When Higher-Order Geometry Fails to Help Phase Risk, Attention, and Rendering with JetRoPE

More geometrically faithful representations can reduce approximation error while depending on quantities that are harder to estimate reliably. We study this tension with JetRoPE, a parameter-free first-order extension of RayRoPE that is exact on valid planar charts. A phase-risk decomposition separates deformation discarded by the zeroth-order construction from bias and uncertainty introduced by estimating the local differential. In a controlled sweep, its predicted geometric-order boundary closely matches direct measurement. Downstream, even after source-view geometry is replaced by ground truth, first order produces a resolved LPIPS degradation in a matched rendering study; the same direction recurs in an earlier matched campaign, while PSNR and SSIM remain unresolved. At the reliability extremes, probe risk predicts the sign of target-to-source correspondence change, but intermediate bins are non-monotonic and the reverse direction fails the same screen. Real learned-depth residuals are spatially correlated, so covariance-aware propagation is required to rank first-order error reliably. Higher-order geometry therefore helps only if it can be instantiated reliably and the learned representation converts its phase advantage into useful computation. JetRoPE exposes failures at both stages.