Is it valid to add the contents of the contract under the signature?
It depends. If both parties have no objection to the added supplementary content or have re-signed it, it will be valid. However, if the added content is not agreed by the other party, then the signature is invalid and the corresponding contract is invalid. Article 465 of the Civil Code: Contracts established according to law shall be protected by law. A legally established contract is legally binding only on the parties, except as otherwise provided by law.