How Far Can Reliability Drift Without Changing the Confidence Distribution?

A classifier's confidence distribution can stay fixed while its conditional accuracy changes. We ask how far the reliability relation can move under covariate shifts that preserve the distribution of the confidence score, with a ${\chi }^2$ budget on the reweighting inside each confidence level; the worst-case movement as a function of the budget is a fragility profile. On an interval of budgets computable from the source, the profile is exactly the square root of the budget times the within-level variance of the correctness propensity, the grouping-loss term of calibration–refinement decompositions. Beyond that interval the profile depends on the tails of the propensity law, and the whole upward profile identifies the centred within-level law; calibration residual and grouping variance therefore do not determine fragility in general, although they do when labels and predictions are deterministic. Because the propensity is unobserved, we restrict reweightings to a learned finite readout within confidence bins, bound what the restriction misses by the grouping variance left inside readout cells, estimate the restricted profile with role-separated labels, and give a separate split-sample lower confidence bound. On ImageNet the bound is positive in both splits for four of six primary classifiers and nine of twelve additional ones as released, and for three of eighteen after temperature scaling. Held-out drift under optimised reweightings, fitted without evaluation labels, tracks the estimated profile; an exploratory label-permutation diagnostic gives near-zero agreement for this statistic but largely reproduces the correlation seen for unsigned random reweightings. On natural shifts, the change in within-bin composition, which the source profile bounds, is smaller than the within-cell change, which it does not control.