I recently built https://debug-me.branchable.com/ which also does quick and easy terminal sharing, but with the addition of a cryptographically secure proof of what was done in the session, rooted at the gpg key of the person who connected to it.
Just say that it's a signed log of the session. "Cryptographic proof" isn't necessarily incorrect but it has other connotations which don't make any sense here and make it sound like it's doing something it's not (think cryptanalysis or ZKPs).