Non-Commuting Covariance Geometry in Filter-Integrated Dynamical-Decoupling Spectroscopy

This paper studies the covariance geometry of filter-integrated observables in dynamical-decoupling spectroscopy. We show that the covariance admits a non-commuting additive decomposition,Ctotal=λCflat+CdevC^{\rm total}=\lambda C^{\rm flat}+C^{\rm dev}Ctotal=λCflat+Cdev,where CflatC^{\rm flat}Cflat represents flat filter-overlap geometry and CdevC^{\rm dev}Cdev encodes spectral deformation induced by power-law noise weights. Numerical analysis of CPMG filters reveals persistent but diluted non-c