Perhaps we're approaching this from the wrong angle. Who have been the controllers of Snow-Throat? From the earliest point that we can assume, the dragons, specifically Alduin. The effect? Dragons held dominion over man and Skyrim almost as gods and they held a monopoly over the Thu'um. Next comes pre-Jurgen Windcaller Paarthurnax. This is the Paarthurnax of the Rebellion, who taught man not only the Voice, but also how to pour their emotions and fury to possess the world. This philosophy and form of the Thu'um overwhelms and overtakes the Dragons. Then the 1st Battle of Red Mountain happens and Jurgen Windcaller comes back chastened and the Nordic philosophy of strength of Thu'um will possess the world. He and Paarthurnax (presumably) start from the ground up and create the Way of the Voice and the Greybeards, teaching restraint and proper application of the Thu'um, not to possess the world, but to perfect their self. Nowadays, Snow-throat is controlled by the Greybeards, who is headed by Paarthurnax.
Are there any through-line symbols here? There's the Thu'um and it's use, but I'd say that that's more an effect of controlling Snow-throat. There's breath and Kyne and words, though excepting one of them, that's not a very tangible symbol. But, perhaps that's all that you need to control Snow-throat. After all, Snow-throat effectively became Human-controlled when they spoke "Joor Zah Frul" at it's summit, declaring to the world that mortality and the finite have come to stay. Perhaps Snow-throat doesn't have/need a stone, that all you need to control it is strength of will, surety of Voice, and a certain philosophy you can express through it.
When Nu-Hatta listed towers, one of them he called "Snow-Throat".
I think there may be four linked entities: the Stone, the Tower, the Land, and the People. There seems to be a pattern of Towers dominating the landscape of each Imperial province, and having a spiritual significance.
Although... considering... Towers prolly don't act identically to one another. Too simple. It's not so much the Mundus that they're holding up as much as a certain interpretation of the Mundus. We saw the Ayleids vanish after White-Gold was appropriated, after all. If Alduin built(?) the Throat of the World or merely destroyed its original stone and substituted himself, it'd explain why the pattern of dragons vanished from the world when he was time-blitzed; his interpretation was no longer being upheld. I suppose during the interim, then, Paarthurnax would have been acting as stone and... yeah. But still, I don't really like this.
To put it a different (better?) way, Towers hold up certain
qualities of Mundus (land, people, whatever pattern the controller favors) as well as just keeping the whole thing going. Not 'as well'; there is no division of function. The Towers hold up the Mundus because their controllers favor the Mundus. (
"http://www.imperial-library.info/content/nu-mantia-intercept" ) Even Alduin did, I suppose, while he was in power. If you go by things as they are presented in Skyrim. MD, you pretty much pointed out the trend (as others may have done). But that's not really the point of this topic, so, eh.
On Stones: if we go by http://www.imperial-library.info/content/nu-mantia-intercept,
"Let the Elders acknowledge this truth: every Tower bears its Stone. The impossipoint of the Convention was the first, though another bears the true title of First Stone." However, also,
"They are magical and physical echoes of the Ur-Tower, Ada-mantia. Ada-mantia was the first spike of unassailable reality in the Dawn, otherwise called the Zero Stone."This seems to imply that Ada-mantia itself is the Zero Stone. That, or the Dawn itself is being referred to as the Zero Stone, but I think that seems unreasonable. The earlier quote names the impossipoint of Convention itself as the Zero Stone. There seems to be some dissonance here, unless we view that Ada-mantia, Convention, and Zero Stone as one entity. I suppose it is named Stone after the fact because it is the foundation of Mundus' existence.
"
The powers also created Red Tower and the First Stone. This allowed the Mundus to exist without the full presence of the divine."
Nu-Hatta makes no mention of Lorkhan's heart, only Red Mountain and its First Stone. Or, Red Mountain
the First Stone, if the implications noted above carry any weight by metaphysical echo. Perhaps the physical differentiation between Red Mountain and Lorkhan's Heart was only due to the Dwemeri tonal machinations, which would explain why it vanished when those enchantments were destroyed. Perhaps the echo just slipped a bit away from the Zeroth Stone, I don't know. To my mind, there is a serious disconnect in the guy's words here, because the way this one is worded implies a difference between the stone and the tower. Convention and Ada-mantia
are the Zero Stone, but Red Tower and First Stone are not the same thing? Only way I think to explain it is echo-slippage; inexact reenactments.
Anyway, my point is that the document (seemingly) contradicts itself unless Towers and Stones are the same, and that metaphysical echoes need not be exact; i.e., not every Tower needs an explicit stone, and Snow Throat probably does not have one as a separate entity. I'm pretty sure we only know of 'Stones' for Red Mountain and White-Gold, anyway. I will submit a few quick theories; that stones are constructs more associated with controlling a Tower than its function; that Stone refers to the reality the Tower upholds; and that's all I've got for now.
EDIT: The Wheel on its side is the Tower. A Tower on its side is a point; a Stone. Different ways of looking at the same thing.