A three-signal stopping rule for iterative LLM refinement derived from the Möbius theory stack: an equilibrium-distance surrogate d̂_R (RZGM meaning-equilibrium layer), an update-free-recurrence and diversity-collapse detector pair (Reflective Homeostasis Layer), and a hard reflection-depth cap (MUSE bounded reflection). Pre-registered study: 500 English prose-refinement tasks across ten domains, two generator models (Gemma4 12B-IT-QAT and 26B-A4B-IT-QAT), 8,000 generations, 999 blind position-swapped pairwise judgments. The governor cuts refinement tokens by 36.6% / 33.1% (bootstrap 95% CIs 33.6-39.5% / 30.3-35.9%) versus an always-eight-iterations baseline — 2.2-3.4x a naive convergence stop — at a measured quality cost reported at equal prominence: 38.0% / 36.6% of judged comparisons lost overall, a majority among actual interventions (61.1% / 59.0%), with measured cost almost perfectly collinear with output length. A full-data ablation shows the saturation signal is simultaneously the savings engine and the dominant cost source, yielding a measured two-point dial (10.0-11.5% savings at 8.2-11.8% loss rate with saturation disabled). Pre-release adversarial verification (four independent refuter passes) confirmed all headline statistics against the raw data and caught an inverted flagship anecdote: the corpus's two catastrophic degenerations (~50 verbatim paragraph repetitions) were selected once and avoided once by the governor, undetected in both cases — set-based trigram signals are structurally blind to within-output verbatim repetition. All tasks, rollouts, verdicts, audit votes, and analysis code are released in the companion repository.AI co-observer: Claude Fable 5 (Anthropic) — working method only; blind pairwise judging by Claude subagents under a position-swapped two-vote protocol; four independent adversarial refuter passes preceded release; the registered author is the human author alone.