Let me preface this by remind you that I have been giving you the benefit of the doubt in all my arguments. I have posted my math working out the minimum amount of energy needed to simply remove all the water from a human cadaver, which is less than the minimum energy needed to cremate the cadaver, and then also assumed an impossibly perfect crematory unit to find the fuel consumption. These numbers are obviously and charitably lower that what would be required in reality, and you have had every opportunity to calculate them yourself, show technical documentation, and otherwise prove me wrong. In my discussion of crematory unit size, I charitably used modern construction standards, which are orders of magnitude more advanced in construction and operation, ending with volumetric requirements much lower than 1940's technology would occupy. Again, you never deigned to recalculate or present any technical evident in opposition to my extremely charitable work.
Instead you responded with personal attacks and pretty loaded language embedded in increasingly hysterical screaming over a number of posts filled with unhinged ramblings that demonstrated no understanding of the laws of physics, the nature of engineering, or the practicality of real world work that a reasonably adult person might have from any experience with manual labor. You purport to be an academic with considerable education and subject matter expertise in this area in particular, and discussions of this topic should not be novel, so why do you seem so ill-equipped to respond in a measured and clear fashion? One might think that the information and demonstrable proof would be at your fingertips, so why has it taken you so long to respond in even this unsatisfactory fashion?
It leads me to believe that you are, in fact, not an educated academic but rather are posting copy-pasted arguments from off-site without understanding what anyone, including yourself, is posting. You just look for keywords and desperately try to stitch together responses with insults and deflection as the mortar. It is tiresome.
The basic problem you have is that your entire analysis is an extrapolation from your (probably real, but marginal) knowledge of how cremation works in Nebraska or rural Canadian or other hicksville funeral homes. But cremation worked extremely differently at Auschwitz. Because you are extrapolating from your personal experience with cremation and "cooking" - which are not technically analogous to what happened in Auschwitz - you are confused about what is technically possible.
Again, you do not know how energy works, or thermodynamics. I will post a video or two here that might help explain things to you, and show you how to do the calculations yourself.
If you still don't understand I'll go through youtube and try to find a Magic Schoolbus episode or something for you.
Another point of confusion you have is that commercial cremation in Idaho and cremation at Auschwitz had different goals. The latter was to burn as many corpses simultaneously with as little fuel as possible. So it is predictable that the technical innovations used at Auschwitz would be of a different kind than the technical innovations you find in commercial cremation across the last few generations. It is not that, in other words, that I am arguing Auschwitz had "better technology" than your uncle's funeral home has today in 2022. Instead, Auschwitz had different technology with different goals.
Again, I calculated an absolute minimum amount of energy required in a perfect application/conversion of fuel. It is physically impossible to require less energy (in the form of fuel) than what was calculated. That you don't understand this is really concerning.
Do we have any physical evidence of the industrial grade facilities need to meet these very conservative, very minimalist requirements? Or just some memo that, assuming it is real and not wildly misconstrued (perhaps to indicate how many bodies could be sterilized of typhus in a day) would at best be the equivalent of 'just trust me bro'?
OK now let me address the specific technical stuff. We know a lot about how cremation at Auschwitz worked because the manufacturer of the cremas, Topf, left quite a paper trail. A lot of the documents detailing the technical workings of the cremation can be found in Robert Van Pelt in his book The Case for Auschwitz,
One of the most interesting documents cited by Van Pelt is a 1942 patent application by Topf, who again was the guy who created the cremas at Auschwitz. In the patent application Topf described his special technique for burning a ton of bodies together, with drastic savings in time and fuel. During the war, due to "secrecy" considerations involving the use of his technology by the German government (gee, I wonder what those were . . .), the patent could not be approved. But post-war, Topf again applied for a patent for his special cremation technology, and his patent was approved in 1953 by West Germany, as patent no. 861731.
So you have no technical documentation, just a 'lol trust me bro we had wicked cool cremators'? This does nothing and proves nothing. As Lemmingwise said:
I like how there's no technical analysis. Only trusting van Pelt wholesale.
At best, you may have a note from a guy who says he knew a guy that totally made a wicked cool new cremation system that would totally, totally work but it was like, wow so super secret but it eventually got a patent (which you don't have) and was apparently never produced or developed and no units are in existence, sucks bro. Even though such a crematory unit would have obvious applications in animal corpse disposal for research labs or agricultural cullings, and despite being so obviously efficient and good it never went further than a patent. Nobody even took elements of it to use in future designs because, uh, reasons. But its okay, because getting a patent proves that whatever you patented totally works, nothing ridiculous or obviously unworkable has never been patented, ever.
This can't be real.
So the Nazis utilized Van Pelt's method during the war, and the post-war (non-nazi) West German patent office considered the method he described in his patent application as technically legitimate and feasible. What was that method? We can tell from Topf's patent applications. Topf (I do not have a copy of his patent application, so I quote Van Pelt) described his cremas as "continuous cremation furnaces" in which corpses are inserted at the top and "as they slowly slide down a system of inclined grids, they are quickly reduced to ashes." Stuttgart Engineers who assessed Topf's patent application supposed that "the furnace could be initially loaded with 50 corpses and that in the upper part of the furnace the bodies would dry out through evaporation."

