The products called PEP-77 and PEP-79 shared the same headset (PEP-71) but used different transformer boxes (regular bias vs self-bias). The ensemble you have is collectively the PEP-79 and that's what was on the outside of the box. But yes, the headphone itself is the PEP-71.
Backstory: If you bought the PEP-77C (which hit the market first), your box could drive two headphones. The headphone was available separately as, you guessed it, the PEP-71. Nice and neat. Once they decided to introduce a cheaper self-bias model with only one output, however, the nomenclature became instantly confusing, but they stubbornly stuck with it to the end. My earlier posts called the PEP-74 a PEP-74E, and that's incorrect-- my belated apologies to facelvega! Just as with the PEP-71, when the PEP-74 headphone was sold with the self-bias box, it was called a PEP-79E. When it was sold with the more expensive AC-powered box, it was a PEP-77E.
Stax did something similar with the nomenclature of their electret line: the SR-80 headphone packaged and sold with the SRD-4 transformer box is called an SR-84. Confusing, but it points up the connection between Stax and Superex.