A/N: Takes place after episode 9 in the anime or Chapter 25 of the manga, a few days after the Shinigami sent to bring Rukia back to Soul Society leaves after witnessing Ichigo's power against Grand Fisher.

The song that disturbs Rukia is "Running Away" by Three Days Grace. Translation of Rukia's words in Chapter 20 are from onemanga. Please be aware that the math presented here is not entirely accurate.

Disclaimer: I don't own anything.

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Title: The Hole in the Graph

Rukia worries, and Ichigo pretends not to notice.

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asymptote: n., on a graph, a straight line which a function approaches but can never cross

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There was a vertical asymptote at -1, but there was an (x+4) in the numerator and the denominator, so there was a hole in the graph…

Ichigo frowned at the textbook and took his pencil from between his teeth to begin drawing the graph.

Just as the lead touched the paper, something icy landed on his back and shoved him face-first into the wooden floor.

The pencil lead snapped.

"WHAT THE HELL?" Ichigo shoved himself up on his elbows, twisting around to glare up at the midget he knew was responsible for the damn cold foot on his back. "That pencil could've gone through my eye, Rukia!"

"That's exactly why I did it, fool," she retorted coolly, arms crossed over her chest and digging the heel of her bare foot deeper into the space just beneath his shoulder blade. "You need to be more alert!"

Ichigo growled a little, turning back to face his homework and jerking his shoulder to push her off his back. He felt her stumble for a second, her foot sliding down his ribs, but she quickly regained her balance, curling her toes into the fabric of the old Nirvana t-shirt he wore and digging her heel into his kidneys this time.

Ichigo groaned and pulled his earbuds out. "Rukia," he said, not quite growling but dragging out the 'a' at the end of her name. "What do you want? You already kicked me off my bed."

He wasn't exaggerating. She'd recently discovered, while he disposed of a Hollow terrorizing a preschool playground, the joys of finger-painting. The fruits of this discovery (and of half of Ichigo's allowance that week) now lay wet and glistening on her closet bed, Ichigo's desk, most of the floor, and his bed, which she'd shoved him off of with her foot when she ran out of space to put the drying paintings. The same insanity that seemed to make her so obsessed with depicting Chappi the Rabbit in every artistic medium possible, including dried macaroni noodles and rubber cement, also seemed to make her function under the belief that Ichigo's room was actually hers and that he was just a five foot nine human she happened to be kind enough to let sleep in the bed.

So she ignored his complaint and demanded instead, "How are you going to hear the Hollow alert go off if you have those things in your ears?" she demanded.

"I won't. I'll hear you screeching at me to move my slow ass," he said unconcernedly, putting the 'things' back into his ears and turning back around to erase the deep black line she'd made him gouge across his graph paper when she'd jammed her foot in his spine. He knew she'd get bored eventually and wander off to draw more Chappis or steal clothes from Yuzu or something, leaving him (and his kidneys) alone.

True to his prediction, as he finished erasing the line and clicked his pencil to push out fresh lead, he felt her foot remove itself from his back.

He grinned to himself, stretching a little and nodding his head in time to the new CD that Chad had burned for him –

Then something sharp drove into the middle of his back.

"OI!" he roared, wrenching around and planning to – to – well, to do something to Rukia in vengeance for stabbing him like that! What the hell had she even used –

It took a moment for the rage to clear from his eyes enough for him to realize that a) Rukia wasn't standing above him anymore, and b) there was a warm and relatively soft weight draped across his midsection.

He froze, half on his side, and looked down.

Rukia was sprawled across him like a blanket.

Ichigo didn't even have time to fully register this position before Rukia had scrambled off him and shoved back onto his stomach with an unceremonious foot.

"Stupid fool," he heard her grumble past the blood and music roaring in his ears, and this time as the sharp jabs – one, two, three, four of them – dug into his back and the backs of his legs, he realized that they were Rukia's skinny elbows and knees, not her Chappi pen or a steak knife from the kitchen. More flares of pain dug into him as she made herself comfortable on his back, treating him as though he was a soft section of floor for her to recline on. "What'd you do that for?"

"I thought you were a Hollow," he snapped, lying defensively. He felt the back of his neck heating up, and he pushed his head back onto his elbows, muttering, "You're the one who just said I needed to be more alert."

He heard her snort and say something about how if he spent more time honing his reiatsu skills, he would've been able to tell she wasn't a Hollow, for God's sake. Then something sharp sank into the back of his neck. At first he thought she was making fun of his embarrassment by poking his flushing neck (it wouldn't be the first time she'd done it), but then he heard the sound of a page turning and realized that it was the base of a manga's spine digging into his skin.

