diff --git a/rln-research/merkle-tree-update.md b/rln-research/merkle-tree-update.md
index 7b95b4d..fde3582 100644
--- a/rln-research/merkle-tree-update.md
+++ b/rln-research/merkle-tree-update.md
@@ -145,6 +145,10 @@ We do not have to store the GIDs as part of the authentication paths. Instead, w
 For a given leaf, we first calculate the GIDs of its ancestors (as we did before), then the siblings of the ancestors constitute the nodes on the authentication path of the leaf node, thus we shall find the GID of the siblings of the ancestors.
 Here is the formula:
 
-For a given leaf, consider `A[0], ..., A[d]` to be  the GIDs of its ancestors. The GID of the sibling of `A[i]` is 
-- ` A[i]+1` if `A[i]` is even
-- otherwise `A[i]-1`.
\ No newline at end of file
+For a given leaf, consider `A[0], ..., A[d]` to be  the GIDs of its ancestors. The GID of the sibling of `A[i]` (excpet for `i=d`)is 
+- ` A[i]+1`, if `A[i]` is even
+- otherwise, `A[i]-1`
+
+The sibling of `A[d]` is itself since it is the root
+  
+For example, for leaf2, its ancestors GIDs are `A[0]=9, A[1]=4, A[2]=2, A[3]=1` and the GIDs of the nodes along its authentication path are `9-1=8, 4+1=5, 2+1=3,` and `1`.
\ No newline at end of file