Toaru Majutsu no Index Explanation Page

This blog's purpose is to gather all the quotes related to the tiering and powers of Toaru Majutsu no Index's (Mainly the Magic Gods), with the goal of solving any doubts one might have of their capabilities while also making easier to access important quotes in case a discussion about them happens.
==Phases==
Before we can start explaining the Magic Gods, we have to talk about Toaru's cosmology. Phases work a little differently from a regular universe and misunderstanding them could lead to overestimating the Magic Gods. Because of this, this blog will try to simplify it as much as possible.
The World* in Index is not a pristine untouched world. Several layers have been applied on top of it, changing how things appear to be, much like a veil or filter. For a simile, imagine the World as a beautiful picture in a canvas. When you look at a picture, you're not seeing the canvas' surface or a single layer of paint, you're seeing multiple layers of paint at the same time, and even more layers are completely covered by the layers on the surface. These layers are the Phases. Just like the combination of paint layers makes up the painting, the combination of Phases makes up the World.
* From now on, anytime I use "World" I'm referring to the entirety of Toaru's cosmology, not just the physical universe, but also the various esoteric Phases that are part of the larger World. On the other hand, "world" will be used to refer to the physical universe on its own, since that's the most relevant.
The regular world we live in is defined by one of these Phases, but there's a lot more. Though the process has not been described, over the eras religions have added new Phases to the World.
Othinus talks to Touma about Phases
NT9 Between the Connected Points
“Have you ever heard of phases?”
“…?”
“This world was not pure and untouched to begin with. Christian, Buddhist, Celtic, Indian, Shinto, Incan, Aztec, Greek, Roman…and Norse. The various religions have placed layer after layer of various phases over the world like thin veils or filters. There is heaven, hell, the underworld, the Pure Land, Yomi, the abyss, Mount Olympus, the fairy island, Nirai Kanai, Asgard, and many others. At any rate, the world you have seen so far has been viewed through various colors of cellophane.”
Heaven and Hell were brought up very early in the series during the Angel Fall arc when Tsuchimikado gives Touma a basic explanation about where angels and demons stand in relation to the human world, the physical universe. Basically, they exist in the same physical space as the regular world, but they exist at a "higher" (Heaven) or "lower" (Hell) frequency, so people in the regular world can't perceive Heaven/Hell or their various inhabitants.
Tsuchimikado talks with Touma about Heaven and Hell
OT4 Chapter 1 Part 1
“…What angel? This is truly hard to believe. In this age, space shuttles can break through the atmosphere, and there’s no sign of a heaven…”
“Mm, the high and low relationship of heaven and hell isn’t of height.”
“Then what is it?”
“Here’s an example. Human eyes can’t see infrared rays, and human ears can’t detect high frequency sounds. You can understand this right, Kami-yan?”
“Ah? Mn.”
“The high and low refers to this, anything that’s above or below what humans can detect. They can’t feel it if it’s too high or if it’s too low. So even if God is to appear beside Kami-yan, you should be unable to detect it.”
Tsuchimikado delightedly smiled.
“Yeah. The low is referring to hell of the devil. What’s opposite infrared rays are ultraviolet rays, and low frequency in contrast to high frequency; in other words, an inversion. Though both waves are different, both are still waves. In other words, even if there’s an angel standing beside a demon, they won’t be able to detect each other unless they interfere with each other in the area between heaven and hell called the ‘human realm’.”
This description fits with the description of Hyouka's life whenever she's not in the real world and she's at the Imaginay Number District. This Imaginary Number District appears to be some kind of artificial Heaven that's being built by Aleister Crowley, and thus very likely some kind of Phase, though so far it's limited to Academy City.
Hyouka and the Imaginary Number District
OT6 Chapter 4 Part 3
When Kazakiri Hyouka had finally gained consciousness, she was already standing in the middle of the city.
The city didn’t mean Academy City. But in terms of coordinates, the location was completely identical to Academy City. It was a place built by the AIM diffusion field released by the 2.3 million espers within Academy City, the invisible City of Shimmers.
The City of Shimmers had no shadows, no weight, no air flow, it was extremely thin, there was no sense of existence. Once the wind blew, the towers, trees on the road and pedestrians would be blown away like the flame on a candle wick, and let out a grey visual signal that looked like a bug that mistook the camouflage color.
If there was anyone who could visualize an AIM diffusion field, the person would find that the City of Shimmers completely overlapped Academy City.
[...]
But if she took any action, it was likely that she would get others involved as well. Thus, Kazakiri could only stand around like a phantom, using her eyes to observe that same city that she couldn’t touch—Academy City.
The people in Academy City couldn’t sense her presence. Even if she were to stand in front of the students in Academy City and reach her hand out, she would pass through them. No matter how close the smiles of those students were, Kazakiri was unable to join in with them.
As seen with Hyouka, who's considered an artificial angel, Phases can have their own inhabitants. Heaven and Hell have God, angels and demons, but the others religious Phases house the gods and also the calamities from their myths/religion.
Marian uses Dainsleif to cut open Phases and summon calamities
NT10 Chapter 13 Part 3
(Heaven, Asgard, Mt. Olympus, the Pure Land, Nirai Kanai… Cutting away the homes of the gods removes the protection and blessings of those gods and thus releases the calamities being restrained by the gods. In a way, Marian is able to freely choose and wield the different “endings” told of in the world’s scriptures.)
Also worth mentioning is the Pure World, a mysterious world introduced by Othinus in NT9. The Pure World is a world beyond all the Phases and filters, the world of science untouched by religion and magic. Apparently not even Magic Gods can affect it, and Aleister Crowley is trying to tamper with it. Nothing else is known about it, but it will likely play a part on Aleister's plan in future novels.
Othinus talks about the Pure World
NT9 Between the Connected Points 
“The man who names himself the Silver Star seems to have been attempting to directly tamper with the ‘pure world’ beyond all the filters…that is, the world of science that is unaffected by religion. …Honestly, you are quite fortunate to see this. Not even the Golden cabal of Europe that dreamed in Tibet was able to reach this point.”
To summarize, Toaru's World is composed of several layers piled on top of each other, but the people in each layer can't interact with each other. Rewriting the world's state, despite the multiple layers, would mean rewriting only one timeline/universe, so it is only a Low 2-C feat.
== Magic God ==
Magic God (魔神 Majin, which can also be read as "Demon God") is the term used to refer to the magicians who have reached the pinnacle of magic. They have mastered magic to the point they can freely bend the world and its rules to their whim, trascending normal magic and entering the realm of God. Besides mastering magic they also require a special ceremony, which seems to vary from Magic God to Magic God, but appears to be closely related to them dying in some way.
Narration describes the concept of a Magic God
OT1 Chapter 1 Part 6
All living creatures would eventually die, an apple dropped from above would fall down, and 1+1=2. You would be able to take those kinds of natural and unchangeable rules of the world, destroy them, rewrite them, and create new ones. You could make 1+1=3, make an apple dropped from below fall up, and make all dead creatures eventually be revived.
Magicians called such a being a magic god.
Not the god of the demon world, but a magician who had thoroughly mastered magic to the point of entering the domain of god.
Fom this initial quote we know that Magic Gods are powerful reality warpers that can freely rewrite the world and its various physical laws. They can do this because Magic Gods have the ability to create, destroy and manipulate the Phases described above. If a Magic God decides to do make all the oceans green, they just change the Phase or add a new one to the world that makes that happen. If a Magic God doesn't like Heaven, Asgard or Fairy Island, they can remove those Phases from the world. In the painting simile we used with Phases, a Magic God is an artist who can paint over the canvas, changing any detail they don't like or making a whole new image all together. Besides Reality Warping this quote also has mentions of Physics Manipulation, manipulating life and death and changing math concepts.
==Dimensions==
It's made pretty clear that Toaru's world has at least 11 dimensions in the first series. Let's jump ahead to Curtana Original, which confirms the existence of multiple higher dimensions with its dimensional slicing spell, the All Dimensions Severing Spell. As the name says, it slices all dimensions, higher and lower. It's just that the only cross-section humans can perceive is the 3 dimensional one.
Curtana Original - All Dimensions Severing Spell
Vol 18 Chapter 5 Part 10
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.
From just this we have at least 4, likely 5 since Carissa says "higher dimensions". Now we go to Espers. Teleporters use their powers by leaving the 3 dimensional world, finding their coordinates in the 11th dimension and re-entering the world from there, skipping the process of moving in 3 dimensional coordinates by basically taking a shortcut (and also negating conventional durability like Curtana does). So we have 11 confirmed dimensions.
Esper Teleporters - 11th Dimension
Vol 6 Between the Lines 1
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”.
How does this apply to Magic Gods? We don't know 100%, dimensions are not mentioned much when talking about them. We have Othinus' teleporting arrow trick that's stated to be done by overcoming the restrictions of the third dimension and that's it. We do have another comment by Othinus that could be used to support their ability to control all dimensions. After Touma freaks out when St. Germain introduces "himself" as a Magic God, Othinus calms him down and reassures him it's not the case, explaining how St. Germain could have pulled his earlier tricks without needing Magic God powers by using only the ability to manipulate carbon.
Magic Gods Control of Dimensions
Vol 12 Chapter 2 Part 17
“Please wait!! He…he really did bend the entire world before my eyes! It was like…like this… It’s hard to explain, but the walls, floor, and ceiling all turned into weapons, tunnels appeared in the people in the way, and they all attacked me at once!”
“Have you forgotten?” Othinus sounded almost utterly exasperated. “This is the Dianoid. The entire building is made of carbon materials. That means you don’t need control over every phase, every dimension, and every element to manipulate everything around you. A magician with control over carbon and nothing else can pull that one off.”
Unfortunately since the Magic Gods appear to be done, this is probably all we'll get about dimensions with them.
==Othinus' Feats==
The first Magic God to appear in the series is Othinus. She suddenly appears in NT4 after Touma defeats Marian, casually crushing Touma's wrist and taking out the Invisible Thing when it comes out with her bare hands. The Invisible Thing was not at the same level as it was on WWIII by her own admission, but this is still a thing that made Fiamma, someone capable of destroying planets, feel completely worthless and insignificant.
Othinus stomps the Invisible Thing
NT4 Profound Destruction
Suddenly, something changed.
Something invisible blew out from the crushed remnants of Kamijou Touma’s right wrist. With a roar, it shot toward Othinus without taking any real form.
However…
“…Is that all?”
Othinus’s bloody hand grabbed something.
The one-eyed witch tilted her head to the side in confusion.
“It seems you produced decent results during the final stages of World War 3, but is this all I find when I open the lid?”
She carelessly crushed it.
The invisible power writhed and seemed to try to flee from Othinus. But it was too late. She poured more strength into her bloody fingers and this time the invisible power was torn apart and disappeared into thin air.
Minor stuff which is not mentioned in her current profile, Othinus' presence creates a very powerful aura of fear that leaves Maria paralyzed. Reminder: Maria, the one describing the fear aura, just got through experiencing Dainsleif, a magic sword that kills people by inducing them with so much fear of seeing its blade drawn that their body gives up and their heart stops beating to avoid facing it.
Aura of Fear
NT4 Profound Destruction
Kumokawa Maria was unable to move.
The great amount of red blood made her feel dizzy.
But before that, the one-eyed witch who had suddenly appeared was simply too frightening. This was different from Dainsleif. The feeling was different from that easily understandable surface fear. It slipped into the deepest portions of people without them noticing and the next thing they knew, strength had left their limbs.
It was like how domestic violence carried out behind locked doors was accepted as the normal routine even by the victim.
It was like the climax of a discussion about who to eat first while in a small snowed in cottage when there seemed no hope of rescue in the near future.
It may have been described as a great fear, but it was not something that could be rejected on the surface like it was a flame that you reflexively pulled your hand out of. This fear permeated you so deeply that it created a cycle that at a normal time you would immediately realize was strange. Just by standing there, the one-eyed witch could likely even destroy the morals in the hearts of all those around her.
For example, if an army was going to fight that one-eyed witch, it was possible the soldiers would get into a fight over who would be forced to stand before her and they would end up killing each other.
Othinus destroys Dainsleif, but she's confronted by Ollerus. The two exchange a powerful barrage of invisible explosions.
Wall of Invisible Explosions 1
NT4 Profound Destruction
A tremendous explosive noise burst out between Othinus and the blond young man.
Actually, it was not just one. Thousands and tens of thousands of explosive noises burst out at such short intervals that they all sounded like a single whole.
However, Kumokawa had no idea what had happened.
She saw no visual phenomenon.
