Given that any angle is an indication that the building's centre of gravity is falling
No, it is an indication that a part of the building (and therefore the center of mass) is sagging. It doesn't mean total collapse is inevitable.
and that, according to OOS collapse theory, the building will collapse naturally
Once the mass of huge parts of the OOS is released the building will collapse "naturally". Imo it's legitimate to ask what happened before. Simple "knowledge" that enough of heat and enough of time and enough of airplane damage possibly and probably would have such effect is not enough.
I'm sure you would investigate the murder of a cancer patient. It's not enough to know that he would have died anyway.
I know, you will protest on that. You probably will say that the buildings collapsed exactly in the expected way. And I will say, no.
NIST tried a lot from pancaking to inward bowing to find any reasonable explanation. Pancaking was wrong. And the inward bowing theory is wrong as well.
So what pulled the exterior columns inward? The weight of noodled floor slaps 20 min after the fire started in a bowed area? Hard to believe but may be we will arrive there with evidence.
So far is was a good idea to split the overall process into observable stages and to find processes to explain the observable. If those processes are "natural" then fine. No problem about that.
It's a little strange that a whole bunch of individuals react like losing their mind about any question that aims to "what is visible" instead of "we already know because we read the report". This is more the behavior of a witch-hunt than any serious effort to learn or share or even defend knowledge. Imho that's the most suspicious part of it.
what do you think the measurement of any angle indicates?
It depends on when and where you measure the angle and of course how big that angle really is.
Example:
After the impact the building had to sag in the north just some inches until the loads are redistributed mostly via the spandrels to their neighbors. The resulting angle indicates a new stage of stability and not the inevitable total collapse.
It also indicates that the center of mass slightly leans towards north and towards the most damage. What ever happens next may or may not initiate a collapse but of course it would be much easier to force a collapse in a hundred different ways.
Given the death of 3000 people, is it legitimate to clear that up? ...especially if the "official explanation" lacks of some plausibility?
It seems that no one here has any real problem with the OOS theory. It's a "natural" process. It works. Any applause? Something like "Bravo stupid twoofer!" No. Loads of shouting and even naked HATE. Why? Probably because it focuses the questions on the very moment of initiation.
Does this line of inquiry have a purpose?
Yes, exactly that. "The good ones go into the pot, the bad ones go into your crop" no matter what the stepmom always said.
Is there a theory you have where the angle is significant evidence in favour of that theory?
No, at least not now. First it was important to know what we really see instead of having a theory what all that means.
Of course the angle is important. It's a difference if the angle reaches a point where a previously cold and straight column will exceed it's capabilities. It's a difference if only the antenna is leaning without any movement of the perimeter. It's important to know if the perimeter collapsed "straight down" due to excessive loads or if these exterior columns buckled due to tilting of the top.
We did a lot of measurements and everything points at the core collapsed first (all 3 towers) and took the perimeter down. So it seems that not the perimeter collapse redistributed extreme loads to the core as described by NIST but vice versa that the core redistributed extreme loads to the perimeter.
How? Oh, that question is not allowed here. How strong was the outrigger system to redistribute perimeter loads to the core for a virtually simultaneous collapse and a virtually simultaneous tilting? That's what the NIST theory requires, right? ...a very very strong outrigger system that redistributes the loads to the core. Otherwise it would probably look like a sequential collapse, parts of the perimeter, OOS, convex deformation of the hat truss, kinking of the unsupported core columns and so on.
Imo it lacks of a theory that describes what really happened to all 3 towers. And that's the point.
Is the OOS theory accepted? Can we move on? Or depends the acceptance on "where will it lead"?