Is Ed25519 is EUF-CMA secure?

Is the signature scheme of shelley (Ed25519) is EUF-CMA secure? The Existential Unforgeability under Chosen Message Attack experiment works like this:

1. The challenger generates a valid keypair (pk, sk) and gives pk to the attacker.

2. The attacker may now repeatedly ask for signatures on chosen messages $(M_1, \dots, M_q)$ of its choosing, and receives the valid signatures $(\sigma_1, \dots, \sigma_q)$ in response.

3. At the conclusion of the experiment, the attacker must output a message and signature $M^$, $\sigma^$ such that (1) the message $M^*$ was not one of the messages requested in the previous step, and (2) the message/signature verifies correctly under the public key (Ref).

Now I guess the used signature scheme by Shelley is EUF-CMA secure since by assuming the contrary it would break the blockchain?

EDIT

The only problem I see with assuming the contraposition of the statement is that the messages $(M_1,\dots, M_q)$ are chosen by the adversary. This is not the case in a public ledger though it could be extracted?