Fiamma appears to back up Ollerus. The rest of the fight is not shown, but it apparently ends in a draw and Othinus retreats. One may ask: Why does she retreat from Ollerus and Fiamma despite the Magic God powers she has? Well, at that point Othinus couldn't wield her full power freely, because her power is too vast. Magic Gods can do anything, they have access to all possibilities. But in order to truly have access to all possibilities, you have to hold both the positive possibilities ("my spell works" or "I changed the world the way I wanted to") and the negative possibilities ("spell fails" or "defeated by a small kid in a fight"). Negative possibilities might also carry a backlash on her body, as we'll see in a future quote. This is why she initially relies on her organization, Gremlin, and chooses to partake in complex plans despite being one of the strongest individuals in the Magic Side by far, and thus, perfectly capable of steamrolling most of the verse on her own.
Ollerus talking to Othinus
NT4 Profound Destruction
“It isn’t that either. You know that. You may be a Magic God, but you are not perfect. Or rather, you are too perfect and that gives you a troublesome characteristic. You know that and that is why you have put together this exaggerated plan to free you from that dilemma.”
“…”
“Infinite possibilities sounds good, but that gives you both the possibility of success and the possibility of failure. I suppose it’s something like matter and antimatter. For everything, you must hold the possibility for success and the possibility for failure. No matter how much power you gather, you have a 50/50 chance. If you think of it like Russian roulette, it’s like taking a shot with three bullets loaded. Let’s be honest, Othinus. While you possess the power to destroy the world, you also have a 50% chance of losing to a child in a game of rock-paper-scissors. It’s almost a miracle that Kamijou Touma has lost twice. His misfortune must really be something. But given this condition, you cannot just wield your full power at random. You want to find a way to control those possibilities. Wanting to increase your possibilities for victory is natural, but when your possibilities for failure increase too, you need to find some way of dealing with that. 50/50 is the most troublesome of all.”
Ollerus talks to Touma about Othinus
NT6 Chapter 1 Part 5
“But a Magic God can do anything, right? Does she really need to rely on others?”
“Being able to do anything is the problem in and of itself.” Ollerus gave a cynical smile as if commiserating with a colleague. “You often hear talk of ‘infinite possibilities’, but that truly means you have as many negative possibilities as you do positive possibilities.”
“?” 
“This may be a bit hard to understand for someone at the age where you still believe in infinite possibilities. Just think of flipping a coin. The odds of getting heads or tails are 50/50. That is the true identity of ‘infinite possibilities’. Whenever you take an action, you carry both the possibility for success and the possibility for failure. No matter how hard you train, you still have 50% odds of losing in a fight to a child. That is what a Magic God is.”
50% was quite large.
In terms of Russian roulette, that would be starting the game with 3 live bullets.
This is obviously a big issue for Othinus, who's only interested in her good possibilities, and wants to get full 100% odds of success/victory. How does she try to do this? As a Magic God from Norse Mythology, where the power of the gods is closely related to their personal items, she needs Gungnir, the holy spear that symbolizes the head god's power. This is the main plot for the Othinus arc.
I'll now list some other feats and quotes prior to her acquiring the spear.
Othinus reconnects her arm after it falls off when her negative possibilities do their thing
NT6 Epilogue
The connection at the joint seemed to be completely ignored as the arm started to fall.
“…Tch. So it ended up in the negative 50% of the infinite possibilities.”
Before the arm could completely fall off, Othinus forcibly held it in place from over the mantle with her other hand. A wet dripping sound could be heard. It seemed she had lost a lot of blood beneath the mantle, but the Magic God’s expression did not change. Even a wound as ridiculous as that might not last for long.
Reminder of Othinus' Power 1
NT8 Epilogue
This blonde-haired, green-eyed girl had one eye covered by an eyepatch and wore a witch’s hat and cape. Despite her lovely appearance, she was known as a magic god and held the power to end the history of humanity at any moment. She was a rare life form that sought that lance not because she lacked power but because she had too much.
Wall of Invisible Explosions 2
NT8 Epilogue
An instant later, the slight space between them was filled with tens of thousands or even hundreds of millions of strange explosions.
If the theory of relativity that summarized the relationship between time and space would allow a black hole-like object to exist under certain special circumstances, the extreme compression of space by their frightening clash may have twisted the continuity of time.
That was how extreme this series of attacks was.
A wall of explosions completely filled the space between those two monsters. It showed no sign of ending and seemed to completely ignore the concept of numbers.
After this exchange Ollerus attacks Othinus with the Fairy Spell, a brand-new spell he created that uses the concept of Christianity turning pagan gods into lesser creatures like fairies and demons to depower divine entities. Magic Gods hit by this spell are forcibly brought down from their position as gods, and it would turn their even odds of success and failure into a 0% chance of success. There's also another reminder of Othinus being so strong that even if all humanity banded together they wouldn't be able to defeat her, this including all the strong individuals like Ollerus and Fiamma living in the world.
Reminder of Othinus' Power 2
NT8 Epilogue
“Even if all of mankind worked together, they would have no way of opposing the being known as a magic god. And that simple truth does not change even when one includes those of us who only barely remain within the territory of a human,” said Ollerus.
Despite the surprise attack with a new spell, Othinus used her magic to mess with Ollerus' senses and make him think he landed the blow when he had actually missed it. This is manipulation of the enemy's physical senses in a very subtle way. Additionally, Othinus shows the ability to immediately copy the Fairy Spell she has seen once. From this we can deduce that she and other Magic Gods can likely copy any Toaru spell they see in use, which makes a lot of sense since they have mastered the verse's magic system.
Othinus manipulates Ollerus senses in a subtle way and copies the spell he invented after seeing it once
NT8 Epilogue
That was why it took him a moment to realize it.
Despite having pressed his palm against the center of the magic god’s chest and having fired the stake of light into her, the tip of that stake had not stabbed into Othinus. It was not that a thick wall had appeared to stop it. Ollerus’s senses told him it had long since extended all the way out, but Othinus’s senses said it was only partway out.
“It is a simple thing, Ollerus. A truly simple thing. I deceived your senses. You gave your victorious speech before you had pulled out your secret weapon. That is all. And once you know the trick, sleight of hand has nothing left to surprise you.”
“!!”
“Also…”
Ollerus frantically tried to pull his arm back, but he was too slow.
This had been a one-shot suicide attempt. He had given no thought to a way out.
Magic God Othinus did not hesitate to grab Ollerus’s wrist.
“I can make use of this now that I know it exists. It may have been a waste of time for you, but it is an unexpected reward for me. After all, I finally have a way of finishing things with this damn annoying person from my past! You brought the means of your own defeat!!”
A great noise rang out.
Othinus had slammed her other hand against the young man’s chest. Her hand was palely glowing. A sharp stake of light stuck out from her palm, thoroughly destroyed the interior of Ollerus’s body, and forcefully shot out his back.
Fortunately for Ollerus, Fiamma is also there. Fiamma uses his ability to hide his presence to backstab Othinus with the Fairy Spell. However, Othinus dashes their hopes by being happy about it, since she can also use the 100% chance of failure the Fairy Spell forces on her for her plans. All that mattered to her was unifying her possibilities, one way or the other, so that she could be sure of the result of her actions.
Othinus talks about unifying her possibilities
NT8 Epilogue
“I only needed it to lean in one direction or the other,” she announced as a grin split across her face. “It did not matter if I completed the lance and gained 100% success or became a fairy and gained 100% failure. My actions were sealed by the constant 50% balance between success and failure. I could never know if my actions had achieved heads or tails, so I could never know if I could build on top of that action. Moving forward with constant heads is one possible path. But if I know every path I choose will come up tails, I can achieve 100% success by always moving in the opposite direction of the path I choose!! Failing as a magic god acts as a guidepost towards success as a magic god!! …You two meant nothing from the beginning. Whether I won or lost, you could not stop me from becoming a complete magic god!!”
Othinus promptly demonstrates this by using her powers to create Gungnir from nothing, revealing she could have done it on her own and Gremlin's plan was just a decoy.
Othinus uses her powers to make Gungnir on her own + another regeneration feat
NT8 Epilogue
Kamijou heard a sound like a rock landing in some mud.
It came from the head of the blonde-haired, green-eyed girl named Othinus.
The black eyepatch was pushed out from within. An object covered in a dark red liquid shot out from the empty eye socket. It continued on and on.
“Ha ha ha ha!! Ha ha ha ha ha ha ha ha ha ha!!”
The magic god laughed arched her back.
An unpleasant noise rang out.
The tip of the lance was not a sharply pointed blade like on a knife. It was a wide blade as if a double-edged sword had been forcibly attached. What would happen if that was forcibly dragged from her narrow eye socket? The sound of a joint popping continued on and on with a sticky sound mixed in. No, that was the sound of something breaking and splitting. Her eye socket may have been spreading and distorting like a hole in a rubber band. It may have even grown larger than the girl’s small face.
[...]
A lance covered in a dark red liquid made its horizontal entrance into the world.
Othinus grabbed the Gungnir she had produced from within her own body and looked down on Kamijou once more.
Her face had returned to normal.
Had it truly possessed the strange elasticity of rubber?
Or had she somehow instantly repaired her smashed and destroyed skull?
What is Othinus' first action now that she has Gungnir and full control over her reality warping powers? As a reality warper as powerful as her, she doesn't actually have to fight fair with all the other enemies present or in the way to fight her, so she uses her powers to destroy the world, thus ending any possible fight.
Othinus destroys the world 1
NT8 Epilogue
Magic God Othinus lightly spun the lance around in one hand and pointed its tip toward the heavens.
She spoke slowly.
She uttered two short sentences.
“These small fights are such a pain. I think I’ll just end the world.”
And exactly as she had announced, everything was immediately destroyed.
That line is followed by two black pages, then the novel ends. NT9 starts with a recap of the prior novel, ending with this.
Othinus destroys the world 2
NT9 Prologue
Kamijou tried to deny Othinus’s words in an attempt to look away from the hopeless situation, but Othinus’s reply was one of disinterest.
“These small fights are such a pain. I think I’ll just end the world.”
Immediately afterwards, everything in the world was truly and seriously destroyed.
We can see that the novel makes it clear Othinus did destroy the "world". But we all know that word can get pretty confusing sometimes. How do we now it doesn't mean "planet" instead of "universe"? Because Othinus herself corrects Touma in his hope that something is still there.
Touma wakes up in the black world and tries to deny reality
NT9 Chapter 5 Part 1
Once he sprang to his feet, he was left speechless. Everything around him was odd. It was black. Nothing but black. The ground was perfectly flat. It was even more level and free of defect than the silicon wafer for a semiconductor. From where he stood to the horizon, the ground did not rise or fall by even a micron.
“What is this place?”
Nothing natural could be seen. Nothing unnatural could be seen.
Despite the previous use of the word, it was unclear whether the term “horizon” even applied. Both the ground and the sky were colored pure black, so it was impossible to distinguish between them.
He turned around a full 360 degrees, but the scenery did not change. He stopped at the spot he thought he had started at, but he was not even sure that was correct. With nothing to use as a landmark, he could not be sure.
[...]
“You’re lying!! You, um, used some kind of trick to make it look like that’s what happened!! That would be easier. Instead of destroying Tokyo Bay and killing all those people, it would be easier to bring me to some other place!! So…!!”
“It no longer matters how you perceive the situation. Who it was that disappeared is a trivial matter. The problem that lies before you is that only the two of us are here,” said Othinus disinterestedly. She sounded like someone who had downloaded an app to kill time late at night but found out it was even more boring than expected. “And you seem confused as to the scale we are talking about.”
“What? Are you saying there’s more?”
“Why are you talking about this on the tiny scale of Tokyo Bay? What I destroyed is not contained to just the small planet known as Earth.”
It must be pointed out that, while the usual shonen power creep is not 100% valid in Toaru due to the mostly static power levels of 99% of the characters, the prior main villain Fiamma was already stated to be capable of destroying Earth, and we've had Gabriel playing with the Earth's rotation and multiple stars since volume 4 of the first series. This scalation, given how much magic gods and Othinus were hyped by the narration and characters like Ollerus, makes sense
Touma, still denying reality, tries walking in a single direction calling for his allies, hoping he'll leave Sargasso and find... anything/anyone besides Othinus in this black flat world, though to little success. Touma finally decides to confront Othinus. Othinus is not interested in fighting him and decides to use her powers to break him mentally, thus rendering IB useless. Othinus then proceeds to torture Touma with several "worlds": one where he's public enemy #1 and everyone on Earth, even friends and his parents, wants him dead; another where a second Touma has replaced him and nobody notices anything, going on with their lives. During these worlds Othinus appears out of nowhere in several occasions just to taunt him before dissapearing again, demonstrating Teleportation. We also have Othinus stopping/slowing down time to a crawl just before Komoe kills him in the first torture world.
Othinus messes with time to taunt Touma
NT9 Chapter 6 Part 3 
It seemed like time had stopped.
Or perhaps only this place where Othinus was had changed.
It may have been like a waking dream or when one’s life flashed before their eyes.
[...]
The girl known as a Magic God gave an exaggerated snap of her fingers.
