The "K in gear" may be a mark of the Suhl barrelmaker family Kelber. 7.7mm is the bore diameter at the time of proof. It may have been just short of 7.8mm, as it was measured using cylindrical gages. You have to add the groove depth. This marking is correct for the 8x57I with .318" bullets. The CROWN - crown/N proofmarks indicate pre-1923 proof using the "4000atm" special proof powder. As the bore diameter is given in mm and there are no other numbers, the gun was proofed in Suhl post-April 1, 1912.