AFAIK, Remington made 356,000 #4 rifles between 1890 & 1933 in five variations:
The Model 4 Solid frame
The Model 4 Takedown (Lever)
The Improved Model 4 Takedown (Knob)
The No.4S Boy Scout Rifle
The No.4S Military Rifle
The #4 was the smallest of the Remington Rolling Blocks, and is easiest ID'd because it's the only rifle w/o a lower action tang - and also the only RB with screws as breechblock & FP pivots, ILO pins.
They were originally chambered only for rimfire cartridges of the day: 22 Short, 22 Long, 22 Long Rifle, 25 Stevens (.25-10"), .32 RF Short, and .32 RF Long.
AFAIK, all solid frame, and early takedown rifles had tapered octagon barrels; later takedowns had round barrels.
The octagon & round bbls were either 22-1/2" or 24" long, the BS & Military Rifle had a 28" bbl w/bbl band & sling swivels.
There were approx 144,000 solid frame Model 4's produced during the period 1890 - 1899.
Some information exists claiming that solid frame production may have extended into 1901.
Early No.4 Lever Take-Down Sporting Rifles were made from 1901-1924 (known SN's 168525 - 318726) -Production of about 170,000 Rifles, before the switch to the later, knob-style takedown.
You can exterpolate from the various datum points, compared to the SN of your rifle, to approximate it's DOM - but remember, many makers made guns widely out of sequence, and in your case an early (ca 1901-24) lever takedown receiver might have hung around the parts bins long enough to get assembled & serial numbered in 1928, just as the maker (Remington) say that was when they did it.
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