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I checked the 12 ga Parker Trojan, that I have, and the ser# is 178### and above the ser # is 0V, enclosed in a 6 sided box. It has a Doll's Head. There is no other marking that would indicate a frame size other than the 0V.
I did check the ser# a few years back, and recall 1912 was the date. Don't think the Trojan started at ser# 1 either.