Shirai Kuroko took some measure of satisfaction in being, at heart, a logical girl. Even her love for onee-sama derived at first from the Railgun's impeccable position: the poster child for Academy City and the achievements of Science as a whole; from the outside she was beautiful, a genius, and part of the elite. A crush on Misaka Mikoto was the sort of thing that made perfect sense. That it endured through close proximity, through learning that for all she was gifted and breath-taking she was equally childish and brash… well, Kuroko was a logical girl. That is: she was still a human, with human emotions, desires, and drives. As with her love, this was usually no problem at all, apart from one thing.

Kuroko had a bad habit of rushing in without thinking.

It was a flaw that she was often berated for, and that the Level Upper incident brought into sharp relief—but not for the obvious reason. It was the reminder, through Kiyama Harumi's network, of how much esper abilities relied on mathematical abilities. None more so than teleportation. Yet, at some point, she had stopped analysing her own calculations and the implications behind them; content to run through the reified mental paths that she knew would move her body from here to there, move a well-placed spike to pin a miscreant. When had Kuroko become satisfied to allow the slow improvements in range and accuracy from the curriculum and her everyday usage to define her improvement?

There was no power more logical at heart than teleportation or at least none so common that Kuroko had ever heard of it. Why it was eleven dimensions and why different teleporters all used incompatible calculations was a scientific mystery, but the principles and how different teleporters' limitations differed was always the same, always explicable. An object's position could be described as a translation by an eleven-dimensional vector in a higher-dimensional space and, by alteration of that vector, its three-dimensional position would be relocated. All the relevant physical properties of a single thing, encapsulated into one complex mathematical description: position, orientation, momentum, physical dimensions, and even the effects of space-altering forces—the effect of an object's own mass, minute as it was, on local gravity impacted the end accuracy.

All that was to say, if there was one power in Academy City that she knew could improve qualitatively, if not quantitatively, simply by a refinement of the user's understanding then it was teleportation. And at some point, between the glamour of her new school, spending time with onee-sama, her Judgement work… Kuroko had simply stopped finding the time to explore the limits of her own potential.

… but pulling herself away from her daily life to find time for that, not being available if she was ever needed, that had been hard. Today, the recruitment event had ended surprisingly early, and Kuroko had considered going off to find Mikoto before it was time for dinner. But the reminder that she had been neglecting chances to improve herself that came with touting how Judgement work was such a chance stopped her.

Instead, she headed to the branch office with the excuse of wanting to be available to respond to any reports that came from having so many Judgement members concentrated off of patrols and settled down at her desk. Fortunately, it seemed that the majority of low-lives were doing the same thing as any other student given the summer conditions: enjoying the weather and staying out of the heat.

That left Kuroko with a mechanical pencil in hand, thinking how she had gotten to this point.

Like most teleporters, and a point many of them never moved beyond, her initial teleportation had been restricted to specific "known quantities". For some, this might mean that only a certain item could be teleported, fixing all variables relating to mass or dimensions. Kuroko had similarly been limited to simplified calculations but instead was limited to zeroing out as many spatial co-ordinates as possible: with her own body as a known reference point, she had been able to move anything from one hand to another. It was only when her mathematical understanding had grown that Kuroko had been able to teleport items away and out into open air.

This had been her limit for over a year. Even on her enrolment, Kuroko had lacked the ability to teleport herself. It simply hadn't made sense, with the way her calculations ran, to move her body. The values it held would be the same at both the start and end of a teleportation, an origin that everything else was calculated around. Logically, the solution had been obvious but the reason to try it… well, she had wanted to meet onee-sama's roommate somehow, and it had been worth the attempt.

Occasionally, the voice in the back of her head that insisted she might teleport her body but leave something important like her brain behind still spoke up. But that had been proven false.

The solution? Quite simply, although her body defined the zero-point for her calculations, there was no need for her body to remain there once this reference was obtained. All that Kuroko had needed to do to breach that boundary was accept that her arbitrary co-ordinate system could describe where she was now in relation to where she had been, that her body was able to separate itself from the reference she had used.

Maybe her current limits weren't so different? Placing the pencil down, Kuroko rested one finger on it and concentrated, thinking harder about the process of moving such a small item a mere few centimetres to the size than she had done for years. Not just performing the calculations, but thinking about what each part meant—at least, those parts she had fully understood.

The pencil reappeared on the desk.