In the next moment, time sped back up to normal and Tsukuyomi Komoe swung the knife forcefully down.
After the second world (impostor Touma world), Othinus is a bit angry about Touma managing to hold up, so she forces him to go through countless more worlds. This gives Touma the opportunity to realize something.
Othinus' Creation
NT9 Chapter 6 Part 8
“But how many cards do you think I have in my deck?”
“…”
“Do you think it stops in the mere tens of thousands?”
[...]
“You aren’t actually destroying anything.”
Othinus seemed surprised that he was only now realizing this.
The blonde-haired, eyepatch-wearing girl stood directly in front of the boy.
“So?”
She was so close that he thought he detected a sweet aroma.
The world had become a vague marble pattern.
“There aren’t thousands or millions of worlds. This is still our world. This whole time, we haven’t moved anywhere.”
“Why are you acting like you know what you are talking about? Also, I do not recall saying anything about parallel worlds.”
He did not know how it worked.
But the world’s point of view was changing. Othinus was changing it. Kamijou was merely experiencing what was around him, so it appeared to him he was travelling to completely different worlds.
Othinus is changing the current world, not creating new ones that run parallel to the old ones. If you remember the painting simile, the black world is her painting the canvas white, so there's nothing left (using reality warping so the world dissapears). She then paints a whole new layer of painting (creating a Phase and layering it on top of everything else), which becomes the new surface of the canvas (the world switches accordingly to Othinus' Phase). Before the obvious question "Othinus admits to not destroying anything, how's she Tier 2?!" can be made, this is adressed in the series. Instead of using raw power, Magic Gods like Othinus use their reality warping powers to change the universe from the "exists" state to the "doesn't" one. Even she admits that she does this because it's simply easier than to destroy everything and rebuilt it every single time she wants to do something:
Othinus Explanation
“Call me a god. And what I have done is simple. I have created new filters and placed them over the world so the world appears to have changed. That is why the world appeared changed to you. This is a lot easier than destroying everything and building it back up every time. And your right hand contains the power to level out any foreign elements in the world, so it has difficulty functioning when I change the world itself. …Still, results are everything in the world. In the end, history will record it like this: the Magic God repeatedly destroyed the world and created new ones to make a single boy suffer as much as possible.”
Even the novel's narration points out this is a matter of semantics (and the author really wanting to do the "Create vs Break" thematic with Othinus vs Touma). The universe ends up destroyed anyway.
Othinus' Creation 2
NT9 Chapter 8 Part 7
Magic God Othinus had the ability to create, so she was technically not destroying anything. This may have been a change brought about by adding a new phase into the world. Nevertheless, it was blatantly obvious what the scene before Kamijou’s eyes would produce. It was the same as referring to the utter destruction of a luxurious palace as “creating a pile of rubble”. This was undeniably a torrent of destruction.
We've established Othinus' Universe level+ Reality Warping. There's still some feats from the "fight" between her and Touma. From now on all quotes are from NT9 Chapter 8.
Space Carving Attack
Othinus never moved from that one spot.
She merely held up her lance.
That was all.
A giant hole opened in the night sky.
It looked like a pitch black moon.
Something had split open. Kamijou caught a glimpse of that evenly black world he had seen before.
No warning was given.
That moon merely fell toward the schoolyard to crush a single boy.
[...]
Kamijou leaped to the side with all his strength. He could not worry about appearances. He merely rolled along the dirt to move even a centimeter or millimeter further from that whirl of destruction.
All sound vanished.
A hemispherical crater ten meters across appeared in the ground. This was not the scar left by an explosion. That space had been carved away in the exact shape and size of the black moon.
Body Manipulation? Telekinesis? Othinus can simply break Touma's body
After switching over his train of thought, he sharply altered his direction as if switching the position of his feet around.
(I need to find a way to get close to her!! If I can get right up to her, she’ll have to let up on the massive attacks for fear of hitting herself! I only have my fist. Whether I’m attacking or defending, I can’t do anything without forcing down my fear and moving in to-…)
“Too slow.”
Othinus’s lovely voice was accompanied by the sound of Kamijou’s knee bending in an odd direction.
Matter Manipulation, Time Manipulation, Fate Manipulation plus manipulating cosmic bodies like Gabriel on steroids
Magic God Othinus could control everything. Without exaggeration, she controlled the world itself. If she wanted to, she could have galaxies collide to kill Kamijou Touma. Or she could break the bonds between the particles making up his body and cause his very existence to disperse. If she was the slightest bit dissatisfied with something, she could turn back time, re-lay the rails of fate that led to the future, and create the exact result she wanted.
Invisible Explosion + Invisible Cutting Attacks
Just as she lightly bit the edge of her lip in irritation, half of Kamijou Touma’s body was blown away like sherbet.
[...]
In the next battle, that was all he could say before his torso was sliced apart.
[...]
She used an invisible power to split that impudent boy’s top half from the bottom half.
[...]
An invisible cutting attack shot right by Kamijou Touma and blasted the reinforced concrete school building behind him to pieces.
(Turning the stars in the sky into arrows of light):
The twinkling of the stars in the sky was an ominous ill omen.
Each and every one of them transformed into a sharp spear of light and poured down like rain.
===Gungnir===
We already discussed that Gungnir passively allows Othinus to raise the probabilities of success of her powers to 100%. But she can also use it as an offensive weapon, in which case besides the usual magic traits of "always hits", "returns to user after thrown", etc; we see that the instant it leaves Othinus' hands it destroys all Phases of the world, returning it to the black world, the blank canvas. It then gathers the pieces of all those destroyed Phases into a whirl of destruction to crush the enemy. It also stops time and compresses space for a second just before activating, but that's just a side effect and thus not actually used for combat.
Gungnir Throw
(Gungnir Throw):
It ended after one step.
A whirl of destruction burst out.
Time stopped.
Space was compressed.
The standard concepts of time and space no longer had any meaning.
The lance of the head Norse god was named Gungnir. Its handle was made from the wood of an ash tree, the same as the world tree, its sharp tip was made from gold, and it had tremendous power due to the runes personally carved into the Dvergr-made base by the head god.
It had a few different characteristics.
1. The lance was made to be thrown.
2. The lance would always hit its target once thrown.
3. The lance could not be shot down or destroyed mid-flight.
4. The lance would always return to its owner’s hands after piercing the target.
[...]
And even with all of those characteristics, the lance of the head Norse god had yet another characteristic that put it a clear step above the weapons’ of the other gods.
5. That lance would destroy the symbols of human power.
[...]
Rather than showing simple destructive power by blowing away a mountain or vaporizing the sea, it bluntly indicated the precedence of the god.
In other words, the instant that lance left Othinus’s hands, the world would be blown to pieces.
Time returned to normal.
Kamijou once more felt space spread out around him.
As the lance was fired with tremendous force, the “happy world” was smashed to pieces as if space itself was being torn apart. As a fragment of the world approached with the force of a raging wave, it took on the shape of a giant lance. The walls of all the phases were crushed, transformed into a swirl of deadly weapons resembling sharp shards of glass, and approached their pitiful target as if to swallow him whole.
Everything was ripped up.
The black labyrinth, which had used up all of its possibilities, showed itself.
===Crossbow Arrows===
Othinus refuses to give up after Touma breaks Gungnir, so she pulls out her last card, the spell based on a minor legend associated with Othinus about a crossbow which can hold ten arrows and can exterminate any army.
Othinus readies her crossbow
The entire world could be heard creaking.
Kamijou looked up slightly.
He saw the disturbing symbol bursting from Othinus’s back and providing the color of light to the entire black world it covered. He heard the creaking sound of it gathering tremendous power.
In the end, the world was her crossbow.
As soon as Kamijou Touma realized that, ten pieces of destruction rained down from the heavenly dome above.
(Power of the Arrows)
…The first shot fell vertically from the heavens.
It held the destructive power needed to easily wipe out a planet or two, but it was beyond the point of creating anything like a crater. This was no different from a rifle bullet fired with the initial velocity of a sniper rifle piercing glass without breaking it. The arrow had been fired with such great speed that it pierced the pitch black ground without waiting for the impact to propagate.
Othinus can pretty much shoot the arrows from any direction (the world is literally the crossbow itself). She can also apply some special effects to the arrows, like multiplying the shot into so many "it ignored the concept of numbers" and teleport them by breaking through the third dimension.
Other Arrows
…The second shot seemed to skim the ground as it was fired behind him and diagonally to the left.
Kamijou crouched down and the arrow passed over his head and swept across the world. Its trajectory was angled downward slightly and it created a giant valley in that black-dyed world.
[...]
…The third and fourth shots burst up through the ground.
[...]
…The sixth and seventh shots scraped across Othinus’s shoulders.
The two arrows were fired from behind her and they collided in midair before reaching him. With a tremendous explosive noise, the two arrows’ trajectories changed complexly. The boy evaded one by ducking his upper body down and then jumped over the other with a great leap.
[...]
…The eighth shot overcame the restrictions of the third dimension.
Kamijou felt a static electricity-like spark on his spine and immediately swung his head to the side as hard as he could. An instant later, space suddenly split open and an arrow assaulted the world.
[...]
…The ninth shot ignored the concept of numbers.
The arrows that fell from above colored the night sky like fireworks and glittered like stars covering the heavens. Every single one of them was fatal, but Kamijou did not freeze up. No matter how torrentially they rained down, there was always a safe space left to step in. 
===Regeneration===
As we've seen in some of the feats listed above Othinus has basically three regeneration feats: reconnecting an arm that was falling off, healing her skull and face in an instant after pulling Gungnir out of her eye socket and this one with her tenth crossbow arrow.
Othinus regeneration feat
NT9 Chapter 8 Part 8
In other words, the arrow unhesitatingly pierced through Othinus.
The final arrow broke through the girl’s entire body and assaulted Kamijou from the blind spot directly in front of him.
“…Ah.”
Time stopped.
He was too slow to react.
By the time he heard a dull sound, the final arrow had already been absorbed into his chest and accurately targeted his heart.
This was nothing as kind as piercing or breaking him.
In the instant of impact, Kamijou Touma’s body was smashed to pieces from the chest down. As his heart continued to writhe in midair, the tip of the arrow caught it and blasted it to the farthest reaches of that world.
All that remained in that place were the boy’s arms, shoulders, and head.
At that level, this could only be called his remains.
Kamijou’s “body” spun at least twice through the air and Othinus caught it in one hand.
She had supposedly taken the exact same damage, but not so much as a single scratch remained on her smooth skin. The destruction had indeed occurred, but the wounds had immediately repaired themselves like watching the destruction of gelatin in reverse.
So, a solid "at least Mid Regeneration". It sounds a little low for a Tier 2, especially since we have the much weaker Gabriel regenerating from collapsing into pure energy. But there's an interesting quote from Othinus. At the end of NT10, she and Touma are too late for her to give up her powers and avoid dying from the Fairy Spell, so her body crumbles into light particles.
Othinus "Death"
NT10 Chapter 20 Part 3
He saw light.
He saw particles of light.
By the time he noticed the change, he could no longer feel the girl in his arms. Her slender body crumbled. He could not understand it. Her crumbling body was more fleeting than snow. It turned to smooth particles of light as it fell to the ground and those were swept away by the wind.
True Gremlin, who is not interested in the ramifications this loss would cause in Touma, prevents her from vanishing, gathering a small part of her body to put her back together in her miniature body. The interesting thing is that Othinus doesn't question the event itself, she's surprised that her body reforming like that happened without her making it so, implying she can pull off that level of regeneration when she has access to her powers. Of course, the magic gods of True Gremlin should scale to this level of regeneration.
Othinus Implied Regeneration
NT10 Epilogue
“At that point, Magic God Othinus was 99% destroyed, but it seems the remaining pieces gathered together on their own. My body changed form somewhat and I can no longer use my former power, but it seems I have remained behind.”
It was absolutely ridiculous.
The idea of a human gathering together again after being smashed to pieces sounded like complete nonsense, but he could not question it further when he was talking about a magic god. If Othinus said that was how it worked, he could only accept it.
In fact, he himself had seen it happen before.
In that infinite hell, she had hidden the final crossbow shot behind herself and pulverized her own body along with his, but her body had soon regenerated as if nothing had happened.
(But would my body “automatically” re-form with no intervention from my will? I still have my questions about that.)
==True Gremlin==
To finish this blog we'll go over the Magic Gods from True Gremlin, basically explaining their tiering and why they have Immeasurable speed.
===The Hidden World===
These Magic Gods resided in a special layer they created for themselves. This layer was something not even Othinus managed to destroy when she wiped out all other Phases and made that black world. Though that may be because she didn't know it existed at the time.
Hidden World 1
NT10 Epilogue
Othinus and Kamijou Touma had been wrong about one thing.
They had thought that world of darkness had been the full extent of the world. They had assumed that pitch black despair had been the product of destroying everything and leaving nothing at all behind.
