Are you sure you're not thinking of gasoline engines? One of the advantages of diesels is the ability to run lean. Using post injection to use up all the leftover oxygen would seem to be counterproductive. It also does nothing for the main combustion event, where maximum heat is produced with an abundance of free oxygen available for NOx production. But what do I know? So lets go to the experts. Most of the studies talk of pre injection as the way to reduce NOx is a diesel.
https://www.sciencedirect.com/science/article/pii/S1110016817302041
There are plenty of papers like this:
https://www.sae.org/publications/technical-papers/content/2002-01-0502/
Or this:
https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=8537&context=etd
At least now I know my memory isn't totally unreliable, yet...
As for the speculation on differences in individual trucks, mine has always had and still does have the cat. Part of the difficulty is that different people will have different tolerance levels for smoke. Some even like "rolling coal" for whatever reason. I want to be able to accelerate however I please without leaving a ball of smoke when pulling away from a stop sign or leaving a trail of smoke while accelerating down the road. The smarty sure woke up the truck, but it smoked too much under heavy acceleration for my taste. That level of smoke might be fine for someone else, though any visible smoke risks triggering the diesel haters now a days.
Crunch, sorry for getting your thread so far off topic.
Ok, so I'm assuming you purchased the SAE paper and read it? If so perhaps you can share the applicable sections? I'm not looking to spend $33 to get them.
I might have been a bit off in my earlier comment, it's more accurate to say the events are to control the pressure/temperature component for the NOx issue than the O2 issue, the O2 issue is where EGR comes in, though it is also true the an addition late injection event will also consume additional O2, though it's not the primary reason for that injection event.
BTW, the 3 injection strategy does not have a true "post" injection. It's an early (pilot), near TDC and after TDC (late) injection, but all 3 are during the combustion phase, a true post injection is something only the 3rd and 4th gens so to conduct a DPF regen, basically to light off a fire in the exhaust stream.
As to the first article, yes the pre-injection helps as well, the reduction of NOx is a complicated issue, it's been the biggest hurdle for Diesel emmissons control, and drove the VW cheating scandal. The soot emmissions problem is easier, NOx is what has been difficult, and it is trying to control NOx that has led to MORE soot (that Iowa Paper, your 3rd link goes into detail on this).
Here is the basic chemical reaction.. and it is in fact BECAUSE Diesels can and do run lean that NOx is such a challenge. Lean means you have excess AIR, thus EXCESS O2, and with N2 being 78% of air, you have plenty of O2 availible if you are LEAN (Lean mean less fuel than availible O2, in a gasoline engine you seek to run a ratio of fuel such that all O2 is used and all fuel is used, which leave no O2 availible to produce NOx, so only in transient conditions does it become an issue. The challenge in Gasoline is often the concern of the gasoline itself not being burnt (or vapor from the tank) as gasoline has low flash point and it's vapors produce air polution an smog.. hence the stupid gas cans with no vents on them.. but I digress.
Here are the basic chemical reactions that are at the root of NOx production (these are in your third link):
O + N2 => NO + N
N + O2 => NO + O
As you can see, the root of the problem is the fact that LEAN means you have O2 availible.. now that is not all that is needed, you also need HEAT, and PRESSURE.. and turns out the high compression of a Diesel is the exact thing that does both. If you look you at historical engine compression ratios for Diesels, you'll note they have been going down, which is also a NOx reduction strategy, in fact Mazda had an engine with a ratio almost as low as a gasoline engine, at the lower ratios the limitation becomes the cold start, so hefty glow plugs become imperitive, and they came up with a valve train to let some exhaust gas to back flow into the cylinder to help it heat up faster.. I thought that was pretty innovative.
This is where the multiple injection events come into play, all of them.. some before and some after and timing is a factor as well. Just because I'm discussing the 3rd injection cycle, because it was mentioined as being tuned out on the tunes in question, does not mean the pilot injection is not also a factor in NOx control. The injection events, all of them are designed and timed to get the most fuel burned, and to decrease the conditions that help produce NOx, and that is the availible air, and the pressure/Temperature in the cylinder.. you can hear it in older diesels with just one big injection event.. that is a big pressure temperature spike that is able to produce NOx better. If they could pull it off they would try to use all the O2 in the cylinder, like a gasoline engine, but that does not work for Diesel as it would be too much energy and then pressure and heat.. Diesel fuel has 20% more energy per volume than gasoline.
So to my point, the original 3 injection event was in fact a strategy for NOx reduction, and in the 3rd 6.7L it's a 7 or 8 injection event (the 8th is post injection for DPF regens only, it's not for in cylinder NOx reduction). In newer Diesels I think it's even more than 7 distinct injection events. This is to help prevent the pressure temperature spike, but also allow the expansion over the piston stroke to produce power an torque, it is one of the ways the emmissions control efforts have actually led to higher power and torque, at the same time, and it also has made the engines more quiet as well.
BTW, that last link (Iowa State paper) is excellent reading. If anyone has ever questioned why the LNT trucks (no DEF) (2007.5- 2012) got such poor MPG, the answer is right there in this paper. The LNT needs the truck to run with too much fuel, thus lower MPG (page 21). So there you have it. That is also the exact cheat the VW pulled off. The other OEMs not cheatng did not enter the market as they could not match the performance and MPG of VW, but that was because they had worked the programing to not run the engine to reduce NOx by not running the excess fuel needed for it to work, and thus they attained better MPG and performance, then when on the dyno.. they would alter the engine fueling to make it comply.. they denied it for years until the EPA finally said no to certifcation of the 2015s, then and only then they admitted the cheat.