Code change:
It seems like there's a major thing missing here, namely how the sender of a Commit transmits the new node signatures to the other members of the group. We need something like that before this lands. The most obvious approach would be to add a field to DirectPathNode, as you have with RatchetNode.
It would also be handy to include in the intermediate node an indication of which leaf signed it. Otherwise you have to do "trial verifications" (cf. trial decryption), which is expensive.
Was this addressed? it's mentioned that the signature should be transmitted in "Synchronizing Views of the Tree" but there's no signature in the transmitted DirectPathNode
NAME changes the strategy for signing the tree, everything should be sorted out there.
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Related discussion:
text: ratchet tree and the members' ClientInitKeys. The hash of a tree is the hash of its root node, which we define <del> recursively, starting with the leaves.  The hash of a leaf node is the hash of a "LeafNodeHashInput" object: </del> <ins> recursively, starting with the leaves. While hashes at the nodes are used to check the integrity of the subtrees, signatures are required to provide authentication and group agreement.  Siganatures are especially important in the case of newcomers and MUST be verified when joining.  All nodes in the tree MUST be signed to provide authentication and group agreement. </ins> <del> The content within the leaf of a ratchet tree is composed of a "ClientInitKey" when the leaf is populated.  The "info" field is equal to the null optional value when the leaf is blank (i.e., no member occupies that leaf). </del> <ins> Elements of the ratchet tree are called "RatchetNode" objects and contain optionally a "ClientInitKey" when at the leaves or an optional "ParentNode" above. </ins> <del> The intermediate nodes contain less information, the hash of a parent node (including the root) is the hash of a "ParentNodeHashInput" struct: </del> <ins> When computing the hash of a parent node AB the "ParentNodeHash" structure is used: </ins> The "left_hash" and "right_hash" fields hold the hashes of the node's <del> left and right children, respectively.  The "public_key" field holds the hash of the public key stored at this node, represented as an "optional<HPKEPublicKey>" object, which is null if and only if the node is blank. </del> <ins> left (A) and right (B) children, respectively.  The signature within the "ParentNode" is computed over the its prefix within the serialized "ParentNodeHash" struct to cover all information about the sub-tree.  The "committer_index" is required for a member to determine the signing key needed to perform the signature verification. To compute the hash of a leaf node is the hash of a "LeafNodeHash" object: Note that unlike a ParentNode, a ClientInitKey already contains a signature. </ins> 7.4.