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Retrieving broadly improves evidence coverage yet overwhelms downstream reasoning with noise; compressing at write time reduces noise but irreversibly discards details the future query may need. We introduce LazyMem, which sidesteps this dilemma by deferring all memory construction to query time. A lightweight 4B model processes the retrieved candidate pool in overlapping parallel windows, selectively retaining and compressing only query-relevant content. The model is trained through supervised fine-tuning followed by group-based reinforcement learning with a format-gated composite reward that combines a rule-based action signal measuring selection accuracy with an LLM-judged quality signal measuring source faithfulness and query utility. 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The model is trained through supervised fine-tuning followed by group-based reinforcement learning with a format-gated composite reward that combines a rule-based action signal measuring selection accuracy with an LLM-judged quality signal measuring source faithfulness and query utility. 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