The Reflective Bound Is Real and Shallow: Reflection Depth, Model Capacity, and the Rumination Regime — First Measurement of Bounded Reflection Across 0.8B–120B Language Models

Theoretical work in this project (the MUSE / Reflective Light Cone line) claims that reflection is bounded — its value saturates with depth — and the underlying RGS theory makes a sharper, falsifiable prediction: reflection is not intrinsically stabilizing, and for insufficient capacity, iterated self-checking becomes rumination — descent into the model's own attractor — and degrades output. Neither claim had been measured. We measure both. Thirteen model rungs (0.8B–120B, seven families, two serving stacks) each answered 15 category-stratified prompts directly (depth 0) and under 1–3 rounds of iterated self-revision driven by a fixed 3-check metacognitive prompt; a single frozen judge scored each depth against depth 0. Results: (1) Rumination is real. At 0.8B every reflection depth degrades judged quality by ≈8 points; at 2B the effect is zero; from 4B upward it is positive — and this reflection crossover coincides with the ~4B governance-dose crossover found independently in the companion dose-response study. (2) The bound is real and shallow. Above the crossover, gains (+1 to +10) saturate at depth 1–2 on 9 of 13 rungs; nowhere does quality rise monotonically with depth, and depth-3 leads only within noise margins (under one point). (3) Reasoning-trained models relocate the bound. An 8B R1 distill is flat under explicit reflection (native chain-of-thought already occupies the niche), while a 32B reasoning model shows the study's largest gains (peak +10.0 at depth 2) — explicit and native reflection compose rather than interfere at sufficient scale. Reflection depth is thus a capacity-gated resource with a shallow optimum: spend one round, rarely two, never three, and none at all below the crossover. AI co-observer: Claude Fable 5 (Anthropic) — working method only; the registered author is the human author alone.