There are two random choices. One of the value, the other by the verifier. There are infinitely many columns and rows to check, which would require an infinite

There are two random choices. One of the value, the other by the verifier. There are infinitely many columns and rows to check, which would require an infinite amount of shared RNG. (or is otherwise finite, a PRNG) Yet this can be done in MIP* because state in A and B is correlated for any state. The problem can be rephrased as "does there exist an ideal PRNG that is not discernible from a true quantum RNG". Discerning between real RNG and PRNG is akin to solving the halting problem and one of the lynchpins if the proof.