It's hard to say from the photos...I don't know early Pinarello well, and even less about track bikes. My sense is that very few pre-80s Pinarellos made it over here, and they were low production before the late 70s (mostly supplying treviso). My mid-60s Pinarello has no markings, other than the Galmozzi fork crown.
I would look very carefully at the frame - especially the front end. The powdercoat combined with missing fork would give me pause.
I think I see what look like markings on the caps...but it's hard to tell in the photos. I think it's going to be hard to find comparison bikes...the guy on the forum most likely to know about this bike is citoyen du Monde.