If it is unaltered & un-messed with, it must be 100% original. So why and how did you restore it?
My guess is that the 4 1/8" barrel is that it would be legal to sold in our wonderful neighbor to the north, Canada.. I've been told that pistol barrels must be over 4" to be able to owned by most new purchasers in Canada... & that shorter barrels on handguns are subject to only being owned/possessed by folks who had them registered years ago.
So S&W chose to only make handguns with 4 1/8" barrels so that any of those (& handguns with longer barrels) could be exported to our good neighbor, rather than to have 4" barrels on some & slightly longer barrels on others...which would be a great burden to see which was legal & which was not to be exported.
It's a shame that Canada is burdened by the same type of silly/non-logical firearms laws that some of our US states & cities have.