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 ("chaining values") 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/leave 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.

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 ("chaining values") 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.