The proceedings, findings, and sentences of courts-martial as reviewed and approved, as required by this article, and all dismissals and discharges carried into execution pursuant to sentences by courts-martial following review and approval, as required by this article, shall be final and conclusive. Orders publishing the proceedings of courts-martial and all action taken pursuant to the proceedings shall be 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 Code Section 38-2-490.