The .22 Eargesplitten Loudenboomer is a real cartridge and holds the record as far as I know.
4,000 isn't even hard anymore. There are several cartridges that beat 4,000 easily.
I load 35gr Nosler BT in 22-250 over 40.5gr W748, getting a true, chronographed 4,435fps and its not even a max load.... that's with a 24" barrel.
QuickLoad says a 36" barreled .22-250AI firing a 30gr Barnes Varmint Grenade could hit 5,077fps at just 57,000psi. Taking it up to 72,000psi, which isn't really all that unreasonable, QuickLoad says you could get 5,281... a mile per second almost exactly.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.