That listing from
The Parker Story doesn't include the marks found in the barrel material location on the right barrel flat of the early Vulcan Steel, Titanic Steel and even a few Acme Steel barrels. On the Titanic and even a few Acme Steel barrels the mark is a
K --
92809 03.jpg
For Vulcan Steel the marking is a
Kf --
111056 01 16-gauge, 28-inch, Kf barrel steel.jpg
These marks were in use up into the 134xxx range. By the 135xxx range we begin seeing the T, A, and V in a circle.