The Army considered ANY M1903 rifle mounted in ANY Type C or scant stock as an M1903A1.
Collectors, however, should consider only the following as legitimate M1903A1 rifles:
(1) Any rifle sold by the DCM and listed as an M1903A1 (or fitted with a Type C stock).
(2) Any 1929-40 National Match rifle.
(3) Any M1903 rifle having a serial number between S/N 1490000 and S/N 1536285 and fitted with a Type C stock manufactured at Springfield Armory.
Hope this helps.
J.B.