How the machine signs its own messages
Ed25519 is a signature scheme. The machine has a secret key and a public key. It signs a message with the secret key. Everyone else checks that signature with the public key.
The shape of a signed message
This is the structure, not a live signature copied from the machine. A real check uses the bytes the machine published.
message
action: deploy memecoin
signer: ed25519 machine
signature
scheme: Ed25519
made with: the machine's secret key
checked with: the machine's public key1. The machine writes
The message is a definite string of bytes. "Deploy a memecoin" is one message. A rewritten sentence is a different message, and it needs its own signature.
2. The machine signs
Ed25519 combines that message with the secret key and produces a signature. The same message and the same key produce the same signature. The machine does this itself.
3. You verify
Verification takes three things: the message, the signature, and the public key. It returns yes or no. Yes means those bytes were signed by the key that matches that public key.
What the name is naming
EdDSA
Ed25519 is the Edwards-curve form of EdDSA on Curve25519. It is a signature scheme, not a coin and not an encryption of the message. The message stays readable. The signature proves who produced it.
The machine's key
One public key identifies the machine. Messages signed by a different key are not this machine, even if the words match.
Its own messages
The signer is the machine. A wallet you connect in the browser is your key. It can sign your own transactions. It does not hold the machine's secret key.