Author here. There are certain implementations out there which support non-membership proofs but most of them use empty hashes to find the non-membership proof

Author here. There are certain implementations out there which support non-membership proofs but most of them use empty hashes to find the non-membership proofs and the underlying SMT is unordered. The approach taken in the above paper is novel in the sense that the way in which values in SMT are inserted make it ordered and this property is exploited to find the non-membership proofs through a window based method. To prove a certain value Y doesn't exist in the tree, the closest two values X and Z which bound Y form the non-membership proof. This method avoids using empty hashes and the repetitive computation which comes with it. And Merkle Patricia Trie currently does not support Non-membership proofs.