No. The serial isn't "out of range" but it doesn't prove it's a genuine carbine either.
The stock, rear sight, and other parts are wrong for an 1898 carbine. Thus it's up to you to "prove" that it is. At this point it's not "proven" either way.
I own an 1898 rifle "in range." I also own sundry 1899 carbines and carbine bits. If I spin a carbine barrel on that receiver, dump it into an 1899 stock, and add the 1901 carbine sight does that make it an 1898 carbine?
1898 carbine stocks are hard to find. Very hard.
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Meet 119066:
Meet 121981:Serial is 1201XX.
That serial should put it as a genuine carbine should it not?
See the problem? What comes between Mr. 119066 and 121981? Could be rifles. Could be carbines.