Translator: Dreamscribe
A na had been quietly added to the research lab naplate.
The rumor that Su-jeong had joined Team Apex spread quickly across the MIT campus.
[Team Apex Lab]
-Seoha Yu, Theodore Langford, Srinivasa Krishnan, Sujeong Lim
It was a team that hadn't accepted a single new mber since Theodore and Srinivasa, and that very exclusivity had only fueled the rumors swirling around it.
"Hey, did you hear?"
Soone whispered from the back row of the lecture hall.
"Apparently Apex added a new mber?"
"A postdoc?"
"No, an undergrad. A transfer student."
"What?"
The other student's eyes went wide.
"No way! Who is it? That's the place where even PhD candidates got weeded out left and right!"
"She's right over there."
He pointed to a girl sitting in the very front row, deep in thought about sothing.
Normally, Su-jeong would have quietly relished rumors like these. The curiosity and envy mixed into the whispers, and even the wary glances cast her way.
But right now, she couldn't afford that luxury.
After her addition to the team was decided, Sri and Theo had led her to the archives.
Creeeak.
When they opened the door tucked into the corner of the lab, neatly stacked boxes ca into view.
Su-jeong had steeled herself before setting foot in this place, but the mont the door opened, she was rendered speechless.
Boxes stacked waist-high, numbered file cabinets lining the walls, and a massive whiteboard covered edge to edge with paper titles.
Short notes were attached beside each entry.
-Too much dependence on initial conditions.
-Local convergence observed, but difficulty in extending.
-Identified interval where limit exchange is not possible.
-Counterexample found. Discarded.
"Is all of this reference material?"
The two of them nodded.
"About half. The rest is data we've built up through our own research. We've personally verified every single reference paper too."
Stability theory, nonlinear flow, variational problems...
Su-jeong was floored by the mountain of papers spanning such a vast range of topics.
"This is what you've been working on?"
It was research on a scale that could turn both the math and engineering worlds upside down.
And it was already considerably advanced. Su-jeong sat down in a chair and began reviewing the progress made so far.
"You must have worked incredibly hard."
Sri and Theo shrugged.
'Don't ntion it. You'll be doing it with us now.'
The aning ca through perfectly clear without anyone saying a word.
Su-jeong shivered at the sudden chill she felt.
"It'd be great if this were everything, but..."
At Theo's words, Su-jeong looked up in alarm.
"Don't tell there's more?"
Sri walked over without a word and opened a laptop.
Click.
He clicked on 'Oracle' inside a hidden folder. Inside were countless subfolders.
eting minutes, interim reports, simulation logs, and experint files that had never even been assigned an official version number.
Every record generated during the project with New York City was in there.
Click.
Opening one subfolder revealed an endless list of entries organized by date.
"This project is going to resu soon. So if you're part of our team, you'll need to know all of it, right?"
Theo winked with an annoyingly smug expression.
'Ah, so that's why!'
Since arriving at MIT, there was one rumor she'd heard countless tis.
Team Apex, an ultra-elite team built around Seo-ha, but one that had stopped recruiting new mbers long ago.
Su-jeong finally understood the reason.
"I'll start right away."
It was a volu of studying she had never faced in her life, but it was a fight waged in the way she had always fought.
And Su-jeong was soone who had been more than tempered for this kind of fight.
'I can do this!'
She didn't want to disappoint Seo-ha, the person who had believed in her.
* * *
Beep beep beep!
Tap.
6 a.m.
Seo-ha's eyes snapped open at the sound of the alarm.
Whoooosh.
After a quick shower, Seo-ha carefully made his way down the stairs from the second floor.
Just as he grabbed a slice of bread from the kitchen and was about to head out, he sensed soone behind him.
"Seo-eun! Why are you up already?"
Seo-eun was standing there holding Justin, looking like she was about to cry.
"...These days, whenever I wake up, you're already gone."
The ears of the beaver she was clutching tightly drooped, mirroring her mood.
"So I thought if I got up a little earlier, maybe I could see you..."
For Seo-eun, who loved sleeping in, waking up five minutes, ten minutes earlier each day hadn't been easy. After repeating this for several days, she had started opening her eyes before Justin's morning alarm even went off.
"Seo-eun."
"Yeah?"
ssy hair, a face still heavy with sleep, yet stubbornly keeping her eyes open to look at him.
Seo-ha set the bread down and crouched in front of Seo-eun.
'How should I cheer her up?'
It seed the disappointnt had been building because he hadn't been able to spend much ti with her lately.
A new ga?
Maybe offer to take her on a bike ride?
Seo-ha decided to just ask Seo-eun directly.
"I'm sorry I've been so busy. I have to head out now, but is there anything you want?"
As if she'd been waiting for exactly those words, Seo-eun's eyes lit up.
"There's one thing!"
"What is it?"
"But they said it's sothing super hard to get."
"Tell . It's sothing you want, so I'll do my absolute best."
"Really?"
"I can't promise for sure, but."
'There's a dal way bigger and cooler than this one.'
Seo-eun hadn't forgotten what Su-jeong had told her.
"A Fields dal!"
Just thinking about it made her happy; Seo-eun bead, showing off the gap where her front teeth hadn't grown in yet.
Seo-ha was montarily speechless.
"Uh... yeah. Hmm."
