Determine whether gauge-contamination magnitude predicts ranking improvement

Determine whether the magnitude of gauge contamination, quantified by the recovered coefficient $(\sigma_s^2+2\sigma_r^2)$ and the mean squared point distance relative to aligned variance, predicts the improvement in ranking metrics produced by removing that contamination.

Background

The paper verifies that unaligned perturbation variance contains a distance-dependent gauge-contamination term and estimates its coefficient across 18 backbone–dataset conditions. It then tests whether stronger measured contamination is associated with a larger reduction in AUSE after alignment.

The observed correlations are weak and statistically uninformative: the reported bootstrap interval is broad and the permutation test is nonsignificant. The authors explicitly state that the analysis does not establish whether contamination magnitude predicts ranking improvement, leaving this relationship unresolved.

References

An additional test does not establish whether the magnitude of the recovered contamination predicts how much alignment helps.

— Revar3r: gauge-aware perturbation uncertainty for feed-forward 3d reconstruction  (2610.07883 - Mahdi et al., 6 Oct 2026) in Appendix, Section “Gauge Mechanism and Verification,” subsection “Recovering the gauge coefficient across all eighteen conditions”