OK, this one has me stumped.

(A) Dimensionally it has to be a .50-70:
Rim: .653 to .660"
C/L: 1.776"
OAL: 2.236"
Head .563"

(B) It is Martin primed with the re-entrant fold.

So far, so good. Now it gets interesting. The case tapers from the top of the rim (head) over a distance about 1.100" from that point, where it has decreased in diameter to .549" . . . then there is a faint but distinct shoulder of about 0.085" length dropping to a neck diameter of .541" and finally there is a taper crimp of about .165" length terminating with a case mouth diameter of .520" . . . the bullet is inside lubed and the standard .50-70 profile.

Then there is the primer. It has a unbalanced ("spokes" predominantly on one side of a central dot) impressed pinwheel design with the spokes angling in a clockwise pattern.

For some reason, the design strikes me as French. And the slight bottle neck is down right weird - at least I don't see it in any of my other .50-70 rounds, including two different Martin primed specimens.

My first reaction was some sort of European variant. But with a Martin primer??

My ISP is off line on uploads at the moment so I can't post pix, but I have scans I can send out.

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My initial thoughts were maybe Mexican production - lots of US Govt rifles made it to Mexico by various means back then - but the manufacture of Martin primed cartridges was limited to just Frankford Arsenal , E. Remington , and Union Mettallic Cartridge Co . So that rules out that idea .
I suggest respectfully that this is a cartridge from one of those listed manufacturers that has less than standard tolerances and some interesting production markings around the primer . An interesting variant and worthy of keeping just for the fact of being different .

Given the reference material I've been able to unearth, I'm leaning toward E. Rem & Sons, but that is nothing more than a very mild supposition so far.