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All three of my 34C's, with serial numbers corresponding to 1980, 1981, and 1982 were made in Singapore. Yours is a 1980 model.
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Michel, I have a 34C the back of which says it's made in USA and that the serial number starts with 19, which puts its manufacture year at 1979. What are the first two digits of the serial number on the made in USA half case? According to this museum's pages, the earliest sighted 37E serial number starts with 1850 whereas the earliest 34C starts with 1928. Hopefully, this can help you.
If not, ask again on this forum if anyone knows when the 34C and 37E respectively had shifted production from the US to Singapore.
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Hi Michel
My 34C has serial no. 2033S and is Singapore made if it's any help.
James
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Have you tried looking for scratches, marks, stains or anything that could allow an association between top and bottom halves ?