Wavelet covariances under fixed finite observations: dilation symmetry breaking and distinct endpoint limits

arXiv:2610.28665v1 Announce Type: new Abstract: For a centered homogeneous generalized Gaussian field with spectral weight $C|\omega|^{-\gamma}$, we prove two-endpoint recovery of normalized posterior wavelet covariances under fixed finite admissible observations. Global dilation symmetry holds if and only if all observation functions vanish. The nonzero wavelet and the observation functions are real Schwartz functions with $M\geq1$ vanishing moments, with $C>0$ and $\gamma0$, $1/2