PGCR: Directional Continuation Substitution for Recurrent LLM Serving

Reusing eight transformer layers across different requests requires a valid autoregressive handoff, not merely a nearby hidden state. The handoff must jointly replace the post-block residual and every key/value write produced inside the bypassed block, and its validity depends on the ordered source–target pair. Provenance-Gated Continuation Routing (PGCR) learns this directional relation: it searches only completed requests at the same observable workflow position, retrieves with a contrastive subroutine key, reconstructs a full residual/KV continuation from a 512-dimensional prototype, and authorizes substitution with a target-conditioned utility governor. On CodeContests-Edit, SWE-bench-Lite, and ToolBench-Recurring with Llama-3.1-8B-Instruct, PGCR delivers a $1.23\times$ median end-to-end speedup while keeping signed quality changes within $-0.7$ points. Against a common-interface LLMCache-style similarity route, it lowers the accepted-request 1-to-0 regression incidence from 18.7% to 10.7% on CodeContests-Edit while increasing speed from $1.19\times$ to $1.23\times$; the all-request regression incidence falls from 6.4% to 2.8%. The lower accepted-request incidence appears in every template- and family-separated comparison, including 11.8% versus 19.6% on unseen Code templates. ToolBench-Recurring reaches $1.27\times$ versus $1.17\times$ for exact speculative decoding, and its high-recurrence stratum reaches 1.31$\times$. Replication on Qwen2-7B and H100 preserves the method ordering, establishing complete continuation substitution as a practical compute-sharing primitive for provenance-rich recurrent services.