Look up Kolgomorov time bounded complexity. The absolute minimum memory requirement is defined by the compression limit which is bounded by the total entropy in the algorithm. Entropy is defined by the input values (the password, random salt).

But computationally limited attackers often can't wait long enough to solve the compressed variant because CPU time explodes, so they can not reach high degrees of compression. Using a certain amount of minimum RAM is effectively optimal for resource usage if you can't break the underlying cryptographic function in password hashing algorithms.

We don't have an absolute proof what the minimum is, but Argon2id is very solid and there's little reason to believe there's some major hidden shortcut.