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Persistent long-lived sandbox reservations incur excessive memory overhead at scale, while lazy on-demand instantiation generates severe cold-start penalties that degrade response performance under multi-tenant, multi-turn agent workloads. To resolve this dilemma, we present SpecBox, a runtime built around speculative sandbox preallocation tailored for dynamic LLM agent execution pipelines.\n  At its core, SpecBox implements keyword matching and streaming semantic embedding to enable intent-driven sandbox prewarming, which identifies pending tool execution demands mid-LLM token generation and fully overlaps sandbox bootstrapping with model inference. 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