I have always believed that the term certificate in these documents meant the pension was approved.
As to her file, I believe you can order these records through a service provided by these message boards. For this, contact:
Ephraim A. Ledford, Private, 5th Regiment Tennessee Mounted Infantry, enlisted December 4, 1864 at Cleveland, Tenn. for one year, recorded absent at the March/April 1865 muster as on detached duty, mustered out at Nashville, Tenn. July 17, 1865, description on enlistment, 45 year old Farmer, born in Haywood County, N. C., blue eyes, dark hair, dark complexion, 5’ 8”, signs his enlistment certificate with an ‘X’ “his mark”
Compiled Service Records of Volunteer Union Soldiers Who Served in Organizations from the State of Tennessee