OK, I understand. This means that both on-chain and lightning transactions can be proved if the invoice is signed by the merchant. The approach with DNS that I proposed might not work very well because the merchant may change the DNS records (the public key) afterwards and then I cannot prove anymore that he signed the invoice. Another approach would be to sign with the private key of the SSL certificate the merchant uses on his website. Even if the merchant changes the SSL certificate, I can still prove that he signed the invoice because the certificate is signed by a certification authority. I only need to save his certificate and then present it together with the signed invoice (and the pre-image if it is a lightning transaction) to prove the payment. Would this approach work? I think this is an important step because today the bitcoin payments are not provable and it is only a question of when a merchant will start to scam people by using bitcoin. With credit cards, Paypal, bank transfers, etc. you can actually prove that you payed (bank statement) but with bitcoin this is currently not possible. What do you think?