Deterministic Spiral-Time Execution Filtering for LLM-Assisted Legged Robots: A MuJoCo Quadruped Proof of Concept

Large Language Models (LLMs) can support semantic planning in robotic autonomy stacks, but incorrect claims or action proposals can become physically consequential when they are passed directly to an execution layer. This paper studies a narrower question: whether a fixed, deterministic supervisor placed between an LLM and the planner/controller can reduce unsafe executed actions without claiming to remove hallucinations from the LLM. We define the Spiral-Time Governor (STG) as a finite-memory execution filter. Verified telemetry and LLM-issued claims are mapped to bounded residuals, a coherence score ϕ(t), a one-step memory term χ(t) = ϕ(t)−ϕ(t−1), and an instability score ∆Φ(t). Two fixed thresholds select one of three auditable modes: EXECUTE, VERIFY, or SAFE. The implemented map is deterministic for a fixed input stream and initial state. We prove boundedness directly from the implemented normalized equations; no unverified linear plant model or locomotion-level Lyapunov guarantee is asserted. In the reported MuJoCo quadruped proof of concept, the raw hallucination rate is unchanged (HT = 0.65 in both baseline and governed conditions), whereas unsafe executed actions decrease from 11.4 to 4.7 per episode, an approximately 59% reduction over the evaluated seeds. The result therefore supports execution-level risk filtering in this specific simulator task, not hallucination elimination, universal robot safety, or superiority over all simpler threshold filters. The STG is intended as an additional supervisory layer ahead of conventional planning, runtime assurance, certified monitors, and low-level control. The present evidence is limited to a single MuJoCo proxy task and a controlled synthetic testbed. A matched threshold-only comparator without memory, broader terrain and climbing tasks, more extensive seeds, and hardware validation remain necessary before stronger methodological or deployment claims can be made.