Irlandes, this is what I think happens:
When the throttle is not fully open then the pilot observes the limiting MAP according to the placard in the cockpit.
When you climb above the critical altitude, the throttle is wide open and because there is no supercharger with boost control to maintain the Manifold Air Pressure, the power of the engine reduces. So far pretty much as FOM suggested….
But, whilst I stand by my ‘DA is DA is DA’ and that the density of the air is the major player in the efficiency of the engine (the weight of charge in each induction stroke to be more precise) the problem is that as you go higher, the static air pressure decreases because there is less weight of air above you as you climb.
Although all your combinations of PA and OAT give the same DA, the actual measured pressure is reduced at higher PA.
Therefore since the MAP is dependent on static pressure, the MAP and therefore the amount of air going into the engine is reduced. The density of the air is the same but there is just less of it going in – the downstroke of the piston on the induction still produces the same vacant space in the cylinder but the pressure outside isn’t sufficient to fill it with as much air/fuel as it was at lower altitudes.
Therefore your max AUM decreases due to PA despite the DA remaining the same.
Does that make sense?
If the R22 was supercharged it would be very different as the Automatic Boost Control would maintain the MAP by squeezing more air and fuel mix into the chamber to compensate for the loss of static pressure.
BTW I am not sure why the limiting DA appears to be 12600 since my (old) copy of the R22 handbook says it is cleared to 14000 DA (maybe it is only for forward flight)