The gadget deals with an columns made of $(2^{i}G)$ vector and enforcing $G{i+1}=2G{i}$ later it could be used by cond_add to enforce the equality of public key to $sk G$.
see https://hackmd.io/@CmbtIje1Sxq-KCOjcxDmbQ/rkquceVCR/edit for more details.
The gadget deals with an columns made of $(2^{i}G)$ vector and enforcing $G{i+1}=2G{i}$ later it could be used by cond_add to enforce the equality of public key to $sk G$. see https://hackmd.io/@CmbtIje1Sxq-KCOjcxDmbQ/rkquceVCR/edit for more details.