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In autoregressive rollouts, the first assumption requires depth's per-step precision to survive composition. We test this with a pre-registered instrument, the shallow penalty $\\rho=\\mathrm{err}(\\text{shallowest-exit rollout})/\\mathrm{err}(\\text{full-depth rollout})$, across nine DeepMind Control tasks under matched single-step ($K=1$) and multi-step ($K=4$) training, three seeds each. We find three regimes: on 6/9 tasks depth helps rollouts (intrinsic, $\\rho$ up to $4.7\\times$), on 2/9 the shallow exits beat the full stack (inversion, $\\rho$ down to $0.85\\times$), and one is flat. The robust inversion (cheetah) is not a property of the dynamics but is created by training: an ablation supervising early exits only at the first rollout step erases it ($\\rho: 0","title":"When Does Depth Survive Composition? 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