Context Is Inventory: A Rent-or-Buy Model for Prompt-Cached LLM Sessions

This paper shows that the LLM session restart decision under prompt-caching APIs is structurally identical to the Economic Order Quantity (EOQ) and ski-rental models, yielding a 41.4% upper bound on timing-addressable cost and a closed-form regret function. Includes the paper PDF, reconstruction scripts, and billing data for reproducibility. This is a preprint. A version will be submitted to arXiv.