I am no crypto expert in any way so please bear with me if my question is kind of stupid.
We use OpenSSH key pairs on a regular basis and due to the asymmetric nature of key pairs, as far as I understood the concept, giving out your public key to the ... well ... "public" - is considered a safe thing to do since it can only be used to verify that you are really you. Creating content or authenticating yourself works against the private key which never leaves your machine, hence the strong security.
Now, given the above mentioned situation as a comparison, can it be considered secure if I created a password hash with the unix tool mkpasswd and a salted SHA512 hash and gave THAT out to the public?
My guess would be that it is not a smart idea to do, same as you would do with hashed passwords in a user database of a website. However, since this is only a guess I'd like some expert opinions.