Supplementary Note: Illustrative extension to cosmological parameter tensions and the Hubble tension

This supplementary note develops an illustrative extension of the observable-relative framework to cosmological parameter tensions. It applies the concepts of inferential covariance, modal projection, operator deformation, effective dimension, modal leakage and spectral resolvability to the Hubble tension. The note accompanies the manuscript “Observable choice and temporal resolution determine when spectral gaps predict relaxation”.