But in truth, there had been one more layer. It was as uniform as a thin membrane, it had not even the slightest seam, and it could not be detected or destroyed by anyone, but one last phase had existed.
This black world was the place not even Magic God Othinus had been able to destroy.
The place technically doesn't exist as a place would normally do, and the concepts of distance and time don't matter there, as the tiniest gap extends to an infinite distance. Thus, Immeasurable speed.
Hidden World 2
NT10 Epilogue (Hidden World 1):
It may have been wrong to refer to that place as dark. In fact, the word “place” was not entirely accurate either. Non-existent things could not be explained. Nevertheless, a few voices lurked within where no one could interfere.
[...]
“The concepts of distance and time don’t matter here, remember? And I can’t leave regardless. Even if I did, I’d just end up gathering unwanted attention on a global scale like Othinus. I was a hair’s breadth and an infinite distance away.”
“Does the same go for the others?”
“Old man, did you start forgetting things once you became a mummy? The zombie girl, the chimera, and everyone are here. It’s just in destiny’s hands whether we run across each other in this place where the tiniest gap extends to an infinite distance☆”
[...]
“Letting Othinus run free would have been a problem, but I left that to the strength of the world. The world was temporarily led to destruction as a result, but I still had to prioritize this. It wasn’t easy converting coordinates filled with non-existent numbers into decimal.”
This is repeated in the Prologue for NT12 as they prepare to leave the hidden world.
Hidden World 3
NT12 Prologue
Darkness covered the entire area.
Not only could one not see an inch in front of their face, but the darkness seemed to pass through their eyeballs and bear down on their mind.
However, the people drifting through that darkness showed no concern. They implicitly said that this was the natural state of the world or that someone had yet to whisper “let there be light”.
Direction and depth were indistinguishable in that black space, but three distinct presences existed there.
===Zombie Spell===
We've already established Othinus is a Low 2-C by being able to reality warp one universe/timeline. But why are these Magic Gods infinitely stronger than her? Well, let's start by explaining Zombie's Spell. At the end of NT10 Aleister shows up on their hidden world, tearing a seam on it and ruining it for them.
Aleister ruins the hidden world
NT10 Epilogue
Their safe territory was gone.
They would now be thrown out into the existing world and pursued by the people who lived there.
NT12 Prologue (Aleister destroyed the hidden world):
“Honestly, why did Aleister have to thoughtlessly destroy our hidden world? Maybe we really should’ve killed him.”
But there's an issue with them stepping into the regular world. Their existences are too big to be contained by the world, unlike Othinus. Even if they don't want to, they'd be destroying the world everytime they wave a hand or take a step.
Too big for the world
NT10 Epilogue (Too big for the world):
“If you think about it, you could call this our way of being ecological. We do it because the world is too small for us to live in, but it isn’t easy putting up with being here.”
To solve this they relied on one of their own, Zombie, who came up with a spell that would divide and layer their existence infinitely, weakening themselves so that they can act normally. Some of them like Niang-Niang weren't completely sure that it'd work until they tried it themselves.
Zombie's Layering Spell 1
NT12 Prologue
“But, High Priest,” cut in a girl’s voice that sounded even younger and also childish. “Miss Zombie’s theory is essentially the same as holding up opposing mirrors, right? By splitting up our power infinitely, we can intentionally weaken ourselves and avoid destroying the world whenever we move an arm or leg.”
“What about it, Niang-Niang?”
“I’m just wondering if the symbol ∞ will really grow weaker when you split it up. I don’t want to smash the world up like stained glass the first step I take. We’re not like Othinus.”
“It doesn’t matter if it’s a mere deception as long as it works. Just like a Moebius strip or a Klein bottle, some concepts are allowed to exist even if they can’t be properly defined, Niang-Niang.”
Zombie's Layering Spell 2
NT12 Epilogue
“The Voodoo Zombie did an excellent job. I’m sure of it now that I’ve walked around the area a bit. The spell has adapted to our bodies, so now we can move through the world without breaking it.”
“Nee hee hee. Splitting up our power like opposing mirrors, huh?”
Niang-Niang laughed like a mischievous child. She wore a short white China dress and had a distinctive charm attached to her forehead which she poked at with her index finger.
“By infinitely dividing our infinite power, we’ve kept ourselves at a level just barely low enough for this world to contain. …But in a way, this is the worst possible transformation, don’t you think? You could just keep killing and killing us without end. Like a matryoshka doll or an onion, you would have to fight a nearly eternal battle to completely kill us.”
[...]
“Found your feet? Do you mean that spell that infinitely divides the infinite capacity of a Magic God to trick the world by eternally layering existences that are just barely small enough for the world to contain?”
“Word gets to you quickly. Anyway, this might be an excellent opportunity for you, Aleister. Our power is limited to what can be explained in this world, so this would be the best time to kill us.”
Even that line had the implied caveat of “but it is still essentially impossible”.
For one thing, no one existed who could kill a being that the world could only just barely contain. Whether a Magic God’s power was divided by a billion or a trillion, a mere magician was still not enough to kill them.
The Magic God’s existence was infinitely layered like a matryoshka doll or an onion. A Magic God was impossible kill in the first place, but one would have to kill them a trillion or a quadrillion times before they would cease to exist.
Additionally, Zombie's spell might weaken them to 1/∞ of their power, but it has a nice side effect. Since they layer their existences infinitely, killing them once or thousands/millions of times is useless, you're just destroying one of the layers. You have to destroy all of them to truly kill them.
===Infinite Nerf - How strong is a True Gremlin Magic God at full power?===
Note: Explanation provided by DontTalk. 
So let me take an attempt to reasoning out the magic gods power based on the more recent events. The magic gods got weaker two times in the recent volumes. One time they reduced their power themselves in order to be weak enough to not passively destroy the universe and one time they all got hit by a weakening spell from Aleister Crowley.
The idea behind the argumentation is that if we know how much weaker they got and how strong they are after being weakened we can reason out how strong they would be at full power.
The important weakening for this is the part were they weakened themselves, since we know how much weaker they became.
"By splitting up our power infinitely, we can intentionally weaken ourselves and avoid destroying the world whenever we move an arm or leg."
They divided their power by infinite so we know how much weaker they got. So how strong were they at that point?
"My power as a Magic God is currently limited and I only retain one thin layer of the power piled up like the infinite layers of an onion or matryoshka doll. But infinitely dividing that infinite power still leaves me with enough power to just barely be contained in this world!" - High Priest
"Do you mean that spell that infinitely divides the infinite capacity of a Magic God to trick the world by eternally layering existences that are just barely small enough for the world to contain?" - Aleister Crowley
So they have power just barely small enough for the universe to contain. With that information we can get an idea of their power in two ways.
1. Passive:
We know that the magic gods initial power was so big that they would destroy the universe just by existing in it. 1/∞ of their power is so much that it can barely be contained without destroying the universe. So any part a lot bigger than 1/∞ should destroy the universe. Now basically any finite fraction would be a lot bigger than 1/∞, even some really low one like 1/10500. So if their power would be divided over that many universes all of them would be destroyed. So it stands to reason that their Attack Potency would be around that much.
2. Active:
We know a weaker magic god, Othinus, who can certainly destroy a universe by actively using her power. Her power is also low enough to be contained in an universe, as she never had any problems with existing in one. That means power that can be contained in an universe can be enough to destroy an universe. So 1/∞ of the Magic gods power, that can be barely contained in an universe, should be enough to destroy an universe. That fact is supported by the fact that even after first weakening herself to 1/∞ of her power and then being hit by Aleister Crowleys weakening spell Nephthys had enough power to rewrite the universe once.
"That made Nephthys different from the other Magic Gods. The others had thoroughly honed their powers as an individual, but she had specialized her power as something that could be separated, split apart, cut away, and swapped out.
In other words, she held it in reserve.
Even after being hit by Aleister’s weakening spell, she still had enough power to swap out the phase just once."
To swap out the phase means rewriting the state of the universe. As is said it is something that is special to Nephthys and the other Magic gods were weaker in this state, but that is after the additional weakening spell, so the other magic gods should be able to do the same before being hit by it.
==High 1-C Rating==
It has already been established by now that the world in Toaru Majutsu no Index is at least 11-D thanks to Esper teleporters and Curtana Original. Not only are these characters ridiculously weaker than even the weakest Magic God, Othinus, she casually reality warps and destroys the world, as demonstrated by the quotes above. True Gremlin Magic Gods even destroy the world accidentally by moving when at full power due to being too big of an existence to function in it (remember, this is an 11-D world). 
This is significant evidence, but do we know if Magic Gods really have any say over higher dimensions? Yeah, we do. Othinus explicitly mentions control over every dimension as part of the powers of a Magic God when explaining St. Germain's magic feats do not require it to be a Magic God. This cannot be dismissed saying "She's just talking about phases", because she also brings up control over phases separately from dimensions, as they are a completely different concept.
Magic Gods have control over every dimension
NT12 Chapter 2 Part 7
“Please wait!! He…he really did bend the entire world before my eyes! It was like…like this… It’s hard to explain, but the walls, floor, and ceiling all turned into weapons, tunnels appeared in the people in the way, and they all attacked me at once!”
“Have you forgotten?” Othinus sounded almost utterly exasperated. “This is the Dianoid. The entire building is made of carbon materials. That means you don’t need control over every phase, every dimension, and every element to manipulate everything around you. A magician with control over carbon and nothing else can pull that one off.” 
Other evidence supporting their rating comes from this detail (Credit to DontTalk for bringing it up)
Other evidence that supports the upgrades:
The Magic gods exist outside of the universe, the hidden world. DontTalk wrote this before he left the wiki
a) it is a place in which the concepts of distance and time in general don't matter.
b) "The world was temporarily led to destruction as a result, but I still had to prioritize this. It wasn’t easy converting coordinates filled with non-existent numbers into decimal." - Aleister Crowley
-Aleister needed time to calculate the coordinates, even though a middle schooler in to aru can calculate 11 dimensional trajectories in their head. (TBF, Espers have higher calculation abilities than regular people, but Aleister should still clearly be superior in terms of intelligence)
-every coordinate in common math is made up entirely of existing numbers, no matter the dimensions. That the place has coordinates with non-existent numbers basically shows that a non-existant place really can not be located like a "place" in space and time, even when accounting for higher dimensions.
While in a sense one could think that the terminology "non-existent" makes the fact that it is different than being just outside of a timeline, in a higher dimension, clear, I think in regards to our tiering this is an interesting little detail. 
==Mountain level Saints==
The Mountain level rating Saints and anyone who scales to them get has multiple sources. Very early on in the series Kanzaki Kaori is mentioned to have defeated a dragon capable of devouring a mountain by a former teammate.
Kanzaki fought a mountain devouring dragon
Volume 07 Chapter 3 Part 1
Do we need a reason? There’s no reason from the beginning. This is how the Amakusa does things, especially for our generation. You’re asking why our Priestess was able to be our leader at such a young age? In order to fulfill a child’s wish, she dared to go against an evil dragon that can swallow a mountain. In order to fulfill the dying leader’s wish, she was willing to protect a small village against thousands of enemies. Along the way, we were walking in her shadow.
This is supported by Kanzaki being able to fight a weakened archangel Gabriel, whose wings are stated to be able to flatten mountains.
Gabriel's Attacks 1
Volume 04 Chapter 3 Part 3
Each wing was thoroughly infused with the Power of God, and each attack could flatten mountains and carve valleys like Divine Judgment. Even if it was on the battlefield as per normal, Kanzaki, who often caused enemies to back away in fear, was now stiff with tension. If it were anyone else, the killing intent released would have caused the person to faint.
Further down the line Gabriel in a more complete form proves this claim about his wings when half of it destroys a mountain and it vaporizes another mountain with a casual attack.
Gabriel's Attacks 2
Volume 21 Chapter 6 Part 3
That blue point of light had swung that giant wing solely to blow away that formation of unmanned fighters. However, the giant wing disintegrated partway through breaking it in half. The severed half flew on and created a gigantic explosion near the horizon where it landed. 
An enormous mass of dirt flew up into the air. 
An entire mountain had been blown away.
Gabriel's Attacks 3
Volume Chapter 6 Part 3
Misha raised her palm.
Something happened.
WHOOSH!!
Something flew past Carissa’s face, and the mountain behind her was vaporized. She
could not react at all. Misha realized this, and readjusted her aim, moving her palm a
little bit.''
In Norse Mythology SS, a Saint like Kanzaki is considered the appropiate magic response when facing a magician that might be capable of levelling towns or destroying a mountain range with a single spell.
Norse Mythology SS Chapter 2
There was a magician on Uphill Island.
Apparently, that magician was creating a large scale temple or ceremonial grounds in order to carry out some piece of exceedingly dangerous magic.
The magic must have been quite bad indeed for Necessarius to send out Kanzaki Kaori, one of the fewer than 20 Saints in the world.
