My research on Military and War Forums & related sites leads me to believe the number on the Windage Dial Mount is the Scope Serial Number and the number (not always found) on the tube is the Rifle/Gun Serial Number the scope was mounted on, updated original post #637
Example: Rifle/Gun (Gewehr - German for Gun) GW. No. 7835
I don´t think so.
First - GW is very unusual for Gewehr. Short form for Gewehr would be "Gew." or maybe even "G." only.
Second - it makes no sense to accompany a scope to a certain rifle. It´s not the same as target shooting on shorter distances, where it might work.
A sniper set is not the same as the same type rifle for the standard soldier, who directs it toward the enemy and hopes for a hit while looking for better cover (over 90% of spent bullets are shot "just in the direction", to force the enemy into his cover or keeping him from good aiming, hoping for a lucky hit. And automatic guns didn´t made that better, most soldiers are wasting to much of their ammo due to auto fire).
I had my rifle´s (the sniper version with fixed stock, and the jump version with foldable stock - used interchanging for whatever is needed to a certain action), on my weapons card, and also the scope given to me - and while my sniper rifle was stored together with my scope in the weapons room so the team there doesn´t needed to search, both parts were assigned to me, not to each other. My scope on my rifle would be not good fo another sniper, as each of us adjusted the combination to his own needs (eyes, how you hold your head when aiming,....all that little differencies that sum up at the end of a several hundred meter shot). Each one of us would have prefered his own scope on a new rifle, not a combination swap.
And i was only a group-sniper, none of those guys with the oversized anime guns for shots over a mile. I assume they are even more picky. But those special guns are no good match to those old Karabiner.
So, i see no reason to combine a certain scope fix to a certain rifle in a way it would help to have the numbers engraved on each other. Just makes no sense.
Additional - as there are way more rifles than scopes in the units, i would always expect a higher number for the rifle and a lower for the scope. Not the way it is assumed on this case.
