Curvature Is a Budget: Coordinates Before Resolution in Second-Order Quantization

A weight rotation preserves the full-precision model but changes the Hessian that measures quantization error. Multiple public repositories contain code paths that pair transformed weights with untransformed curvature: we reproduce this error in ModelTC/LightCompress and identify the corresponding metric-collection pattern in spcl/QuaRot's export source. Users can unknowingly trigger this silent failure by omitting one setting in LightCompress: the run completes without a frame warning while Llama-3.1-8B perplexity rises from 6.525 to 7.456, worse than rotated rounding at 7.283. In a controlled four-bit panel, stale dense curvature makes GPTQ worse than round-to-nearest on five of seven checkpoints, while aligned block-32 curvature beats stale dense curvature on all seven. At three bits, the median stale-to-aligned dense-metric perplexity ratio reaches 25.31. We derive the exact output error of a complete GPTQ sweep under a mismatched metric and characterize when block projection commutes with coordinate transport, enabling exact transport within compatible block representations using O(db) stored coefficients. Curvature must be aligned before it is budgeted.