Well there's lots of weird things I see there. As Bob mentioned, there were no center pockets on the smooth side short beds (late 51 & 52 F1) There were center pockets on the long beds installed on the F2 and F3s. But these still had the panels on the bed sides and also the back wheel well protrusions into the bed. I cant see if yours has those or not - I doubt it since there are no panels either.
Funny thing I see abut this one also is it looks like the back fenders butt right up to the back stake pockets or may even be slightly flared into them. On the F1 short beds with the correct fenders on it there is usually about 1 1/2 inches between those. On th e53-56 short beds that was about 6 inches.
So, no matter what, the bed has been highly modified if not, as Bob mentioned, made from scratch. I don't have a source that gives me the dimensions of the 53 to 56 beds, but I think they were slightly wider (help me guys) than the 48-52s because the tailgates weren't interchangeable (I think). Here are the inside dimensions of an F1 short bed: 78.06" from front to roller pan; 49" wide from side to side; 20.25" from top of roller pan to the top of the beds rolled top edge; and, the tail gate (and thus the bed sides) were 17.56 inched from top to bottom. It was called the "6 1/2 foot pick-up." The "long bed" called the "8 Ft Express" Measured 96.05" from front to roller pan; 54" wide at the tail gate, 48.38 inches between the fender well indents; 21.73" from the top of the roller pan to the top of the rolled top edge; and the tailgate (and bed sides from roller pan to the flair) was 19.2 inches. Maybe these measurements can help.
The 53-56 beds I believe were used on step sides up to 1972! So getting dimensions from them shouldn't be too tough. According to the Parts and Accessories Illistrations catalogue for the 53 - 56, the 1/2 ton short bed didn't have the center pocket either. But the long bed had TWO center pockets and the wheel well indents into the bed. This may be a 53+ long bed that's had the tail chopped off of it.
There is one more give away I just noticed: On all the beds 51/51 F1-F3, and 53-56 short bed, the front panel comes up level with the rolled edge of the bed sides. Only on the 53-56 long bed did that panel only go as high as where the bed sides started to flair. I believe those back fenders were also used on all the Ford Step side to 1972 (along with the beds) so you might just have a later model bed on it. But, Liek th eman said, it's definately not a 51/52 short bed.
Maybe......(drum role please) "Number Dummy" has some books that show these beds better in their later form. Who has Bills Magic Lamp this week?
Looks like a pretty nice truck though!!!!
PS. Also, the sides of you r bed a re very tall. On my F1 there is only 3 1/2 inches from the top of the fender to the bottom of the flare.