Does the Blake3 hash have identities, due to its merkle tree structure? I've read that the Blake3 hash uses a Merkle Tree.
Does it follow that there are identities such as:
b3sum(&quot;This is &quot;) xor b3sum(&quot;a test.&quot;) == b3sum(&quot;This is a test.&quot;)

The example above does not work, perhaps because the block size is not eight bytes.
Are there any real Blake3 identities of a similar form?
No, any simple identity like that would violate the cryptographic properties that BLAKE3 aims to have. Finding these cases is supposed to require a brute force search.
BLAKE3 is a Merkle tree, but it isn't constructed by XORing things together. Instead, parent nodes in the tree are constructed by concatenating the hashes (&quot;chaining values&quot;) of each child, and then calling the compression function again with that concatenation as the input. Other important details are that the compression function domain-separates chunk/leaf outputs from parent node outputs, and that it domain-separates the root node from non-root nodes. (As an aside, it also domain-separates each chunk/leaf based on its index. That's not necessary for the security property we're talking about here, but it accomplishes other things. See section 7.5 of the BLAKE3 paper.) Putting all that together, it should be difficult to find any relationship between the BLAKE3 hashes of any two distinct inputs.