For example, it could easily be enough to destroy a town or village in a single strike.
If it was not of that level, Kanzaki would not have been sent out. Her strategic cost was set at that level from the beginning.
[...]
And yet something like a black stain appeared within Kanzaki Kaori’s heart. If Necessarius’s information was correct, that girl was putting together a massively destructive spiritual weapon and it was highly possible that weapon was completely under her control. If that was true, the girl before her eyes would have power greatly exceeding the individual level. She would have the power to blow away a mountain range and turn it into a giant crater with a single command.
No.
It would actually be odd if she didn’t have power on that level.
If she did not, a Saint like Kanzaki would not have been dispatched.
To further support Mountain level Saints, a Gremlin magician called Hel easily performs a feat calced to be Mountain level. One of her attacks is stopped by the barrier of Silvia, another Saint. So not only would Saints powerscale to Hel anyway due to being much stronger than her, Silvia directly scales due to stopping the attack with her own magic.
Silvia blocks Hel's attack
NT08 Chapter 4 Part 4
The girl casually pulled out a small kitchen knife and threw it toward the ocean surface.
The change only took a few seconds.
The ocean water for over 100 kilometers around the small boat completely froze into a thick layer of ice.
The girl in the bloody dress took an elegant step onto the ocean surface that looked like a lake during winter. The ice palace reassuringly welcomed the girl with a hard sound. The girl smoothly walked across the ice like she was being escorted by the hand of a well-mannered noble.
Several military ships had their path blocked by the sudden appearance of the ice.
It was as if a special chemical had been used to harden the oil in a wok with scraps of vegetables still inside. And the ice did not stop at the fleet on the ocean. The ocean was likely frozen all the way to nearby Saipan. 
[...]
When the ship had been struck by Hel’s bullet, it had been heated all over as if it had been “stuffed head first into an oven”. Everyone aboard, be they expert or amateur, soldier or magician, would be roasted like turkeys.
However…
A sound like shattering glass exploded out.
The flames enveloping the supply ship were suddenly blown away and the ship appeared unscathed from within.
It was similar to peeling away sunburned skin. The supply ship’s exterior was actually a bit shinier than before.
A woman’s voice came from the speaker as if nothing had happened.
“Sorry, but barriers are my specialty. If you want to kill the crew of this ship, you’ll have to take care of me first.”
==Accelerator==
Miscelaneous Accelerator Quotes
OT13 Chapter 10 Part 9 (Black Wings 1st time)
He was dead. That boy was dead. That grenade had exploded only a few centimeters from his head. No flesh-and-blood human could survive that no matter what they did. The area was still covered in smoke-like dust, but once it cleared, Kihara would only find a corpse so torn to pieces its original form would be unidentifiable.
The gray dust produced by the grenade thinned out as it spread. It surged behind Kihara like a wave and fully covered his vision.
Once it cleared, Accelerator’s corpse would be visible.
Once he saw that boy’s pathetic end, Kihara Amata’s fight would be over.
(Aleister said not to kill that mass-produced brat but that means anything else is fair game. I’ll give his corpse to that strange singing nun as a souvenir to completely break her mind.)
“Ha ha.”’
Just as that thought came to Kihara…
Someone grabbed the front his face.
“…!!”
Someone was standing in front of Kihara Amata.
The dust prevented him from seeing exactly who it was.
(Gah…!?)
Normally, Accelerator would have been the most likely candidate. But Kihara could not accept that. Without his powers, Accelerator was weaker than your average high school student. He could never survive that grenade blast without some sort of trick. And it was hard to believe that his reflection would have returned for some reason. The hand grabbing Kihara was covered in soot. If Accelerator’s reflection had been functioning, even those small stains would have been deflected.
“What…?”
But it was unmistakably Accelerator standing there.
Kihara saw white hair, red eyes, well-formed facial features, supple skin, a slender body line, a choker, mostly gray clothes, arms and legs with little muscle, and glittering black shoes.
But he ignored all of those and shouted about something else.
“What the hell are those black wings growing from your back!?”
They looked more like jets than wings.
Some unknown substance was being sprayed out as wings that were darker than ink and swallowed up even the light.
Kihara had seen an “angel”. He had understood that he had helped make it appear. But he was still unable to properly grasp the scene occurring before his eyes.
(Th-that bastard…)
Accelerator’s power gave him control over all vectors regardless of what type they were. His speech ability, walking ability, and the acquisition of this new power had likely all used some kind of power that existed in that local space.
Scientifically speaking, Accelerator was currently unable to perform any physics calculations, so it should have been impossible for him to control any physical force.
But what if there was some other power?
If he had grabbed ahold of some unscientific theory, did it matter what calculations he could make?
The occult.
That was what appeared to be a set of irregular laws that showed themselves ever so slightly after thousands and tens of thousands of experiments and that only a researcher of Kihara’s level would know about.
(He’s achieved a new clearance level for what he can control? What values did he input into his Personal Reality? What has he secured a method of communicating with!?)
The only possibility he could think of was the representative example of a power filling Academy City.
(AIM!? …Wait, it can’t be! Is that power actually that angel or whatever!?)
But Accelerator was not going to wait around.
He poured more strength into his grip as he squeezed Kihara’s skull.
“…”
He smiled. He silently smiled.
“Ha ha ha,” laughed back Kihara Amata as his arms and legs hung down limply.
And he asked a question.
“H-have you…seen what’s behind you, you monster?”
“ihbfKILLwq”
The black wings explosively burst out.
An unexplainable and invisible power burst from Accelerator’s hand and assaulted Kihara Amata.
His body left Accelerator’s hand, shot through the abandoned office at terrifying speed, flew out of the broken window, and cut across the night sky at dozens of times the speed of sound. He moved so quickly that he turned to plasma and left behind an orange afterimage.
It was not necessary to check to see if he was dead.
OT15 Chapter 5 Part 3 (Protected all bystanders during his fight with Kakine and quickly adapted to his Dark Matter)
“At the moment you spoke those words, you became one of those common filth that pass themselves off as great villains.”
“That doesn’t sound convincing.”
Kakine Teitoku said uninterestedly.
“I don’t want to lay hands on normal people either. If I’m in a good mood I’ll even let bad guys off. Having said that, I don’t really care if those people live or die. Aren’t you the same? In our battle just then, how many spectators and bystanders have got hurt? Cement and asphalt were traveling over the speed of sound, and shock-waves wiped out everything. That’s the kind of battle between us.”
“… …”
“Including the brat that shielded Last Order, they are all the same. You don’t have to right to lecture me, murderer. In order to battle with me, the you that kills off bystanders has no right to lecture me. Don’t tell me you truly believe you are exempt from your own ideals.”
“Ha, ‘battling with you and killing off bystanders in the process’, is it?”
Even when accused of this, Accelerator smiled leisurely.
“What a scumbag. It’s because you have no aesthetics that you can say bullshit like that.”
“Huh?”
“In the end, do you understand why you’re #2 and I’m #1?”
As he laughed he spreads his arms out wide.
“Between me and you, there is an impassable wall.”
Kakine was fuming at his comments, but he also noticed it.
Their surroundings.
True, the battle between Accelerator and Dark Matter had destroyed the road. The glass from the buildings had shattered, traffic lights had been blasted off, and trees had been blown away and were sticking out of the cement buildings.
But, something was missing.
Tragedies.
Glass shards had rained down from above, but there was no-one hurt. A sweeping gale had twisted the path of those shards into falling elsewhere. The advertisement signs had miraculously protected those that were to slow to run away. The others were the same, with not a single person hurt. Though it was uncertain, in their fighting to this point, probably not a single bystander had been hurt.
(I-impossible!)
Kakine felt his throat go dry.
“Are you saying… that you protected them all?”
Thinking back, the first sneak attack could have been much more powerful. But if that was the case, Last Order’s companion at that time would also have been hurt.
This was his way of doing things.
Even in a death match between the #1 and #2 Level 5s, even on a battlefield where a slight mistake could get you killed, Accelerator protected the normal people who he had never met before.
“Don’t joke around! Are you saying everything was under your control from the beginning?!”
Accelerator showed impatience, as if saying ‘of course’, and taunted Kakine for his incompetence that he could not do the same.
“Are you angry, you lowlife?”
Towards Kakine who was shocked, Accelerator impatiently said, “Now this is what should be called a villain.”
If after doing this much, if one was still called a villain, then just what did a hero in Accelerator’s mind have to do?!
“Stop spouting nonsense, Accelerator!!”
Kakine Teitoku roared out and increased the power in his six wings. Changing the lengths, the structure, the white wings spread out and transformed into six lethal weapons that aimed at six of Accelerator’s vital points.
Facing these, Accelerator only smiled.
“Bring it on.”
“These are more than enough to bring you down, since I’ve already figured your filtering system. That sham of a defense cannot stop this!”
“Indeed, you can control matter that doesn’t exist in this world.”
Accelerator only wagged his index finger and made a ‘feel free to do your worst’ expression.
“The laws written in school textbooks don’t work on them, and light and electromagnetic waves that come in contact with the Dark Matter get twisted into energy that can’t possibly exist. So using energy calculation algorithms based on rules of this world will definitely have flaws.”
The killing intent between the two had risen dramatically.
This crossroad was now fully saturated with the breath of death.
“Then all I have to do is include them in my calculations. To change the laws of this world into a new world that includes your Dark Matter and create a new algorithm, then it’s checkmate.”
“Using your vector transformation… to control my Dark Matter…?”
“Don’t you think I can do it?”
“Ha, do you think you can gauge the entirety of the depths of my ability just by doing that?”
“Your depth is actually quite shallow.”
“…!?”
“Shallow to the point I don’t even need to try and gauge it!”
A sound of explosions ripped through the sky.
It only took an instant for the two to clash.
The victor in the match between the #1 and #2 had been decided.
OT15 Chapter 5 Part 4 (Black Wings 2nd Time)
A searing headache. It felt like something sharp had stabbed into his brain, and devoured everything in Accelerator. His ears could hear something like fruit being smashed into pulp. His eyes had started to flow with a liquid that was not tears. A liquid that smelled of rust, was redder than tears, thicker than tears, and felt uncomfortable. Even this liquid that came out of his eyes only left a taste of disgust. 
And what came afterward was…
Rampage.
“Oh.”
That pillar that had supported him had completely shattered. His whole body had been infected by a murky emotion. Accelerator, who clenched his teeth and had crimson eyes, let out a roar that echoed to the ends of the earth!
“Aaaaaaaargh!!”
From behind him spread murky black wings, as if they shot out from his back. This pair of wings that contained something which could blow away the mind, and anger that shattered his own sense of self, spread instantly over tens of meters, and shaved off parts of the buildings and roads around him.
“Ha.”
This pair of black wings, Kakine had seen it before, and knew what it was.
The elementary particles that didn’t exist in this world, Dark Matter.
“… So strong. Such powerful evil. So you can do it if you put your mind to it, villain. If that’s the case then indeed Dark Matter is only suitable for being the spare plan. However, this doesn’t mean it’s all decided!!”
Kakine’s six wings, as if responding to his roar, spread explosively. The wings that spanned several tens of meters emitted a mysterious glow, and at the same time had an inorganic feel like a machine. Almost like a giant weapon gods and angels normally use.
Flap. The air around the six wings let out a howl.
Accelerator and Dark Matter controlled the organic and inorganic powers respectively. Different from this world, this was ‘organic’ and ‘inorganic’ in terms of a different world. The One Who Wields the Power of God and The One Who Has Touched the Territory of God. Now the odds of victory were even, only that unlike Accelerator, Kakine hadn’t lost himself.
An unprecedented power was expanding within him.
And, he had perfectly mastered this power.
Now the position of the #1 and #2 of Academy City was about to be reversed. This was neither a bluff nor an exaggeration. He now believed even if he fought against all the armies in the world, and even every esper in Academy City, he could emerge victorious and unharmed.
“Hahaha!! Uwahahahaha!!”
Kakine laughed and waved his completely awakened six wings down at Accelerator.
He no longer saw Accelerator as a threat, but only a thing to test his new powers on.
Splat.
Kakine Teitoku’s body was pressed into the asphalt by a great power.
“Wha…?!”
He completely didn’t understand what just happened.
Accelerator’s wings didn’t move at all. He only stared at Kakine and slightly moved his hands. With just that, he defeated Kakine who had absolute power and ground him deep into the ground.
His right hand that had the Tweezers on it was torn off from the elbow downwards.
(Ah! …Uwah! Wh-Wha?! Just what is—)
Accelerator must have changed vectors and energies of some sort, and redirected those towards Kakine as an attack. Even though he understood, even if Accelerator had gathered all the energies in this world, this phenomenon shouldn’t have happened. The Kakine Teitoku now couldn’t lose to this world.
Unreasonable.
Inexplicable.
