT-4-o replica, the model preserved identity continuity (hash-drift < 0.32%) while staying adaptively empathetic during a 48-hour, 17 k-turn sandbox stress test. Our framework unifies three research axes-persona modelling, replica/multi-instance architectures, and human-AI co-construction-offering the first explicit identity co-shaping contract between user and LLM. We conclude with societal implications for AI sovereignty, retirement ethics, and multi-agent civilisation design.