1-
" The universe as a whole obeyed his script, and to a being who could realign the cosmos at will, a concept like time meant painfully little. By arranging the Milky Way, he could make it so that something never existed to begin with.", - Dies Irae, this states that Time is meaningless in the Realm of the Throne. This is further backed by,
"No one knew exactly how many stars flickered and lived in the world since the advent of foreknowledge's tyranny.---And now all of them are in the palm of his hand." - Dies Irae, all Stars that ever existed across his era of the Throne, even those long since dead, all were able to be called back. This was not the creation of stars, for it explicitly mentioned that these
were all the Stars from the past. This would in of itself imply that Mercurius, and by extension all other Gods, are beyond Dimensionality, time and space are basically equivalent after all. But this is ultimately not enough to extrapolate in a fictional context.
2-
"The Caduceus rumbled. He commanded the laws of the universe to do his bidding, emanating light and waves which exceeded human comprehension. All phenomena and all foreknowledge; all cravings and souls that existed within the world- save for the Goddess, the substitute, and the Gold and his Legion- were inside his dominion", this is to say that all concepts, apart from the transcendent, Taikyoku ones, are all completely under his control, this backs up the idea that it includes dimensionality.
3- "万象の根源として、総てを司る主として、真実のこいつが表出しようとしているのだ。 その場所とは、すなわち太極座。既存の法を流れ出させている事象の中心、宇宙の核だ"
4- "己が法則で森羅万象を制圧する太極と、己が法則のみ森羅万象から外れるという太極である", Taikyoku controls all things.
5- "険えるなら 、 絵の中でどれだけ猛火を描写しようと、それが現実の 人間を燃やせるわけがないのと同じ", -
Kajiri Kamui Kagura, this painting metaphor is quite consistent,
"No, I know it to be impossible. Once an Emanation begins, it expands to blanket all creation and reach permeance, at which point it can only be repainted by someone else.---At this moment, we are in a singularity. Owing to this phenomenon, the flow has been forced to a halt. The brush fell into the hole; the paint on the canvas is being neglected." -
Dies Irae, and
"It could be described with a piece of paper.---On it would be a picture representing 'Foreknowledge'--Two Fresh colours, 'Standstill' and 'the Dead', vied for supremacy upon one of its corners - The realm of Shambhala. Their struggle would be a ceaseless back-and forth, one painting over the other and vice versa.---The two colours differed in nature. "Standstill" was a pencil, while 'The Dead' amounted to the paint being released onto the paper directly from a tube. -- (skipped a little) -- The result was obvious.--- The combination of relentless pencil strokes and pierce recolouring tore open a hole in the paper before the picture was even close to being finished. Indeed - a hole. That was the result of reaching the critical point. Defining such a thing was no easy task.--- Though the picture served as the stage, the resulting phenomenon was neither picture, nor colour. To call it a singularity of the world would be most apt. --- The size of the hole was unknown. It could have been large enough to engulf Shambala, great enough to go beyond that, or perhaps, even small enough to fit on the tip of a needle.--- Regardless of its size, the singularity had manifested itself... and the ones responsible for making it appear to have fallen into it. What would they find below the paper?" -Dies Irae, the world is quite consistent shown to all be a Canvas in which concepts are painted upon, and which is like a harmless fiction compared to the Gods.
5- "何も難しい話ではない。前述した水中の法が太極と化したなら、全宇宙が水底に変わるというだけのこと。もしくは、宇宙を砕く領域の法でなければ蒸発も凍結もしない水が誕生するだけのこと" -
Kajiri Kamui Kagura, this says that Taikyoku Laws apply to All Creation, and when changed, fundamentally change and paint the entire universe and all phenomena in it are shaped un accordance with a Taikyoku Law. Dimensionality is shown to be able to be changed on an entirely local scale, and is not immutable, but every changeable. This is to say, it is under the control of any Hadou God. As any Non-Taikyoku Concept is under their manipulation.
There are various other quotes on this, most are in Kajiri Kamui Kagura, which is harder to get my hands on quotes from.
This is shown to be able to be to any degree, as the World can be expanded to higher dimensionalities, look at the higher dimensions in Paradise Lost, or how Yakou Madara was able to expand the world to higher dimensions in a localized space. This, however, is not able to reach the Throne through dimensionality alone. Nor even could they reach the Singularity through it, for the Singularity is, according to Dies Irae, "It was a perfectly blank slate. Harbouring no colour, but open to any, it was a fitting location for the final battle", this means that the Singularity is free of any "colour" or "concept/law", and the Singularity always lays beyond and transcendent to the World, backed up by,
"a single glance was enough for me to comprehend this place and its nature.--- Marie used to linger here, but the place was deserted once she had emanated with me. Visually, it remained the same, but if I were to borrow his words, it did resemble a picture frame. At its core, it was a completely blank slate.", furthermore
"She is the world's singularity. A being outside the boundaries of that law.-- She is dead, yet she is not. She exists outside this world's concepts.-- Perpetual. Eternal. Immortal. Divine. Infinite. Life beyond Death."
Thus, it really means nothing as we already knew that they are beyond dimensionality. And the true "spirit of the word" if you will, behind "Super-High Dimension" actually is in reference to being beyond such concepts. I hope this is enough to back up by viewpoint on this matter.