Beyond Frame-Correctness: Non-Identification and Actionability of Equivariant Attribution

Attributions for structured inputs can depend on arbitrary choices of coordinate frame, gauge, or discretization, and a growing literature addresses this by enforcing *frame-correctness* — requiring explanations to transform consistently with the symmetries of the model. We ask what this property establishes beyond soundness. First, equivariance and completeness do not identify a unique attribution rule: for path attributions on a Lie group, we show that left-covariant path families yield frame-correct attributions, construct a second complete left-covariant family on $SE(3)$, and give an explicit analytic witness showing that two admissible rules can assign different credit. On a docking scorer, two frame-exact rules select different degrees of freedom on $60.4\%$ of inputs. Second, we test whether correcting frame dependence or adding finer attribution improves model-external outcomes. In matched intervention studies, repairing IG removes frame-dependent decision flips but does not measurably improve pose quality; adding four exact-Shapley-derived features to a matched reward-model policy changes Success@1 by $-0.33$ pp ($95\%$ CI $[-1.55,+0.88]$). Together, these results separate frame-correctness from rule identification and downstream decision utility.