When was the next Fields dal ceremony again?
Was it possible?
Thinking about it objectively, the odds of winning were about fifty-fifty.
Considering his age, there was a real chance they might not award it to him this ti.
In that case, what he'd need would be an achievent so monuntal that the committee simply couldn't refuse.
"Oppa?"
Seo-eun's voice snapped him back.
"Yeah, I'll definitely get it for you. As a present for your tenth birthday!"
Her eyes went perfectly round.
Then she glanced at the clock on the wall and said rapidly,
"Then there are 649 days, 17 hours, and 20 minutes left?"
"That's right. Exactly."
Seo-ha nodded.
"Promise!"
"Promise."
When Seo-eun stuck out her pinky finger, Seo-ha found himself making the promise before he even realized it.
On the bike ride to school,
the image of his little sister bouncing happily lingered in his mind.
"Well, I've got a deadline now."
His grip tightened on the handlebars.
* * *
During Team Apex's regular eting,
Seo-ha set down the chalk and stepped back.
The entire lab was covered with the equations he had written.
'He's already gotten this far?'
The theorem that had been stuck was beginning to unravel, bit by bit.
Theo stroked his chin with a satisfied expression.
'A solution for the Minimal Energy Surface exists.'
That was a fact Seo-ha had already proven, a flawless proof that left no room for counterexamples.
It was a remarkable discovery on its own, but the problem lay in what ca next.
'Proving existence is only the beginning.'
'It exists.'
But no one knows where.
Which path leads there, or whether that path is even unique, remains unknown.
Theo glanced over at Su-jeong.
Long hair tied back tightly with a rubber band, a dark gray hoodie that didn't show minor stains. It was Su-jeong's battle gear, unchanged since her days at Gifted High School.
She was silently scanning the equations Seo-ha had written, her eyes moving rapidly as if determined not to miss a single line.
She was keeping up with Team Apex's accumulated research while also handling MIT's grueling undergraduate curriculum.
"From this point on, we can't go any further down."
When Su-jeong's perspective as a Number Theory specialist was added during the preliminary investigation, the entire landscape of the discussion shifted.
Gradients, limits, convergence.
The Minimal Energy problem that he and Sri had been thinking about until now was a proposition that only held on a continuous flow. But Su-jeong placed integer endpoints on top of it, one by one.
When integer conditions were added, points erged where further progress was impossible, states where energy was at its lowest but transitions were not permitted. A minimum defined not by value, but by the irreversibility of the state.
"Hm?"
Seo-ha had been examining his own equations when he tilted his head and picked up an eraser.
"W-wait!"
Theo hurriedly grabbed a cara and recorded the work Seo-ha was about to erase.
Click!
A cold, sharp focus settled into Seo-ha's eyes.
'It's ambiguous.'
This problem had too many uncertain points from the very beginning.
The questions he'd had from the start surfaced one by one in his mind.
Can this solution be approached as the limit of a continuous flow?
Or does it require a discontinuous leap at certain points?
Does the variational flow actually converge to the minimum?
And can the entire process be laid out without a single gap in logic?
Seo-ha bit his lip slightly.
The form of mathematics he wanted, the proof he sought, could only be found by clearing away every last bit of fog shrouding the mountain range.
'It has to stand as necessity, not intuition.'
There were hints in the data his team had compiled.
Seo-ha began rewriting the equations.
Graphs and diagrams flowed from his hand as if gliding.
'Show what you really are!'
Sri and Su-jeong stared blankly as they watched.
"Shh!"
Theo brought a finger to his lips, signaling the two not to interrupt.
The air inside the lab had shifted.
Seo-ha was completely absorbed in the problem.
It was so quiet that even the faint bzzt of current running through the fluorescent lights seed audible.
Scratch scratch.
Intuition can be a starting point, but never the destination.
Ambiguity is the enemy of proof. It had to be stripped away.
Scratch scratch.
On the board, several candidates that could be the solution remained.
Different forms, different conditions.
All of them had minimal energy, and on paper, every proof made sense. But an inexplicable unease held him back.
'A disguise?'
Seo-ha's gaze slowly swept across the board.
As the graphs and surfaces overlapped, a vast mountain range unfolded in his mind.
Rummmmmble.
When the integer conditions were applied, ridgelines collided against each other with a thunderous roar.
The fog was still thick, but Seo-ha's eyes could see through to its true nature.
"Now I understand."
The fog was not a lack of information, but a phenonon created by overlapping structures.
It was an optical illusion caused by different solutions appearing to share the sa value when superimposed. And among them were points that could never be reached in a three-dinsional world.
Seo-ha turned around.
"As expected, there wasn't just one solution.
But the existing minimum and the reachable minimum are different. We need to find the solution that can survive actual mathematical computation."
A solution that exists but has no path leading to it.
That was the true identity of the fog they had been facing ever since they began tackling the problem.
Theo looked at Sri and Su-jeong.
'A proper team has finally co together.'
Gathered in this room were rare talents who trusted Seo-ha's intuition and wouldn't slow him down.
Su-jeong narrowed the path with Number Theory, and Sri supported the theory with computation and simulation.
And Theo himself was the topologist and the analyst who scrutinized the logical consistency of everything they proposed.
'Yes. With this team.'
How far could they go?
A thrilling shiver ran down Theo's spine.
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