It stands for "Pulsed Air Injection Reaction" and was used by many auto manufacturers (including Honda). It uses exhaust pulses to scavenge fresh air into the exhaust system to help keep the cat temperature up. I don't know how triumph controls it, but it sure could throw a wrench in the works if its allowed to function in closed loop under load!!
I know this is semi-unrelated, but my 08 touring came with a evap canister and about 20 feet of related plumbing that I ripped out and disposed of. I have seen a couple other 07-08 Rockets that had no evap system (located behind LH side cover). My bike was originally sold in Mass and conformed to Calif emissions.....is it possible this PAIR on the newer bikes is another Calif emissions gimmick???
Note: I only eliminated the evap system to make room for my horns,,,,which I feel are MUCH more important than capturing a few hydrocarbons