No hits in Mallory, but interesting numbers nearby.  Closest carbine with lower number is 35597 that went to the 25 Infantry (probably for an officer).  Closest higher number is 35741 that went to the 1st Volunteer Cavalry (Teddy Roosevelts Regiment) and that's a good neighbor hood to be in - only 135 numbers away!

Your carbine is marked with only the date "1896" and without the "Model" prefix. That's an uncommon dude, too, so you really did very well!

Maybe one of our kind gentlemen who has access to the SRS records can check further.  I have a similar situation with an "1895" carbine and I have been hoping to get up the courage to ask someone.  It has an interesting bunch of neighbors, too, in Mallory, but I don't have the SRS information.