I do wish a different acronym had been chosen. When I search for "[language of choice] JWT" pretty much all results are relevant. But even if this new token schema takes off it will forever be a hassle to find relevant results for "[language of choice] PAST".
I spent two weeks (my Christmas vacation) working on rough drafts for several problems I wanted to solve in 2018. PAST was one of items I listed. (The list is here: https://github.com/paragonie-scott/public-projects/issues/6 ) 99.9% of that time was spent trying to come up with a better name/acronym, without success. I decided to just give it a plain/obvious name until a better one surfaced.
You could also drop the use mapping: change 'sign' to 'public-auth' and explain that it's a 'sign' operation (a.k.a. digital signatures)