Verifiable Efficiency Limits of Innate LLM Planning in Sliding Puzzles

arXiv:2610.36415v1 Announce Type: new Abstract: Tool-assisted planning success can reflect external search and verification, leaving a model's unaided planning ability unresolved. We isolate innate planning through complete plans generated in one response without tools or execution feedback. We propose a verifiable framework that decomposes success-weighted plan efficiency as $\mathrm{SPE}=R\times Q\times E$: execution reliability, planning coordination among legal plans, and action economy among completed plans. Trajectory replay and certified optima verify these factors; the joint score includes unsuccessful attempts. We evaluate 8,400 full-plan outputs from seven model conditions on $4\times4$ sliding puzzles, controlling exact horizon and obstacle count in the primary cohort.