But GMelius is a client-side application, right? According to your whitepaper, the insertion is done when the _client_ receives the response, I don't see anything about validation from the GMelius servers to GMail.
"SHA-512"
It's not the SHA part which is the problem, it's the RSA part. 512-bit RSA is well-known to be broken and there have already been multiple exploits. 2048 bits is the bare minimum anyone should use nowadays.