"We can tell from his patent.....which I don't have, just trust me bro lol."
Reading these supposed 'technical innovations' makes these narrative assertions even more laughable. First of all, human bodies do not slide down inclined planes at smooth, even, predicable rates because human cadavers are big, long, awkwardly shaped and foldable organic sacks full of bones and sticky liquids. The variability of friction on skin alone would be problematic, before we start to consider the skin fusing to the metal grates, or the presence of blood, urine, feces, etc that can stick the cadaver to the surface, to other cadavers, or other limbs. Punching holes or 'grids' into your ramp just adds more problems - what happens when a hand or foot snags into those gridholes and hangs up the cadaver until the bones and ligaments are incinerated? Are we constantly opening up the top so Sonderkommandos can shove the corpses down, wasting heat with every second the top is open? Or are we letting the cadavers stack up on top of each other and losing the efficiency gains in having the full surface area of the cadaver exposed? Okay, okay, assuming that you can have the cadavers roll down to the lower level now we have another issue where the water vapor from the lower levels can condense on the upper levels, depositing the water on the upper level cadavers. Unless you're running multi-level flues to extract the water vapor, in which case you're not letting the heat rise to the upper levels anyway, so which side of this devil's bargain is going to be more efficient?
Again, where is any technical documentation that somehow proves this design exists and its efficacy in cremation?
If you had it, we again come back to where the fuel comes from - you cannot push the fuel requirements below the minimum numbers required to chemically extract just the water from these cadavers.
So yeah the bodies were mostly burned outside .
That just leads us back again to where does all the fuel come from?

"Where does the fuel come from?"

"Well they don't need that much fuel, they had crematoriums."

"Well that doesn't seem possible and the evidence you're showing is burn pits, not even crematoriums."

"That is because they did most of the burning outside."

"SO WHERE DID THE FUEL COME FROM?"

"They don't need much, they had magic crematoriums!"
I just notice that his arguments stand unaddressed. There is a lot of long storytelling of "x is what happened", but no engagement with anything he wrote. It's like reading out a callscript like a telemarketer. Maybe I was wrong, maybe this is paid shilling after all.
That or a really bad NPC dialog script.
I've asked you to present evidence of a conspiracy to fake the Holocaust and I think the best you came up with was a few Nazis got beaten up and mistreated immediately after the war in interrogations.
Honestly it is quite easy to forget completely discrediting counter-arguments to deniers

"You can't prove the moon resettlement, therefore we are correct!"
Stop trying to shift the burden, you're the ones advancing claims and you need to prove that they happened.