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If it’s an original 8-spline, 32-3/8" long, I believe it fits all 1929s and 1930s, plus LATE 1928 81s, per Hollander’s 8th Edition (1938). There are no published serial number points for the Series 81 application. This is Hollander #121 and also fits 1929-31 Studebaker President 8s, serial numbers 6013301-6022000 on the 125" wheelbase, and serial numbers 7013501-7038000 on the 135" wheelbase, and 1929-31 Studebaker truck models GK, GN, 30 and 40.
Suggest you first confirm that you don’t have a newer rear end installed.
1931 Pierces (all series) used a 10-spline axle 31-7/8" long (Hollander #120), which fit nothing else.
1932-38 Pierces used a 10-spline 32-7/8" long (Hollander #220), which fit nothing else.
The 10-spline axles are more robust than the 8-splines, but still have problems, as Bob Jacobsen can attest . Accordingly, at some time in the past, someone may have swapped out the differential to be able to use 10-spline axles.