$a$ = private view key
$B$ = public spend key

$v$ = view spent private key
$V$ = view spent public key

$sign(message, privateKey)$ = standard signing ED25519 function
$verify(message, publicKey, signature)$ = standard verification ED25519 function

$I$ = key image

$v = H_s(aB)$
$V = vG$

$signature = sign(I, v)$

Inject signature into transaction data

On incoming if true, then we spent funds

$ours = verify(I, V, signature)$