Long-term conversational memory faces a timing mismatch: write-time summaries and graphs organize history before a future query is known, while independent retrieval can allocate a limited evidence budget to redundant or fragmented turns. We introduce Chain on Demand (CoD), a query-time evidence organization framework over an unchanged turn-level memory. Given a broad candidate pool, CoD constructs a temporary evidence chain by allocating a fixed anchor budget according to query relevance, lexical diversity relative to selected anchors, and newly covered query terms, followed by deterministic restoration of each selected anchor's same-session neighborhood. The resulting chain is used only for the current query, while the underlying conversational memory remains unchanged. In a paired comparison over all 1,986 LoCoMo questions, CoD achieves 82.2% accuracy on 1,540 non-adversarial questions and 76.3% on all 1,986 questions. On LongMemEval-S, one fixed configuration that indexes both user and assistant turns obtains 86.6% across all 500 questions. These results show that long-term memory can preserve the original conversation while deferring evidence organization until the information need is known.

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