The proceedings, findings, and sentences of courts-martial as reviewed and approved as required by this code and all dismissals and discharges carried into execution under sentences by courts-martial following review and approval as required by this code are final. Orders publishing the proceedings of courts-martial and all action taken pursuant to those proceedings are binding upon all departments, courts, agencies, and officers of the state, subject only to action upon a petition for a new trial as provided by section 28-3.1-416 or action taken on appeal as provided by section 28-3.1-420.