"What the hell, Rukia," he muttered half to himself as he glanced around to see where his pencil had rolled to this time. "You did all that so you could read a frickin' manga on top of me?"

"Yes, fool," she said matter-of-factly, digging her elbow into him warningly. "Now shut up, I'm at a good part."

Ichigo huffed and reached for his pencil, which he had located sticking out from under the bed. The sensation of his shoulder blade moving beneath Rukia's weight was strange but not unpleasant, and he propped himself back up on his elbows, feeling her weight slide down him a little. He pressed his lips together and frowned fiercely at the exponential graphs in his notebook.

And just when he had finally managed to focus on exponents and denominators and the heavy percussion blaring in his ears instead of Rukia's bony body, she flicked his ear with a finger.

"What?" Ichigo exploded.

She pulled at the earbud cord. "Give me one."

Ichigo let out a frustrated sigh but tugged the earbud from his left ear and passed it to her waiting fingers.

Not even a minute passed before she ground her elbow into his abdomen. "I don't like this song. Change it."

"No way," he said, gritting his teeth but refusing to show weakness to the elbow nearly impaling him. "My iPod, I listen to what I want."

"Ichigo…" The elbow dug deeper. It was practically boring a Hollow hole into his back. "Change it."

Ichigo ground his teeth together and clamped his elbow down until the music grew to a deafening roar in his ear. 'YOU'RE RUNNING AWAY, YOU KEEP TURNING YOUR BACK – '

"Fine!" Rukia yanked the earbud out of her ear. Her hands dug into his shoulder blades as she pushed herself up to stand. They were shaking a little, and Ichigo realized with a sudden drop of his stomach.

"For Christ's sake, Rukia," he snapped, shoving himself abruptly up on his elbows so that she lost her balance and "oomph!"ed onto his back again. He felt and heard her chin land on his shoulder blade, her teeth snapping together with a clack, but before she could yell at him, he dropped back onto his stomach again and threw the earbud back over his shoulder at her. "I'll change the damn song, okay! Now shut it and let me finish my homework."

He kept his voice annoyed so she wouldn't know he'd noticed that anything was wrong. She had gone out of her way to keep him from realizing that something was bothering her – hell, she'd almost succeeded – and after the sacrifice he'd asked her to make after the Great Fisher got away, he owed her enough to respect her silence if she wanted to keep it.

I don't have a method of stepping into the depths of your heart without getting it dirty.

She had, after all, respected his.

Scrolling to one of the bands Yuzu liked, Ichigo pressed the play button and let his head fall onto his fist, staring at his textbook. He pretended to start drawing graphs again, but the lines were random squiggles until he finally felt Rukia's muscles relax on top of his. The tension eased from his body, and he let himself focus on his homework again.

He had gotten through three more graphs, for real this time, when he became aware of Rukia's cold toes tapping against the back of his ankle. He tensed, confused, until he realized that her foot was moving in rhythm to the song.

He smothered his second smile of the day and bounced his shoulder. "Oi."

The movement jarred her shoulder; he felt it slip and thud against the wooden floor as she flailed for a second before clawing, cat-like, back into her precarious position on his back.

"What, fool?" she said, voice heavy with suspicion.

"You wanna listen to that song again?"

He could have sworn he felt her grow lighter, as though the suspicion that evaporated from her had been an actual weight.

"Okay," she said happily. If Ichigo had been able to see her, he had the feeling her face would have had the same oblivious-to-the-world smile she usually wore when she was lying on the floor coloring Chappi pictures with a brand-new set of markers and kicking her legs back and forth in the air.

As he thumbed his iPod to play the song again, he angled it so that the screen reflected Rukia's face and saw that he had been right.

The opening chords began again, and Ichigo felt her arms shift and a warm pressure, much less sharp than her elbows, settle between his shoulder blades. Without using his iPod to look, he knew that she had laid her head down on his back.

This time he didn't bother to smother his smile, letting it curve his lips as he drew the last graph. There was a vertical asymptote at -2, meaning that the lines on the graph shouldn't have been able to intersect –

– but there was an (x+2) in the numerator and the denominator, making a hole in the asymptote.

With Rukia's exhalations steady and warm against his back, Ichigo drew the intersection of two lines that never should have been able to meet.

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hole: n., on a graph, occurs when the numerator and denominator of a function share a common factor

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A/N: This is my first foray into the fandom, so please leave a review. Are they in character?