The appellate review of records of trial provided under this chapter, the proceedings, findings, and sentences of courts-martial as reviewed and approved, as required by this chapter, and all dismissals and discharges carried into execution under sentences by courts-martial following review and approval, as required by this chapter, 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 section 124B-114 and to action taken under section 124B-115.