RE
As for the existence of PP*,
Back in college 25 years ago, I had a class in logic taught by a mature professor who was an emigree from Nazi Germany. One phrase sticks out so profoundly form that class that I will never forget it. He would start his logical arguments not once a class, nor a couple, not most, but all of his logical progressions with a tautologically statement "If Nixon was a liar".
In honor of that professor I will preface all references to the PPT with "If the PPT is not a figment of our imagination" <g>