[doc/spec] add sparse merkle tree

doc/src/spec/crypto/merkletree.md

@@ -12,5 +12,12 @@ hash of leaf up to certain depth root(tree, depth), hash the leafs including the
 
 ## witness
 
+authentication path to given `depth`, and bridge frontier, or position.
 
 ## sparse merkle tree
+
+is a merkle-tree with leafs stored in a search tree, has advantage over merkle-tree that is a allow non-inclusion proof, through membership proof to index of data in the search tree.
+
+### membership proof
+
+given `index` the proof is a `path` from the leaf at `index` to the root.