Had she walked just slightly quicker, Izuku might have gone straight into the embrace of the slime villain as he slopped through the sewer grate.
Eugh, is all she can think as she closes notebook No. 6. He's probably absolutely coated in germs.
"Oh, a vessel," the villain cackles, slowly encroaching like she wouldn't notice when he's right in front of her. "Not what I'd usually go for, but I can't complain given the circumstances-"
He cuts off abruptly, lunging towards her, and she deftly slips to the side. "W-who are you?" she asks shakily, honestly terrified of him - but she just needs to stall, right? Stall until someone else can get help?
She glances around, but she can't see anyone else around around here. "None of your business," the villain snaps. He clearly knows what her plan is, because a wave of gunk slams into her before she can react, the uncontrolled force flipping her around and knocking her prone.
Her chin clacks heavily against the floor and she lets out a whoof of air, but despite the spots in her vision, she makes another attempt to move-
"TEXAS..."
Izuku automatically checks her mind for All Might's collateral record. Thankfully, there's nothing there to remember, so instead of fleeing as she might from another hero's area of effect (say, Endeavor), she spins on her knees to watch first-hand her childhood hero at work.
"SMASH!"
She's blown onto her rump by the wind, but the villain fares much, much worse. The lone set of teeth clattering on the floor is a testimony to that. It's also vaguely disturbing to look at.
All Might stands proudly for a moment, dressed in oversized yet tightly-fitting civilian wear that clearly shows this is cutting into his personal time. Izuku feels a little guilty, especially with what she knows about him.
But wait, she can help him!
With insane speed and accuracy that nobody else without a very specific quirk could match, All Might scoops the remainder of the goop into a few bottles - clearly Texas Smash vaporised a large quantity of it, which probably meant that it has a lower or equal boiling point to water, considering All Might's current average power output. The eyes and mouth still move of their own volition, though, so the brain is likely able to shift to inhabit undamaged parts of the gunk.
An amazing quirk like that, and this guy's a villain? That's actually kind of upsetting.
"Indeed it is," All Might agrees with his signature grin turned in her direction, and Izuku tunes back into the real world, realising with a blush that she's been muttering again. "You have an incredibly sharp mind, deducing all of that from what little you must have seen from the villain. You wish to be a hero, yes?"
"O-of course!" Izuku nods with a beaming smile. She's talking to All Might! "You've been my inspiration for so long, I- wait, let me just-"
She cuts off, focussing on her backpack and the notebook splayed open on the floor. That one's Ingenium, she recalls, deftly folding it closed and piling it into the back, before turning her attention to the other books inside as she leafs through them. Japanese, English, Mathematics, Notebook No. 0-
Wait, All Might's getting ready to jump! She can't let him leave now, even if his time limit is almost up! She needs to help-
Suddenly she's flying through the air, grappling onto the leg of her idol.
At first she locks onto the leg with a death-grip, but then the rustling of her still-open bag draws her attention.
Just when No. A - the study on famous non-combat quirks - is about to fly from its still-open storage, she realises that she's already been given the kinetic energy that she needs to follow the same arc as All Might, so she's free to make a grab for it without losing him.
She does.
Once No. A is back in its rightful place, she figures that there's no point wasting this extra time, so she dives back into the bag to search for No. 1.
This kid is insane, is Toshinori's first thought when she latches onto his leg just as he makes his leap into the distance, which was supposed to let him escape and keep his secret hidden.
Then she lets go.
To search through her backpack.
Logically, that makes a certain amount of sense. Toshinori's never been especially academically inclined, but even he knows how momentum works. But still, it's difficult to believe that someone would place so much trust in him - even being the symbol of peace that he is - that they'd let go of their lifeline like that.
That she'd do that for something as mundane as protecting her books... this kid's kind of scary.
With a sigh, he gently wraps a hand around her waist and pulls her towards himself. It wouldn't do to have her Smash her head into the concrete, after all.
Idly, he wonders which state he'd need to call on in that instance. Probably Florida; it'd fit right in with their wacky news stories.
They land fairly lightly on top of a roof - he's made that exact jump thrice during his time here, fortunately enough - and the girl stumbles and regains her balance without ever looking away from the books she's been sorting through - and it looks like she found the one she's looking for, if her cry of "a-ha!" is anything to go by.
He can already feel the tell-tale strain of his body's attempt to return to normal. But he can't just run, can he? He needs to give a proper excuse or this kid might just try to figure out why the No. 1 Hero fled without so much as a goodbye.
Granted he's already tried that (and it was a dumb, split-second decision, he chastises himself), but to do it again would really be pushing his luck.
The girl takes a calming breath, and holds up one of her many notebooks. "All Might, I know you're not at full strength anymore, and I think I..."
...What?
What?!
Why does she know that? How could she know that? She's just some kid! Why did he have to cross paths with the only person to figure out his weakness by herself in such a long time? Why is she a kid?!
