The Beltrami-welding conjecture for an independent construction of the SLE loop

Consider the Jordan curve obtained from the Beltrami welding of the independent quantum disks, with the associated welding homeomorphisms and maps as constructed in the paper. The resulting curve is to be interpreted as a random SLE loop.

Beltrami-welding conjecture. The above Beltrami welding yields an SLE loop measure and thus an independent second construction of the SLE loop in Theorem 1.3 of Ang (2021).

This would provide an independent proof of the SLE loop construction from the Gaussian multiplicative chaos and Beltrami-welding framework, complementing the quantum-zipper approach. The statement is presented as a research problem, and no resolution is supplied here.