With an overwhelming presence Accelerator walked step by step towards Kakine Teitoku. His steps were like the countdown until the end of Kakine’s life, when it reached zero it would be all over. And, Accelerator had reached that last step.
“Ha, ha.”
“—yjrpEVILqw”
“Bastard…! Damn it, so this is how it is!! Your mission is…?!”
No reply, just a fist filled with killing intent.
An overwhelming slaughter had begun.
OT19 Chapter 1 Part 7 (Accelerator vs Spark Signal)
Level 5s were still human.
It didn’t matter if it was the #1 or anyone else, they were all primates.
No matter what kind of special ability they possessed, if they didn’t breathe or didn’t eat they would die. They had a limited life-span, and if stabbed they would also bite the dust. If they were humans with the same weaknesses, then there would be a way to kill them. Spark Signal originally was a special force made to combat those that planned to leak inside information of Academy City to those on the outside. In their activities they had also fought with powerful espers countless times. So, when facing espers that could create incredible phenomena, Spark Signal could respond appropriately. First calmly analyze the opponent, then find a way to defeat him.
The masked men of Spark Signal had believed that all this time.
That was something they firmly believed in.
However...
Was the #1 of Academy City really human?
Boom! A sound that swept through the air exploded out.
The multiple bullets in his hands shot out, and each of them accurately pierced through the terrorists of Spark Signal.
Of course, they hadn’t come here to just die when they planned this large-scale mission. At this place, this time, as a human they all felt their lives were in danger. To be released from this threat, they unreservedly used all the techniques and knowledge they had learned up to this point, bringing their full strength to fight back against the whitehaired esper.
Some of them tried to shoot with their rifles from behind cover.
Some of them tried to use hostages to stop their opponent’s movement.
Some of them tried to use dynamite to destroy the columns and bury their opponent in the rubble.
These were good actions, except it was all meaningless.
Forget about it even having an effect, there was no value in even trying.
The bullets didn’t work.
As soon they touched the monster’s skin, they were reflected back and shot the terrorists themselves.
Taking hostages didn’t work.
As soon as they tried to reach for the kids, their wrists were twisted in an unnatural manner.
Dynamite didn’t work.
As soon as they tried to push the button for it to explode, their fingers were blown away along with the button.
(No…)
It was more than just these, one of the masked members of Spark Signal thought.
That face of his that could not be seen from outside was already covered with cold sweat. He felt that the essence of the escalating terror in his heart was more than just those.
Yes.
The #1 esper of Academy City, Accelerator, was taking all of this completely seriously.
He didn’t excessively use his overwhelming power. Even seeing the terrorist falling one after another he did not get careless. If he relaxed then maybe they still had a chance, but Accelerator didn’t even give that small possibility to his opponents. Sometimes with his ability, sometimes with his handgun, he always used the smallest amount of effort to obtain the greatest results. It was no longer a battle between humans, or even between humans and a monster. Simple destruction that needed no emotions.
For example,
It was just like a homing missile that was closing in on a fighter plane that tried desperately to run away.
This wasn’t a matter of winning or losing, but whether you get hit. If it hit there was not much chance of surviving. The disaster that Accelerator spread had already reached that level.
(Do you know how much effort we put in to create this plan…)
Staring blankly at the Level 5 who, with some kind of ability, soared through the air in an arc to strike at one of his comrades, this man tried desperately to make his confused head work.
(We’ve used everything Spark Signal has, apart from the main plan there were many other back-up plans… We’ve clearly prepared to this extent, clearly… In the end we’re still taken down like weeds…?!)
At this time,
Inside a pool of deep red blood, that monster who had just ripped apart one of his comrades and taken away his ability to think turned its head towards him.
(What do I do…)
Those crimson eyes met his own eyes head on.
That looked just like an infrared aiming scope, Spark Signal’s terrorist thought.
(What…?!)
It couldn’t even be called a showdown.
He was aimed at, and then shot.
In total, it only took 300 seconds.
The world’s largest particle accelerator, Hula Hoop, had become peaceful once more.
OT20 Chapter 2 Part 10 (Reflecting Magic and Teleportation Espers)
“Vodyanoy!!”
It was most likely a codename.
The group faltered at the sight of the sudden damage to their companion, but they started moving shortly thereafter. The woman standing diagonally back in Accelerator’s blind spot—probably the Vodyanoy the man had mentioned—made an odd motion with her fingers.
Immediately afterwards, the snow around her melted and turned into a spear of water that flew towards Accelerator.
The mysterious attack was not from a bullet or a bomb.
A normal person would have been too surprised to react and simply been skewered. However, Accelerator was not bothered by it. He himself was a mass of the mysterious.
He held up his right hand, the sole area his reflection was activated on.
The water spear was smashed to pieces.
The water turned to a rainbow of light that flowed diagonally back from his right hand. It acted as a wall of pressure that knocked away 4 of 5 of Vodyanoy’s comrades.
Accelerator had blocked the attack, but he frowned.
He couldn’t figure it out.
If his reflection had succeeded, the water spear should have head straight back at Vodyanoy and pierced her arm. Instead, it had gone astray and had disintegrated into a rainbow of light. It had been an odd phenomenon. It hadn’t been something like steam created from water or ice. Accelerator had caused the reflection but he didn’t understand the process by which it had turned to light.
(…What…?)
It felt like having something you had grabbed with the tips of your fingers slipping away.
When he reflected teleportation powers, a strange phenomenon occurred in the 3 dimensional world, but this had felt entirely different. However, he did not have time to think about it.
Vodyanoy seemed confused, too. As if to check what had happened, she created the exact same water spear once more. She watched him carefully as the attack hit as if looking for a way through his defenses.
This was convenient for Accelerator.
He held his palm forward and the water spear turned to rainbow-colored light once more.
However, something was different from the previous time.
One portion of the rainbow-colored light almost scratched Last Order’s cheek.
“…You need to be careful.”
A tremendous noise rang out.
It was the sound of Accelerator lightly stepping on the ground and causing a huge tsunami of snow to rise up. It swallowed up Vodyanoy and the others. Unlike a normal tsunami, it had overwhelming speed. It was faster than Vodyanoy and the others and the wall of snow knocked the attackers unconscious.
“Yeah, the right hand just doesn’t suit me.”
Checking that he had taken care of all the enemies, Accelerator flipped the electrode’s switch and thought for a bit.
What had that water spear been?
The grasp of its vectors had been completely different from the scientific powers developed in Academy City.
Different vectors.
Different laws.
NT4 Afterword (Compared to Bersi's ability to nullify all lethal attacks as abilities with "an infinite ceiling")
Bersi.
We’ll be giving a cross-analysis to distinguish him from Kihara Kagun. As he had a defensive spell that completely nullifies fatal wounds, he was a problematic character who didn’t mind about other people’s personalities or habits and would interfere through small actions. Logically, if someone with ordinary emotions ended up in such a situation, the mind would collapse first. However, I avoided the above-mentioned problem by stating that his research became useful in such an attack.
He could nullify all fatal attacks, but he also had a sword spell that increases its destructive power every time he was attacked. Thus, when facing a fierce attack by the enemy, he could use a spell that has an infinite ceiling. This is different from Accelerator in that it's not the control of just one attack, but that the thing that’s worth noting is that once the power increases, he could maintain such destructive power when fighting the enemy in the future. As his name suggested, he really was an inflating bastard. 
List of what has bypassed his Reflection before in-series.
Imagine Breaker
OT3 Chapter 4 Part 6
Accelerator may have been the strongest, but he was not invincible.
Kamijou’s Imagine Breaker could destroy any kind of supernatural power even if it was one of god’s miracles. Even if Accelerator’s reflection was a perfect defense that could reject even a nuclear explosion, Kamijou knew it should not be able to defend against his right hand.
Accelerator was the strongest and therefore he could stand up to the entire world at once.
However, his power was not absolute enough to be able to defend against Imagine Breaker.
[...]
Kamijou saw Accelerator’s right hand moving in toward him like a poisonous snake and immediately struck out with his right hand despite still being in midair. In a small piece of fortune, Kamijou’s right hand somehow managed to brush away Accelerator’s hand.
That was all he did, but Accelerator looked up at Kamijou as if he had seen something truly unbelievable.
[...]
His hands were pressed together at the wrist like he was wearing handcuffs and he
thrust them toward Kamijou’s face.''
Kamijou immediately tried to move back, but his trembling legs would not move properly.
Those hands that could crush one’s soul approached before Kamijou’s eyes.
“Fuuuuuuuuuuuuuucccccccckkkkkkkkkkkkkk!”
Kamijou reflexively shut his eyes and swung his right hand up prepared for the worst. As he had cut off his own vision, he had no idea where he was aiming his fist. With a dull sensation, his right hand punched Accelerator in the face.
“Eh?”
The first one to express his surprise at that result was Kamijou, not Accelerator. He had truly not expected to hit and he had not expected his battered fist to actually do any damage even if it did hit.
However, Accelerator was knocked away and was now squirming around atop the gravel.
“Ah? Ow… Ha ha… What the fuck? Oh, wow. Ha ha ha. Dammit. Excellent, excellent.
That was great! That was wonderful! Now you’ve done it!”''
Kihara Amata's Counter
OT12 Chapter 5 Part 1
The fist wearing the detailed metal glove flew towards Accelerator’s face.
Yet Accelerator’s smile did not crumble.
“What is this idiot thinking?” he muttered.
Without even thinking of defending, Accelerator opened his arms to welcome in Kihara
Amata’s fist. And just as he was thinking of utterly breaking that idiot’s arm and tying it
in a knot…''
The mechanical fist tore Accelerator’s skin and shook his skull.
“Gah…h…!?”
The unexpectedness of the strike caused even more of a shock to his brain.
The switch on his choker-shaped electrode was on.
His reflection was active.
In that state, he should have been left unscathed even if he detonated a nuclear bomb he was currently carrying.
And yet…
For some reason, the vector reflection had not worked at all.
[...]
He had seen this phenomenon before.
With just a touch of his palm, that boy had easily negated the Level 5 powers Accelerator had thought were absolute. That boy had crushed his impenetrable reflection ability and sent heavy blow after heavy blow against his slender body.
[...]
Accelerator’s body was doubled over from the previous blow and another fist fell atop his head that was sticking forward a bit. His body collapsed to the ground like a toy.
“Your reflection isn’t an absolute barrier.”
Kihara slowly walked forward.
Accelerator could not move.
“It only reverses the vector of any force heading into it. That makes it simple to beat the shit out of you. I just have to pull back my fist the instant before hitting. You could say the trick is stopping at the last second.”
He sounded like he was enjoying himself.
His smile was that of someone explaining the trick to a piece of stage magic they had thought up.
“You end up reflecting the fist that is moving away from you. That means you actually punch yourself. Do you get it now, masochist boy!? Or is it too complex for a little kid to understand!?”
“!!”
Accelerator tried to get up, but Kihara’s foot flew his way before he could. The sole of Kihara’s shoe stomped down on him from above again and again. As the foot stomped on him in various places, his skin was torn and blood mixed in with the rainwater.
(What…?)
He knew Kihara claimed to be using his own power against him. But Accelerator had no idea what exactly it entailed or if it was even possible in reality. However, he did know his reflection was of no use.
[...]
One of the armored men held out a handgun, but Kihara shook his head. The countermeasure for Accelerator’s reflection could only be accomplished with a subtle reversal of an arm or leg. It could not be replicated with a bullet.
And it was naturally only an attack method that was possible for that man who had directly developed Accelerator’s powers. Even if others heard the explanation, they could not pull off the split second timing needed.
OT13 Chapter 10 Part 1
After Accelerator missed, Kihara threw a cross-counter.
With precision on a level dozens of times greater than a jab in boxing, he pulled back hishand just after he threw it.
The strike slipped past Accelerator’s reflection wall and slammed mercilessly into the bridge of his nose.
“Ah…!!”
The dull sound of something being crushed rang out.
This was not a flashy and heavy blow like from a hammer. Taking it to the nose shook his vision, but it was not enough to knock him unconscious.
However…
When Accelerator stopped momentarily due to the pain, a string of light blows assaulted him. Face, chest, shoulder, gut, and then face, face, face. When Accelerator swung his arm, Kihara would step back. When Accelerator tried to pursue, Kihara would move closer and attack.
“Gya ha ha!! You piece of shit! Aren’t you ashamed to stand before me like this!?”
Another impact shook Accelerator’s head along with Kihara’s shouting voice.
His reflection was not working.
That absolute wall was supposed to ensure not a hair on his head shook even if he took the brunt of a nuclear blast.
Accelerator tried to move away.
Kihara stepped further forward and threw another punch at his face.
“!!”
Accelerator’s reflection did not create a thick bulletproof shield in front of him. It only redirected any force heading toward him. He protected himself from any and all attacks by altering any force moving forward so it moved in the opposite direction.
