Just to straighten up some things: Though the German proof law dates from 1891, it took some time to decree the proof rules, establish proof houses and so on. So that 1891 law came into full force on April 1, 1893. The "in stock" crown/V Vorratszeichen, a proof exemtion mark, was stamped during March 1893 only. If you doubt this, I may provide the original German orders and decrees.
This "H.Scherping, Hannover" rifle was actually made for Scherping by Sauer & Sohn, Suhl. The "caveman" was a registered S&S trademark. The two crowns were S&S own quality marks for best execution and guarantied shooting. As the crown/V mark shows, it was in stock at either S&S or Scherping during March 1893, ready for sale.
Some years later it was maybe rebored or rechambered, at least reproved, crown/R mark, for a smokeless load, crown/N, in 4,06 = April 1906, by the Zella –Mehlis proofhouse, as the ledger number 984 indicates.
The bore/land diameter (NOT groove or bullet!) was established at the proofhouse in 06 as gauge number 62,78 = in between .420 and .429". You will have to make a chamber cast and to slug the bore to find out about the chmber and groove diameter. I assume it is for one of the German LK cartridges, 11.15x40R Lk, 11.15x50R LK, 11.15x52R LK, 11.15x55R LK, 11.15x60R LK or 11.15x65R LK. AFAIK the LK cartridges were the only ones of the many German "11 mm" cartridges regularly offered with a smokeless, copper jacket "light nitro" load.
Pehaps you should post the rifle on the forum of the German Gun Collectors Association www,germanguns.com too, as there are several Scherping and Sauer & Sohn collectors active there.