A stateless inference server (vLLM, SGLang, TensorRT-LLM) idles between requests while the accelerator waits; a stateful session reclaims that idle time. Speculative pre-positioning decodes the session forward to its next decision point with the target model's own forward pass and no draft model, moving the cross-request prefill and entry-decode off the critical path: the next request resumes from a pre-paid entry on its delta, or, when a confidence gate fires, is answered from a cached distribution in one near-constant vocabulary scan with no decode, at a cost only of energy and a rare, bounded false accept. The payoff is conditional on capability: a capable model fires the gate at near-full coverage and about 87% precision (a smaller one never clears it), returning the first token in about 1.0 ms versus the 39 ms decode a prefix cache still pays.