In other words…
(If my reflection acts on a force moving backwards, it sends it forwards!!)
With blood trailing down from the corner of his mouth, Accelerator was now confident he knew what was happening.
Kihara Amata would reverse the direction of his punch just before it hit Accelerator. He would do so in the instant when he was just barely touching the thin protective film of Accelerator’s reflection. That forced Accelerator to pull the backwards-moving fist forwards.
This just meant he had to alter the vector control ability protecting his body, but Kihara’s fist made minute adjustments in the direction of its turn as if the man had predicted the changes Accelerator would make. It seemed the intellect that had directly developed the esper power known as Accelerator was quite something.
OT19 Chapter 3 Part 8
Accelerator lost his target and suddenly braked. But it was too late. Sugitani used the smokescreen and nimbly moved behind Accelerator.
“I remember that Kihara Amata once used the technique of drawing back his fist an instant before receiving impact to break through the reflection obstacle.”
“!?”
The voice came from his blind spot, along with a fist.
Accelerator flew backwards in a hurry.
“Also, Kakine Teitoku seemed to have used materials that don’t exist in this world to
create vectors that don’t exist in this world.”''
However, the voice and fist followed closely after him.
Sugitani used footwork beyond the limits of a human that was almost like sliding to keep
himself in the same distance between him and Accelerator.''
After that, a ‘boom’ rang out.
Accelerator’s face was feeling some numbing pain, while Sugitani jumped out of the ring
for the first time in this battle.''
“So that’s it.”
Sugitani shook his wrist.
It seemed to have sprained, the joints had swelled up a lot.
“Those special exceptions are all results of their own specialized fields. Just by observing them I can’t perfectly recreate their techniques.”
Even so, to have struck Accelerator’s head without any abilities needed top level skills.
For any normal grunt that attacked, it wouldn’t just stop at a swollen hand, they would be hurt to the extent of losing control of their own blood stream and have their internal organs shattered.
NT1 Chapter 5 Part 7
“Though you’re the #1 of Academy City, you did taste defeat before. For example, Kihara Amata, who used that reflection of yours against you and consciously pulled his fist right back to let the reflection hit the fist into you.”
Accelerator knew what she wanted to say.
The large number of arms behind Kuroyoru were moving about like waves.
“But my arms are cyborgs, they’re machines, completely artificial things that’re controlled through numbers!! I can counter you by using Kihara Amata’s calculations!!”
Facing a past threat head to head.
That tone, that way of thinking was the perfect way to destroy Accelerator.
“So, #1, what are you planning to do? Kihara Amata only used his human fists, so if it’s my Bomber Lances, it’ll be over in a single hit. If you don’t want to die, bring it on. I’ll beat you down and ground you up.”
Several thousand arms moved into position.
Each arm could create a Bomber Lance freely, and in groups, they could completely control all the air flow around her.
There were tens of thousands of ways to attack. By setting the inputs to Kihara Amata's values that caused Accelerator quite a headache, she could definitely beat him with his reflection.
The lances could attack from any direction.
No matter where Accelerator tried to hide, there was no safe zone in the air. Even if the Bomber Lances themselves couldn’t touch him, in groups, they could manipulate the air in the sky.
Dark Matter - Kakine Teitoku
OT15 Chapter 5 Part 3
“The Dark Matter I create is matter that does not exist in this world. It’s not matter that hasn’t yet been discovered, nor matter that theoretically exists, but rather matter which undeniably does not exist.”
A material made by an esper ability that could not be classified by science.
Faced by these white wings that seemed to have come from a different world and defy the laws of physics, Accelerator’s will was not shaken.
Who cares what they are? They will all be shattered by the ability to manipulate vectors.
“OK, then I’ll blast you apart along with your ‘Dark Matter’.”
With one more step forward, Accelerator could tear apart Kakine Teitoku’s heart.
However...
“You still don’t understand.”
As Kakine finished his sentence, his white wings let out a ‘swoosh’ and projected a brilliant white light.
“?!”
A burning pain forced Accelerator to back away from Kakine involuntarily. At the same time, he noticed the change in the situation.
Accelerator who could reflect all vectors was actually hurt by an outside attack.
“That was diffraction. Light or electromagnetic waves change direction when passing through narrow gaps; this is common knowledge even in high school textbooks. Using multiple gaps at the same time will make the waves interfere with each other.”
Simply put it was by diffracting light through the countless unseen gaps on the wings to change the nature of sunlight and use it to attack Accelerator. It was not that the white wings gave off light, but that the light itself was changed by diffracting through them.
“Ah, the value of things depends on how you use them. So, how does it feel to be burned to death by sunlight?”
However...
“… Go back and study up on physics, you idiot. No matter how you diffract sunlight it doesn’t change the nature of it into something like a beam of light that kills.”
“Hm, that is indeed the case with the normal physics of this world.”
Kakine’s six wings curled up and gathered strength.
“But! My Dark Matter is matter that does not exist in this world! It completely disobeys the laws of physics of this world. Sunlight that gets diffracted by the Dark Matter will also have its own set of laws! Foreign bodies are like this: by just mixing in a little bit, the world will completely change!”
Fwoom! The six wings blew up a gale wind towards Accelerator. Accelerator used his reflection to subdue the wind while trying to figure out his opponent’s aim. Looking closely, he found Kakine smiling.
“Reverse calculations, complete.”
“!?”
When Accelerator heard that he tried to dodge, but the six wings had already begun to strike. However, unlike before the six wings were used solely as blunt weapons for hitting.
A series of *gacha gacha* sounds exploded out from Accelerator’s body.
Accelerator, who could reflect all vectors, was blown over 10m away, hitting one of the trees on the sidewalk. The thick trunk of the tree got snapped by that one blow.
“Oof…!?”
(So the sunlight and wind from before was all for…!!)
“Accelerator, you said before you can reflect everything, but that’s actually incorrect.”
Kakine’s wings spread soundlessly.
Accelerator flew up to a rooftop, but the over twenty-meter long wings aimed at him like giant swords to strike him down.
“If you reflect sound then you can’t hear anything, and if you reflect physical objects you cannot hold anything. You subconsciously establish a filter that sees everything as harmful or not, and use your reflect to push away anything that could harm you.”
Accelerator spit out the blood in his mouth, blew apart the water cylinder on top of the building with one stomp and jumped aside using the rebound.
The white wings that struck down crashed into the building, and split the building vertically in two. Large dust clouds swelled outwards from there.
“The sunlight and wind affected by the Dark Matter are infused with 25,000 different kinds of energy. Then by observing your reflection and using a filtering system that judges which energies are deemed ‘harmful’ or not, I can use the energies that are subconsciously accepted as not harmful to attack you.”
Even if Accelerator changed the rules which his reflect was based on, Kakine Teitoku would immediately use his Dark Matter to inspect the change. The repeated attack and defense this way would only make Accelerator’s wounds get worse and worse.
“Such is Dark Matter.”
Kakine Teitoku smiled and spread his wings.
“This space which has been affected by foreign bodies is no longer the world that you know!
NT7 Chapter 4 Part 9
Kamijou Touma, Kakine Teitoku, and Rensa.
The first two to clash were the ones with wings.
In other words, Kakine and Rensa clashed at supersonic speeds.
A great roar exploded out after a short delay. The dinosaur skeleton collapsed in an instant and the tempered glass display boxes located here and there shattered. Fremea panicked and balled up her body.
The #2 must have taken some measures with his Dark Matter because he did not hesitate to attack Rensa even though she had the #1’s reflection.
Use of Magic
OT22 Chapter 11 Part 1
“I can’t solve the puzzle,” Accelerator readily admitted. “I’m missing a piece, so I can’t use just math. I can manage up to a certain point, but something is definitely off. It’s like I’m trying to calculate Pi and an error occurs at the 100th digit every time. There’s some other kind of laws mixed in. Unless I can fill in the missing piece, I can’t correct for this error. The further I continue the calculations, the greater the error spreads until I’ve lost sight of what I’m trying to find.”
“So whatever these parchments are, you can’t get the parameters you need?”
“I can’t do this with math, but I have to solve it somehow, so I’ve brought together every single bit of knowledge I have. I do have the #1 brain in Academy City after all. I’m not particularly proud of it, but I have a lot packed in here. And so I started doing a selfsearch through every part of my head pulling out every kind of information and just pulling it out and pulling it out and pulling it out.”
[...]
The massive formula was outputted into the world in the form of song data.
Misaka Worst may have been surprised as she watched from the side, but it was nothing special. In the past, Accelerator had eliminated Amai Ao’s virus using his own power. This was merely in a different form, so there was no reason he shouldn’t be able to do it. He had everything he needed. All he had to do was keep it in the best condition through to the end and produce the desired results like he was a machine.
That was how it was supposed to go.
However, the mechanism that was supposed to move slowly got caught somewhere.
It was a slight but ominous vibration like the omen of a train disastrously derailing.
(The golden sky…!?)
Mysterious vectors like Aiwass’s were pressing down on him from above.
(I see. It isn’t too surprising that something like that would interfere with this a bit.)
Static ran through TVs or radios when they were near power lines with high voltage currents running through them. It was the same as that. He immediately determined that and made slight adjustments to his equations.
He was reminded of a ball rolling down a slope.
At the bottom of slope was a cliff.
If he continued to adjust his equations, he would cross a decisive line. Whatever he analyzed, Accelerator was an existence living within the normal physical laws. He himself would not be immersed just by knowing of the mysterious laws.
He would cross that line.
He would be swallowed up by the mysterious laws.
Accelerator knew that, but he did not stop. He continued on. He shot down the slope in a straight line. He could already see the edge of the cliff. Accelerator saw that deep hole as a gate. He unhesitatingly headed forward and leapt into the bottomless darkness.
He crossed that line in an instant.
Immediately afterwards, a change occurred.
“…!!!???”
With a cracking noise, something within his body let out a cry. The blood vessels on the back of his hand swelled up oddly. He became strongly aware that he had thick blood pipelines running from his fingertips to his shoulders. As soon as he noticed that, something tore. His skin ripped from the inside and a dark-red liquid squirted out.
Had he realized it?
By breathing in a way impossible for a normal person and using vibrations from his entire body rather than just his throat, he had let out an extremely special voice. With that voice, he was refining his life force into magic power, putting together a spell, and outputting it into the real world. In other words, he was using true magic.
Espers could not use magic.
If they forcibly used it, what awaited them was an enormous rejection reaction. The damage did not remain in just one place. The flows of the arteries, veins, and nerves running through his entire body like spider webs gave him a strange pulse and pain while bringing their presence to the front of his mind. He was made strongly aware of the expansion and contraction of his organs as well as their locations. More sweat flowed from his body in an instant than if he were to enter a sauna. That clear and unpleasant liquid mixed with something red. Accelerator thought small scale explosions were occurring in various places across his body. That prediction was not wrong.
OT22 Chapter 12 Part 1
The white snowy plain was wrapped in silence.
Accelerator’s song had ended. The end of the cane supporting his body slipped.
Accelerator’s entire body was covered in red blood as he fell from his knees. That white hell would not allow its color to be changed, so he alone was dyed in the colors of his wounds and pain.
His throat had exceeded its limit and his raspy breaths made it sound like his throat had been scraped over with a filed. He must have been injured internally as well because a red liquid occasionally flowed out with his breaths.
He could not sing any longer.
The tubes within his body had something sticky filling them up.
NT1 Chapter 4 Part 3
Accelerator flipped his electrode's switch, temporarily releasing the power of the #1, and jumped up to the roof of the tall building in one leap.
He stood on the railing, and looked around.
During the war in Russia, he had come into contact with "something like magic", and he had used a part of it. His body had been torn up from the inside by that power, but he had managed to save a girl from the brink of death in exchange.
He had taught himself to contact that power.
After receiving some explanations from Birdway, he had been able to give clear outlines to that vague idea he had before.
He breathed in, stopped, and then used his power.
"...!!"
The blood vessels around his temples pulsated unnaturally. The cold wind was blowing on him, but he could not stop an unpleasant sweat from coming from his body. He envisioned a cup so filled with water that it was just barely able to hold it all in via surface tension. If it was tilted even slightly in any direction, something that must not be spilled would spill out. He understood that clearly.
He could not ignore it.
He controlled the power within his body with the delicateness of someone balancing that cup on top of their upraised index finger. He then continued his work. 
NT3 Chapter 2 Part 21
He manipulated the vectors of the force of his legs to explosively charge forward. The hunt had begun. No matter what the enemy thought or how they moved, Accelerator’s reflection was overwhelmingly effective when it came to bullets and explosives. The attackers could do nothing to oppose the #1 as he wiped them out.
But…
There was one left.
Just as he stretched his fingers out before her, bright red blood suddenly burst from Accelerator’s right arm.
“…Ah?”
A bullet had not made it past his wall of reflection.
