I'm afraid Hayes "jumped the gun" on this :)
The serial numbers Hayes provided are for (what collectors call) the Model 1860 Spencer made by SPENCER. Your carbine is a Spencer made on contract by BURNSIDE. Your 1863 date is actually 1865 (there is no Model 1863 Spencer).
Burnside Spencers are generally considered post war/Indian War period, though some may have been delivered in the closing weeks of the Civil War.