I wonder if anyone would like to hazard a guess regarding how this lens may have been used. The only reference I can find to the 13.5cm f3.8 Hexar is in a camera called the "Lily" made for military use. However this was a folding camera and the lens was mounted in a shutter. There are also references to the Rokuoh-Sha Hexar being used in a machine gun camera but only in 75mm focal length. Similarly some reference to aerial cameras but in longer focal engths above 200mm.
The thread would suggest that the sleeve was screwed into some sort of housing where it was quite deeply recessed. The three raised studs on the brass collar I would think are an aid to gripping the sleeve when screwing into and unscrewing from whatever housed it.