Long-term memory for an LLM agent requires more than retrieving a relevant passage. Many existing systems address belief revision, causal connections and cross-domain abstraction primarily through storage and retrieval mechanisms, limiting their ability to support implicit personalisation as a user’s preferences evolve. We present DPCM, which organises memory into a capability hierarchy spanning raw inputs, atomic facts, belief trajectories, identity, domain schemas, prospective intentions and cross-domain patterns. A synchronous daytime writer (SYSTEM 1) records revisions as doubly linked supersedes chains; an asynchronous nighttime engine (SYSTEM 2) induces schemas and intentions, then uses cross-domain collisions to derive core schemas. Dual-process theory motivates this separation between online encoding and offline abstraction without implying that agent memory reproduces human cognition. Across single-run evaluations on LongMemEval, PersonaMem and PersonaMem-v2, SYSTEM 2 yields its largest observed gain on implicit cross-session inference (+5.20 on PersonaMem-v2) and its smallest on the recall-oriented LongMemEval aggregate (+0.33). When the inference budget is limited to 8k tokens and the full history no longer fits, DPCMfull exceeds the long-context baseline by 10.5–17.9 points across both backbones.