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According to the serial number chronology in James Tipton's article on the Remington Autoloading Shotgun/Model 11, serial number 116134 would be a 1911 vintage gun. That would put it right at the time that Marcellus Hartley Dodge combined his Remington Arms Co. and Union Metallic Cartridge Co. into Remington Arms - Union Metallic Cartridge Co., so the guys on the floor at Ilion might not have quite settled on how the gun should be marked. It doesn't have a couple of lock screws the Model 11 got just a bit later --
Would be nice to see additional pictures of this fine gun, especially the ledgend on the barrel and the engraving on the bottom of the receiver in front of the loading port.
It appears your gun was back to Remington Arms Co., Inc. a couple of times for repairs or modifications. The stampings WW3 and AH3 are both repair codes -- W = August, W = 1928 and A = March, H = 1939.
I have the 1911-1912 catalogue and they are referred to at that time as No. 11F "Premier" Grade.
In my collecting it appears that the grade designation on the barrel near the normal barrel address came into play around 135,000 and lasted only into the low 200,000's as standard issue. Although there are many examples afterwards it is far from common, from the examples I have seen.
The numeric grade designations were continually used in the grade markings on the wood, receiver tangs, and barrel bellies as far as I know.
I live in West TN about an hour and a half from Dexter, MO and will see if I can locate any additional information for you.
I have been on both sides of the coin in internet auctions against a MrWheaton which I can only presume is you.
Seems like we share a common interest, congratulations on a great gun.
If you decide that you are going to attempt to restock the gun to original configuration and checkering, please let me know and I would be glad to offer any photos or catalogue drawings that may help. I also have a person in mind to do just that kind of work if I ever undertake that type project.