Weak uniqueness and autonomous approximation for the SLE-reversible Weil-Petersson response diffusion

We study the self-consistent common-noise equation associated with the Weil--Petersson response differential of the rotationally marked SLE welding probability. For 0<κ≤4, we prove joint weak uniqueness among continuous adapted weak solutions whose law at each deterministic time is the welding probability, and obtain the Markov property in the original filtration. A conditional Gaussian lift and capacity localization give the required L¹ generator-range density. Identification with the canonical law gives stationarity and reversibility. We also construct autonomous Fejér and Poisson regularizations with pathwise-unique global strong solutions. Their joint state-noise laws converge to the canonical law for every initial probability absolutely continuous with respect to the welding probability.