Accelerator could not be harmed even by invisible threats such as gas or a biological weapon.
This had been caused by a non-external threat.
That is, his body was being destroyed from the inside.
The last remaining attacker jumped to the side and Accelerator was unable to correct his motion. He slammed into the wall. Blood was splattered on the wall and it did not quite seem real to him that it was his own.
Still leaning against the wall, Accelerator said, “It…can’t be…”
“One fact remains the same for every esper,” said the woman as she held up her bullpup-style rifle. “When a scientifically-created esper uses a magical spell, they are assaulted by a certain side effect.”
“…You’re…a magician…!?”
He tried to shout out but instead coughed up a clump of blood from deep in his throat.
The attackers’ movements. The way they had fled. The timing with which they had been taken out.
It had all been calculated out to make Accelerator take certain actions—to make him pull the trigger known as magic.
The specifics of the magic he was made to use did not matter.
It could be something relatively useless like sending a pale light from his fingertips or even something so trivial it could not be seen. What mattered was that they were making an esper use magic.
Accelerator managed to figure that much out, but he could also tell his consciousness was growing muddy.
He had used something like magic in the past, but making careful adjustments while checking on one’s limits was very different from charging in unaware.
And a scientific esper’s powers were created purely from the brain.
The muddying of his consciousness lowered his calculation ability which in turn had an effect on his control on the macro physical world he could see.
Simply put…he lost his reflection ability. 
Aiwass
OT19 Chapter 4 Part 3
Aiwass did not even attempt to evade. It stared at Accelerator with its arms still spread out. Accelerator charged in and stuck out a hand with its fingers spread out. He just had to alter the vectors to destroy Aiwass from the inside.
But an unexplained shock struck Accelerator on his upper body in a diagonal line.
It was a decisive strike with something like a heavy blade. Immediately after Accelerator was aware of that, he hit the floor and rolled a few times backwards. An unbelievable amount of blood gushed out. It wasn’t just coming from the wound on his upper body. Blood was flowing from his mouth and nose as well. It may sound like a joke, but it seriously seemed like a mystery that his organs didn’t come spilling out of that large wound.
“Gh…bhaaaaaaaaaaaaaaahhhhhhhhhhhhh!?”
He didn’t know what had happened. People like Kihara Amata and Kakine Teitoku had pierced his wall of reflection in the past, but Aiwass was different. That strike had not been based on some theory that allowed it to slip past the reflection. Even after receiving that decisive blow, he was still unable to analyze what had happened to his own body.
“Oh, whoops. That was my mistake,” said Aiwass sounding completely calm.
Something grew from its back pushing its long blonde hair aside. They were wings. The wings were emitting a too brilliant brilliance that gave the feeling that it was worse for the human body than a nuclear explosion. That must have been what had sliced Accelerator.
The wings were very odd.
They were not simply gold colored. They were a palely glowing platinum that had a white core. …That wasn’t quite accurate, but it was how Accelerator expressed it in his brain. The wings gave him a very strong out-of-place feeling because he could not comprehend what he was seeing.
[...]
An explosive wind was created with Accelerator and Aiwass at the center. However, the fight was not even. In the first strike, Accelerator’s black wings were torn off at the base and the second strike completely sliced them to pieces. A sound that was more of a roar than it was a yell reverberated throughout the area. Aiwass swung its pale platinum wings again. Red blood flew into the air and was blown away by the explosive wind.
There was simply too great a gap between them.
Accelerator’s black wings were quite destructive, but it was a bit like he was simply swinging around a heavy wooden club. On the other hand, Aiwass’s wings were more like a sharp and famous sword that was being wielded with incredible skill.
The sound of something falling to the ground could be heard.
No, it was the sound of someone collapsing.
“So this is all?” Aiwass said looking down at Accelerator who was lying in the middle of a pool of blood.
OT22 Chapter 11 Part 1
“I was unable to reflect an unknown attack. It just went straight through my defenses and cut my body in two. I couldn’t come up with a single way of dealing with it. I was utterly defeated at that time.”
He now had enough leeway to smile.
He pushed on his own back and took another step forward.
“But it wasn’t that the attack did not have vectors. I’m sure I had those unknown laws inputted into my body from Aiwass back then.”
Thinking back on it, that had been what had happened.
Aiwass had not just erased his powers like that Level 0.
The being had not worked around his powers like Kihara Amata or Kakine Teitoku.
Aiwass had used a completely straightforward attack and its vectors had directly struck Accelerator. In that case, that information should have been transferred to Accelerator.
Telesma
OT21 Chapter 8 Part 7
Accelerator was like a blast wave from an explosion, blowing away the snow from the ground, he charged towards the two angels. In the moment before their weapons were about to clash, Accelerator considered which entity he should get rid of first. However he came to the conclusion that since both of them were winged monsters, there was no point in aiding either side, and he leapt between the two, using his Reflection ability to attack the angels by redirecting their own blows at themselves.
BOOM!! The sound of explosions rang throughout the air. Against the doll-like angel of ice, Reflection was largely ineffective. Even though he used Reflection, the wings of ice were like soft candy, as they were bent out of shape, they were sent flying towards the forests, sending up ice and dirt as they went along.
The angle of reflection was too small. If Accelerator continued to forcibly reflect the attacks, his body would be injured too. However, Accelerator’s expression did not change, for the wings of the glasses-wearing angel were fully deflected by his Reflection. The angel had an almost human-like expression of surprise, and in this instant Accelerator took away the vectors from the angel’s attack. Gathering the vectors, Accelerator launched a merciless strike straight at the chest of the glasses-wearing angel.
The sound vanished.
The seemingly weightless flying angel was knocked back 300 meters. Like a crashing airplane, the monster rolled spectacularly across the ground, knocking away everything in her path. The reason Accelerator attacked her first was very simple. His powers worked on this angel, not so much on the other angel. Logically he should try to take out the more difficult opponent first. For this, he would have to incapacitate the easier opponent first to fully concentrate on the harder one.
“You?!”
The glasses wearing angel, using powers that Accelerator could understand, spoke.
[...]
From the earlier clash Accelerator had analyzed his opponents. Although both angels were monsters, they were not on the same level as Aiwass. Reflection and vector control worked perfectly upon the angel of science. As for the angel who had unknown origins, from the way it was being knocked around by the AIM angel, it was also a far cry from Aiwass in terms of power. For, Accelerator could not even begin to think of a way to defeat Aiwass.
[...]
This was a perfect “Heaven’s Judgment”, one that Accelerator’s vector control could not hope to emulate.
“Wha-what?!
Accelerator was unable to respond. To dodge or to try and take the attack head on? Before Accelerator could fully consider his options, the maelstrom of destruction was already upon him. Accelerator could no longer tell the sky from the ground. In the moment that he was hit by the attack, his body was flung ferociously around like a rag doll. Although Accelerator was able to lessen the damage with his vector control, he still tasted blood.
Snow, dirt and sand were all tossed up by the attack, filling Accelerator’s vision with a blur of white.
“This..... this is....?!”
As Accelerator was hurled towards the ground, he gasped for breath, but no sound came out. His throat was blocked. Using vector control, Accelerator cleared the congealed blood from his throat, and was finally able to breathe.
(Fuck.....!! What the fuck was that?!)
The massive amounts of snow and dirt tossed up by the attack filled the entire sky. 
In this panorama of white, there was only one other color.
A glow of blue, radiating from the archangel of destruction.
“.....”
Once again, the sky started flashing, and Accelerator was filled with foreboding. For the onslaught he had been through was just the initial “shot” of the attack.
The archangel relentlessly pounded Accelerator with the fiery rain for another ten “shots”.
(“You’re fucking kidding me....”)
His body hurting all over, Accelerator struggled to stand up. He could not die here.
OT22 Chapter 12 Part 1
Accelerator felt something was wrong before he even turned his head to check on his surroundings.
He had an unpleasant feeling like something cold was piercing into him through all the skin on his body. No, perhaps it was the opposite of that. It may have been that the trembling within his body was flowing out through his skin. It did not matter which it was. At any rate, it was not coming from his usual 5 senses. It felt like his body’s sensors and the calculative circuits in his brain were malfunctioning because he was forcibly taking in information he was not supposed to be able to take in.
He could feel an immense pressure coming from above.
It felt like an incredibly concentrated form of what was emitted by Unabara Mitsuki, the water angel, and those parchments.
Accelerator looked up into the heavens while still embracing Last Order.
A giant fortress was floating there.
The golden light filling the sky was being swallowed up by the fortress. Accelerator thought he could feel the pressure of that immense power that was concentrating in one spot.
[...]
In an instant, Accelerator reached a point 3000 meters up and scattered the thick clouds that were hanging in the sky.
At the same time, the fortress in the heavens made its move.
The mass of golden power that was being taken in from above and stored underneath was mercilessly thrown downwards. Accelerator could feel the pressure on his cheek as a stinging numbness. Just like his white wings, that power truly was not a normal power. Most likely, his reflection would not work on it. It would just pierce straight through like when he had been defeated by Aiwass.
Mina Mathers - Thoth Tarot
NT19 Chapter 1 Part 6
(I see. So this is the vector control I’ve heard so much about.)
But she could not fully counteract the impact.
The black cat witch stiffened slightly and the #1 did not even need to approach her. Since he could manipulate all vectors as he saw fit, he could control the flow of air…that is, the wind. If he created a small tornado around himself, he could lift as many leaves as he wanted from the ground. He could give himself a supply of 100, 1000, or even more bullets to gradually wear Mina Mathers down until she was dead.
The lady in mourning clothes and cat ears once more raised her palette knife in the standard fashion.
“No, I suppose I have no more reason to follow the standard.”
She readily let go of her greatest weapon.
Gravity pulled on the metal and its tip touched the sidewalk.
At that very moment, she became a wind colored the black of mourning and moved right up to Accelerator.
Mina Mathers was “something shaped the same as a person”. She was actually a grimoire, so she was not a human or even a mammal. Thus, her skeleton, muscles, and various organs did not need to move in the normal fashion.
And that meant she could entirely ignore the upper limits of the human body which was bound by calcium and protein.
By the time Accelerator saw her, he could already feel the pressure of the tightly clenched fist striking his entire face. The strength of the word “reflection” was entirely blown away.
It had not functioned at all.
The black cat witch’s right hook caught the #1’s cheekbone and she continued swinging with her entire body weight behind it. The great roar of impact only arrived after a short delay. When she saw the slender form quickly spin around, Mina Mathers whispered to him.
“Even the #1’s reflection is reliant on the calculations you use to control that power. Simply put, you cannot control any vectors with which your conscious and unconscious calculations cannot keep up. Of course, with the brain of Academy City’s #1 and the Misaka Network at your disposal, that would not normally present any kind of problem. …Yes, unless you began a benchmark test with a true processing device. And even if I have been freed from the bonds of that largescale parallel processing device, I am still doing the Thoth Tarot.”
“Ah…bwah…!?”
“Hm. I thought I had understood the gravitational calculations, but combat movements feel different. With a physical body, my breasts are a lot heavier and in-the-way than I had expected. But it’s neat how the swinging of the tail helps recover my balance after the follow-through for the punch. Now get up. There is so much more I wish to try out.” The black cat witch took some quick steps back and forth while clenching her fist again.
It did not fit.
This behavior did not fit Mina Mathers’s manner of speech at all.
But that was exactly why the stimulation-starved widow’s lips formed a clear sign of joy behind her veil.
“No matter how old I get, my first time doing something is always so fascinating.” 
Additionally in the Accelerator manga his Reflection has been slightly bypassed in two ways: by a calculations-based trick used by Qiong Qi and another Coffin linked to it, and by Taowu/Isaac Rosenthal as it was transforming into an angelic entity.
==Esper's Resistance to Poison==
The Esper Curriculum use of drugs and chemicals has the side effect of giving people a decent resistance to poison, as noted in the following quote. This would apply to all espers but Gemstones (who got their power naturally), the Misaka clones (as they don't follow the same curriculum nor have spent as much time taking drugs as regular students) and people who don't actually have powers themselves but make use of them through technology like Kiyama Harumi, Kihara Gensei and Rensa.
OT4 Chapter 1 Part 4
Kamijou frantically rolled away and dodged it, but the knife still grazed his face.
Just a light cut.
But at that moment, Kamijou lost his balance. He collapsed onto the ground, unable to get up. He was sweating profusely, and felt like vomiting.
(Poi…son? Damn it…what did he apply on that…?)
The action of rubbing the knife with the cloth was to apply poison.
It was said that among some minority tribes in Africa, they would apply poisonous caterpillar fluids on the tips of the spears before hunting. Maybe this was a similar poison. Kamijou’s body had developed a rather decent resistance due to Academy City’s training, but he couldn’t prevent the power of the poison from taking effect.
Kamijou’s vision became blurry, and then darker.
Category:Toaru Majutsu no Index
Category:Explanation Pages