12-D A Certain Magical Index

[Aseka]

11-D Justification
We at least certainly knew that Toaru's 11 dimensionality comes up from Teleporter's ability to calculate vector of space of eleventh dimension.

Shirai’s ability was called Teleport. It was not limited to three dimension rules, so she could move about freely within space.

However, there was a weakness to this ability. Though the phrase “to teleport within space” sounded simple, the theory behind it was to get away from the three dimensions, find her position in the eleventh dimension, and then calculate the vectors to teleport. Such calculations' complexity couldn’t be compared to the simple commands that ordinary espers would have, like “fire a fireball”, or “fire electric strikes”.

- Vol 6 Between the Lines 1

And how we can know if it's a higher dimension or not, because Curtana Original showed us that it can slice all dimensions, higher or lower, with All Dimensions Severing Spell, and causing a dimensional cross section.

She curtly swung down the sword.

In the next instant, Kamijou Touma saw a dimension being severed for the first time in his life.

Its range was a little less than 20 meters.

With a strange noise, something passed through along a line that Kamijou and Acqua had been on just a moment before. Something like a belt or a wall that was only about as wide as Curtana Original expanded. It was white and looked a little like a plastic model before it was colored. That object that looked not entirely complete appeared before Kamijou’s eyes.

“I could feel it when I was practicing before. This spiritual item is quite old, but its disposition seems to change a bit when someone wields it based on modern military knowledge. …Well, I’m sure my mother would be able to do something similar because she has the same nature.” A tone of enjoyment could be heard in Carissa’s voice. “Did you know that the cross section you get by slicing a 3 dimensional object is 2 dimensional? And slicing a 2 dimensional object creates a 1 dimensional cross section.”

With a clunk, the mysterious belt-shaped object that had been irrationally floating in the air fell to the ground right next to Kamijou.

It felt something like pottery, but it was actually extremely heavy despite how it looked.

Even after it fell, it continued to sink into the black soil.

“Similarly, when a dimension higher than our 3 dimensions is sliced, the cross section appears in this world in a 3 dimensional form. As a result, the ruins of a cross section appears like this.”

The second princess rested Curtana Original on her shoulder.

She was not attacking.

Even so, the dimension was sliced apart in the trajectory of her sword and a colorless belt-shaped object fell to her feet.

“This simultaneously severs every dimension at the coordinates whether they are higher dimensions or lower dimensions. It seems the only cross section objects created that we can perceive are the ones that can appear in a 3 dimensional world.”

(What…?)

Kamijou was completely dumbfounded.

If what she was saying was true, that sword was a monstrous weapon that could cut right through dimensions which did exist but were more of a concept than anything. No matter how much steel someone used to protect his body, Curtana Original could cut right through the dimension to cleave him in two.


- Vol 18 Chapter 5 Part 10

By this, we can conclude that at least currently Toaru have 11 dimensions.


12-D
If you read the scans above regarding 11 dimensions, you can see that Teleporter calculate a vector of eleventh dimension, it means a spatial dimension, because we know that generally a temporal dimension or time we usually say, doesn't have a vector. Time is a scalar thing, at least in Toaru they don't say that time have a vector. For one thing, Accelerator had reflected on the Teleporter's abilities before, which caused a strange phenomenon in three dimensional space.

When he reflected teleportation powers, a strange phenomenon occurred in the 3 dimensional world, but this had felt entirely different.

- Vol 20 Chapter 2 Part 10

And by this wiki, Teleport have kanji 空間移動 which means Spatial Movement.

So in this thread, I would like to propose that Toaru have 12 dimensions by counting the temporal dimension with 11 spatial dimensions.

 

[Axscell]

From what I understand here, I remember bringing this up once awhile ago, and the argument against it was that the dimension of time doesn't necessarily need to be the 11th dimension. It can the 4th dimension, and all higher dimensions above that can still be spatial. Unless there's something that proves contrary, I think the same point would still stand.

A better argument for higher-D, I believe, would have to do with countless individual phases being 11-D, existing within a higher-D world at large, similar to how Madoka Kaname got Low 1-C once upon a time (depends on if that is still a valid criterion for higher-D).

 

[Aseka]

From what I understand here, I remember bringing this up once awhile ago, and the argument against it was that the dimension of time doesn't necessarily need to be the 11th dimension. It can the 4th dimension, and all higher dimensions above that can still be spatial. Unless there's something that proves contrary, I think the same point would still stand.

By that standard, then we believe Teleporters using Temporal Axis as a vector to calculate, and this is contrary to general beliefs that Time don't have a vector, unless it stated. Because of that I mentioned that Teleporters calculate only Spatial Axis.

 

[Aseka]

A better argument for higher-D, I believe, would have to do with countless individual phases being 11-D, existing within a higher-D world at large, similar to how Madoka Kaname got Low 1-C once upon a time (depends on if that is still a valid criterion for higher-D).

As for this, we still don't know if there is a larger space that contained single universe with phases within.