I still don't understand your intangible mental aspects claim. That seems a nonphysical, and really nonscientific subjective evaluation. You didn't go back in time and interview the builders, so how do you know what the intangible mental aspects were? It's guesswork.
Physical size isn't necessary, and I didn't mean to clean that it was. The more fundamental connection would be labor expenditure, and directed organization. There's a bunch of old cities in the Levant that were occupied for thousands of years and which developed into very large beehive-like structures. These aren't monumental architecture in the way a smaller, but purpose-built temple or city walls would be.
The connection to 'civilization', as I understand it, is that a social organization beyond mere family units making incremental home improvements over generations is required to build monumental architecture, so it directly implies the existence of some form of societal structure to organize the work. That's what turns a 'culture' into a 'civilization.'
That seems a nonphysical, and really nonscientific subjective evaluation.
We're talking past each other a bit because we're referring to different things with our use of "monumental" though. I'm talking about monumental as a way of understanding how the structure was perceived and used by humans. You're using monumental as a way of understanding to the social organization of the society that constructed it. This is much more in line with Childe's use that I mentioned earlier.
Part of the problem is that the scale and sophistication of social organization associated with the classical mesopotamian states is not at all reflective of what would have been going on with Gobekli Tepe. In other words, we wouldn't traditionally call the GT builders a "civilization" (civilization being a bad word that makes archaeologists cry).
So let's go back to the scale and grandeur thing. If we have to understand the intention, that's one of the tangibles encapsulated in my definition. What I'm saying is that it's the mental relationship between the human, the structure and the context that gives rise to monumentality. The physical structure can facilitate that creation by intentional design (e.g. large imposing size, etc), but it can also arise naturally or change over time.
We don't actually understand enough of the ancient world to definitively establish monumentality everywhere because our understanding of those intangibles is so patchy. The tower of Jericho was thought to be monumental for many years because of the obvious size and labor investment it represents. The thinking nowadays is that it had more utilitarian purposes and probably wasn't monumental. The structure is the same either way, the only thing that's changed there is our understanding of how ancient people would have engaged with it.