But how could she do the opposite? Even if she could now perfectly describe the pencil's location, it was physically out of reach. Yet only an instant ago she had been "touching" it, its full eleven-dimensional movement propagated by the esper along its entire path. The movement had been so brief as to be instantaneous, but she had still been touching it with something.

The sticking point felt familiar and simultaneously wrong. As a younger child, Kuroko had spent hours agonising over a similar pencil or any other small item that came to hand, struggling to cross the gap between knowing there should be some solution to place the pencil just out of reach, yet always guessing at what this would be. It would reappear inverted in her other hand or moving, or she would teleport it but found that her hand had moved without thinking and it had simply teleported in place. Intuitively, she had known that teleporting something away from her would mean reaching without reaching, mathematically describing a push through a space that could only be comprehended by mathematics. In those days, her intuition for being an esper had been more advanced than her mathematical ability. Now, she had the mathematical understanding to describe the inverse teleportation but not the intuitive reach to attempt it.

Teleportation was a logical power. This, Kuroko believed absolutely. Everything about it could be described in eleven dimensions and, therefore, so must any clairvoyant component. Anything that would allow feeling out one's surroundings or reaching an object out of reach must operate on the same rules. How, then, could a teleporter reach out to the world around them? If a teleportation normally described moving an object from some reference to another, what about if there was no object and just a set of null values; a vector describing naught more than the abstract notion?

What if Kuroko tried to move nothing from her hand to the pencil?

As expected, nothing happened. But there was still a flittering feeling of… something. Almost like teleporting, ephemeral and instantaneous. So, she did it again. And again. Focusing on that feeling, not the result, like trying to build muscle memory. It was evening, now, and no doubt dinner was a missed opportunity—if she didn't want to miss curfew, then Kuroko would have to stop soon. But she felt so close to… something.

Again, this time targeting the air. The feeling was similar, air wasn't a vacuum, but there was something there… no matter how empty and smoke-like the entire process was. Back to the pencil, then the air. There was a solidness to it; either she was feeling something or starting to hallucinate. Maybe both.

This time, Kuroko tried to split her attention. The idea was entirely familiar, like talking and teleporting at the same time. One part of her mind would run through the calculation to teleport, and the other would be talking. Or preparing a kick. Only this time, the calculation was backward and the second part was a half-empty calculation itself, a movement of nothing to something.

The first time, the feeling slipped through her fingers before she was done, no matter how many times this exact movement had already run through her head. The second time, the separate thoughts crossed, and from the stinging in her hand, Kuroko had somehow grazed it, a small bit of skin caught distinct from the rest of her. A rookie mistake. But the third time…

The pencil wobbled.

All thoughts of making it back to the dorm before curfew forgotten, Kuroko's attention grew narrower and narrower. Even the thought of worrying onee-sama was pushed to one side, the lack of any sort of texts or calls indicating that, at least, she wasn't overly worried about the younger girl's late return to their dorm.

The pencil wobbled. It rocked. It turned itself around entirely—annoyingly, Kuroko had to turn it back before that set her back to square one. It wobbled some more. And then, so surprisingly easily that she almost stopped mid-calculation, Kuroko took hold of that ephemeral feeling.

The pencil was in her hand. It had been moving, the inverse equation was imperfect. But… she had done it. An object teleported without starting at a 0 point. It was only a small thing until it could be generalised, but the very idea… she would need to practice some more and then show onee-sama—

Left unnoticed this entire time, the computer had still been displaying any reports that came in. Many of them would be automated, Academy City's security processing any disturbances that needed manual intervention and sending them to the authorities. Normally, Judgement would be handling nothing at this time of night. Even if it had been, the automated note of gunfire in the area of a shipping yard could never be investigated before the crime scene was evacuated.

But for the teleporter that had been seated at the desk all afternoon, it would only be a matter of minutes to arrive. The ones responsible might very well still be there or still fighting.

She paused just long enough to commit the time and date to memory for the sake of a report:

August 15th, 21:00.

AN: Personally, I've always thought the 11-dimensional technobabble used for teleportation had the setup for so much potential and exploit-but both Kuroko and Awaki are occasional side characters. So, why not take the opportunity to explore what you can really do if you focus on all the potential requisite abilities pulled into moving something from A to B? I can promise one thing, though; no sudden, huge jumps in range or weight. Really, there's not the time for that sort of training arc here~

And as the name suggests-well, one stubborn little teleporter added to the mix could really start to change things, no?