That's for crankcase ventilation. Hose at 2 goes to the air cleaner box, not the exhaust port. As you said, it mounts on the back of the gearbox, driven by the rear end of the crank, behind the alternator. I believe part 6 spins in order to separate some of the oil back into the crankcase before crankcase air goes to the air box, and through the intake valves.
There's a video cutaway of the LC engine here: https://www.youtube.com/watch?v=wcrFi3ZCi7U
It seems to show everything in the engine, and I do not see any points where anything could be injected into the exhaust. I find it helps a lot to use the YouTube settings to slow it down to half or even quarter speed, otherwise there is too much going on to comprehend.
My understanding is that un-burned fuel in the exhaust would cause changes in the O2 sensor output, causing the amount of fuel to be reduced, so that there would be no need to add air or cause burning within the exhaust.
Thank you for the video it is very cool for sure.
Also excuse my attitude at times I am old and cranky and sometimes both of me can not agree how to act, especially before the meds kick in.
A PAIR or Air Induction System to me is when un burnt gases are sent into the induction system to be re burnt.
The air induction system burns unburned exhaust gases by injecting fresh
air (secondary air) into the exhaust port, reducing the emission of
hydrocarbons. When there is negative pressure at the exhaust port,
the reed valve opens, allowing secondary air to flow into the exhaust
port. The required temperature for burning the un- burned exhaust gases
is approximately 600 to 700 °C (1112 to 1292 °F).
Air cut-off valve.
The air cut-off valve is controlled by the signals from the ECU in
accordance with the combustion conditions. Ordinarily, the air cut-off
valve opens to allow the air to flow during idle and closes to cut-off
the flow when the vehicle is being driven. However, if the coolant
temperature is below the specified value, the air cut-off valve remains
open and allows the air to flow into the exhaust pipe until the temperature
becomes higher than the specified value."
This link will help you see what I am describing.
The air induction system - Yamaha FJR Forum : Yamaha FJR Owners Forums
So when I see the only thing that is labeled a fresh air system I believe it to be this system in some shape or forum.
A PCV is in all my years of trying to turn a wrench was passive.
With this on the end of the crank it is not passive at all.
I also did not see or could not see if there is a tract or port from the back side of this where it fits on the crank, to the exhaust ports. As that is where I believe it will inject unburnt gasses.
So I see this fresh air intake and a hose up to the air box. So it is drawing air from the air box continuously? It draws it down into the motor but then what? It has to be dumping that air into a exhaust valve right? I mean it is already got fresh air intakes coming off each side of the air box.
So where is this air being pulled by the crank spinning the fresh air intake going to? Or I guess the real question is how is it leaving?
EDIT: And I guess this is all based on my thought that the air is being pulled into the motor FROM the air box. Now if it is being pushed into the air box then that is the answer. It is still sending gases of some type into the fresh air intake which probably will affect AFR also.