I had to shoot w/the T-4 lenses at one time because they were all I could afford. The glass lacked optical brillance, but could pass on some fiber papers (esp. the paper Kodak used to make for the Fotorite machines.
It's indeed a Vivitar/Soligor TX/T4 lens mount.
I have a Vivitar 24 mm f2,8 with some mounts (Canon FD, Nikon F, M42, Pentax K, Minolta MD,...), bought in the 70's : it was a good lens but I prefered Tamron with its Adaptall mount.
Many of the T4 and later TX Vivitar lenses were very decent performers. Some people questioned whether their aperture mechanisms could withstand heavy use with motorized cameras. At that time motorized cameras were very expensive and most people who used them did not use third party lenses. Mirror lenses were a exception. Soligor also sold T4 lenses but I have not seen Soligor TX models. There are a few TX lenses marked Tokina. Tokina made most or all of the T4 lenses but not all of the TX lenses. Komine also made some of the TX lenses.
Back "then" I had a motor-driven Nikon F and I used a lot of third party lenses. I had a Spiratone preset 105mm f2.5 lens that I used to photograph a "secret press conference" held by the Beatles prior to their concert at the Hollywood Bowl. It was kept secret because they knew if the word really got out there would be a thousand photographers and fans there, not the 100 or so who knew about it and got in. The third-party Spiratone lens took great photos and the ones from the Beatles confab are a treasure. I have newer camera bodies now but I have never found a sharper lens than my lowly Vivitar 19mm f2.8.