She's stopped talking now, but try as Toshinori Might to play back the conversation, it seems to have passed straight between his ears as he had his little breakdown.
The notebook's still hovering in front of him courtesy of a tiny hand, so to take his mind off the fact that this insane girl knows about his injury, he takes it.
Upsettingly familiar skeletal arms come into view.
Ah.
"I think I'll have to rework some of my ideas," the girl murmurs, peering at his true form from several different angles, and he feels strangely exposed despite wearing clothes big enough to parachute with. "I knew you had some kind of injury - you always favor your left side since five years ago, after all - but I didn't realise it was preventing you from eating properly too. I assume you've already been seen by doctors soyoushouldprobablyignorethepartsabou..." Here she devolves into muttering that even Toshinori, with his endless experience dealing with starstruck gibbering, can't begin to decode. She pulls out a pen, as if to jot something down in yet another notebook (And how many of those does she have, Toshinori finds himself wondering).
He sighs, finally looking to the cover of the book in his hand.
"Hero Analysis 2.0, Number 1: All Might," he reads. He thinks he'd be more flattered if it weren't for the fact that this kid knows his secret (and he knows he's hung up on that fact, but it's kind of a big deal that a mere child has enough information to figure that out, given that his enemies could certainly do the same).
He flips to the first page, which jumps right into the thick of things with a mostly blank page, the word Alabama written at the top. He flips the page again, and realises when the next two page spread has the titles Alaska and Arizona, that it's a catalogue of his current and potential Smash moves.
Now he actually is flattered, as he flips over to North Carolina. It's one of his lesser-used attacks these days - Carolina Smash is his go-to chopping move, since he can't get much power behind a single-handed chop anymore - but clearly the kid's done some research. In fact, there's a list of all five times All Might has publically performed the attack since his injury, with an estimated power output for each one, and a comparison with pre-injury versions of the same move.
That explains it then. This girl is some kind of analytical genius.
Wondering just how deep this rabbit hole goes, Toshinori bookmarks that page with a finger, and flips all the way over to South Carolina, the move's left-handed variant. If his hunch is correct... it is. The kid (he really needs to get a name) notes how little he's used South Carolina Smash, how he always uses it against the weakest enemies, and on a little scrap of paper which has been painstakingly pasted in, pieces together where exactly the injury might be, and that All Might wants to hide his weakness and present himself as an unshakeable pillar.
It's a frighteningly accurate assessment; she's guessed wrongly that the injury was on his back since he's actually less careful with his front than he strictly should be, but otherwise he'd think she was spouting facts instead of theories. Toshinori knows how little information there is of him as a living, breathing being as opposed to some god among men. The ability to spot such well-hidden flaws, especially through the haze of hero-worship that the girl clearly has based on her starry eyes and All Might-themed rucksack, is a skill that many heroes could only dream of rivalling.
But he still doesn't see why she gave this to him. It's clear that she doesn't just want to be praised, with a mind like that. She obviously believes that whatever's in this book will help him. And despite the tens of specialists who aren't able to help an iota, he finds himself optimistic.
So he turns forward the pages, through all the other US states, past the gushing praise and what he already knows, through the evolution of his hero costume, and finally comes to a stop at the page titled simply: Ideas.
It takes a moment to decipher the seemingly random sets of words like 'wide-area force, p67', 'aerial recoil dissipation, p82' and 'exo-skeleton a-la Skeletoni, p59', but with a glance back at the title, he realises:
These are Ideas.
When All Might emits a gurgling cough and spits blood to the side, Izuku isn't sure what to do. They'd never expected to meet their hero in the first place, but to see him in such a weak position, having hitched a ride on his leg just minutes before...
She's known about his injury for a few months now, but this hits a little too close to home.
"Is this normal?" she asks warily. She doesn't want want to panic when this is probably a common occurrence for him, but at the same time, coughing blood isn't usually a sign of impeccable health.
"Yeah, nothing new to see here. Most of my stomach is gone, this is kind of a given. I've gotten used to it." He grins at her though, eyes wild with energy that she hadn't seen in him since his All Might form boiled away. "I'd all but given up ever staying a Hero, but these ideas of yours are truly magnificent! I'd wager that this exo-skeleton design..." he points to the corresponding diagram, and Izuku can't help but blush and look down, "could keep me in the business for at least another two years, and the training regimes might keep me going for five! What's your name, young lady?"
Izuku freezes. She knows that All Might might want to find her in the future to discuss some of the weirder ideas. But if he does that by knocking on the door, Izuku's mom will answer. Their mom thinks he's a boy but All Might thinks she's a girl...
But if he asks for a different name, their mom might get suspicious.
"I'm Izu," she states firmly, silently thanking her mom for going through all those baby names. "Midoriya Izumi."
"My name is Yagi Toshinori. I can't thank you enough for this opportunity."
All Might bows.
Izuku's world breaks.