Do we have the crypto to build an asymmetric variant? The way that I’d immediately think to do it is have the authenticator create a signature over the current

Do we have the crypto to build an asymmetric variant? The way that I’d immediately think to do it is have the authenticator create a signature over the current time (chunked into 30-second windows) and the service verify that signature, but obviously those signature texts are way too long to manually enter as a one-time code. (Symmetric) TOTP solves this length problem by just truncating the output of a hash function, which both the authenticator and the service can produce because they have a shared secret. But in the signature case the service would need the entire signature to validate it; any truncation would make it useless. It’s been a while since I did any crypto. But it feels like the shortness of the one-time-code probably makes it impossible to do asymmetrically. If this is indeed the case there is probably an elegant proof or some better way of thinking about why it’s impossible. I would be interested in reading that.