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 and conclusive. Orders publishing the proceedings of courts-martial and all actions 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 in § 30-13-72 of this code.