Is this a legit US military shotgun

Picked up a 18" 'cyl' chocked ithaca 37 about a month ago. Its got a factory serial number of just over 1,005,000 on the right side of the receiver (1968 if I read Ithacas production numbers right) and "US" stampe on the right side near the front. The left side of the receiver has an "S8--5" stamped down underneath, right next to the trigger guard. Proofs are regular genie lamps with small "p" in them on the right side of the receiver. All these marking are under the obviously old, thin parkerizing that is turning in color like you would expect., so I do not think it is a fake. Canfields book leads me to believe that the S prefix serial numbers were sometimes also stamped on the receiver face and that the misaligned numbers on the side stamped ones are not unheard of. What do you all think?

Never heard of any 18" Ithaca US Military shotguns.

Can you post some photos including one of the US mark?

Tom...here you go. I fear it is a fake but the markings are under the parkerizing that seems original to the gun (it is much darker than the photos show)

https://www.milsurps.com/images/impo.../thaca_B-1.jpg

https://www.milsurps.com/images/impo.../thaca_E-1.jpg

It is a definite fake. As well, there are two extra plugged holes in the side of the receiver. Those did not come with. Buttplate is wrong. The trigger group screw in the photo is totally wrong, I don't know if that is a washer or a sleeve or what, but it didn't come that way. As well all military Ithacas were 20" And the U.S. are just so obviously wrong it is sad.

In fact, there is a SCREW above the serial number. That does not belong there. It should be the flat end of the trigger group screw, which goes in from the left. Bubba has totally had his way with this gun.

Anyway, I hope you paid a shooter price because I am sure it is still a good shooter.