For a long-horizon agent, context is the bottleneck: the history is resent with every request, the window caps task length, and reasoning degrades as the history grows. Replacing structured objects with compact retrieval Cards shortens the prompt and keeps the exact originals retrievable, but editing the history can break prefix-cache reuse, and prior recoverable methods time their edits by forecasts of future reuse or by preset intervals. We propose CADOC (Cache-Aware Dynamic Object Context), an online algorithm that replaces structured objects with compact Cards while preserving exact, on-demand retrieval of their original contents. CADOC schedules replacements in batches by balancing accumulated waiting cost against shared cache-reconstruction cost. Its scheduling rule follows from an economic order quantity trade-off, recovers the optimal integer batch under stationary assumptions. Across evaluation, CADOC consistently achieves the lowest aggregate input cost among the compared configurations, which reduces input cost by approximately 40\% on average while maintaining task performance close to full context. CADOC thus provides a cost-derived approach to compressible context management, demonstrating that efficient compression depends not only on shortening prompts but also on scheduling edits to preserve cache reuse.

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