He had written the note the night before, with his left hand, on a small piece of paper torn from an unremarkable notebook purchased two weeks ago at a convenience store three stops from his usual route home. He had worn gloves. The handwriting was nothing like his — cramped, slightly left-leaning, the hand of someone who had learned to write in a different system and carried the trace of it. The note said:
3:52pm4th, Tuesday
That was all.
Second period. History. Teacher Cha had assigned a reading response due by Thursday and was now discussing the response format in the tone of someone who had learned, from the Yuna incident, that this class would argue about anything if given the opening. He had preemptively closed most of the openings. From across the aisle, Kael was aware of Yuna registering this strategy and deciding, apparently, to let it stand. She had her pen in her hand and was writing something. She wrote too fast for it to be notes.
He looked at the front of the room. He looked at the clock. He looked at the shape of the morning as it currently stood — where Sungho was, where he would be, the window between first and second period that had already passed and the window between second and third that was coming.
The windows were narrow. He had prepared for this.
Between second and third, the corridor outside the year-three lockers would be at its fullest for approximately four minutes and then drain entirely as the late bell approached. He had walked this stretch six times over five days — not conspicuously, just as part of moving through the building, building the geography into his body the way he built all geographies. He knew which locker was Sungho's because locker assignments were in the administrative network along with everything else, and the administrative network remained secured with its chain on a screen door.
The bell rang.
He moved into the corridor with the rest of the class and joined the flow heading for the stairs.
It took eleven seconds.
Not because he was rushing — rushing was how people got remembered. He moved at the pace of the corridor, in the density of the corridor, a student among students, his bag on one shoulder, looking at nothing in particular. Sungho's locker was in the third row from the door, upper tier. The combination lock was a standard school-issue model with a default factory reset of 0000 that approximately sixty percent of students never changed because they were seventeen and thought security was something that happened to other people.
He was past the locker before the corridor had finished filling.
He continued to his class.
Min Haewon was in the library at lunch for the third day running, in the same seat, with what appeared to be a maths problem set open on the table in front of her and the expression of someone who had found an error and was working backward through her own reasoning to locate it.
He sat down two chairs away and opened his own book.
She looked up briefly — a single, efficient look — and returned to her problem set.
"You're a year ahead in applied maths," he said, without looking up from his book.
A pause. "How do you know that?"
"The exam rankings are in the school network. Your name is in the top three for your year and the notation says accelerated placement."
Another pause, longer. She was deciding something — not about the maths. "What do you want?"
"I'm trying to understand the proof structure for a problem in the national exam prep materials. The proof I have works but the steps aren't clean. I wanted to see how someone who thinks about it differently would approach it."
He showed her the problem. It was a real problem, genuinely resistant to the approach he'd used, and he had done this deliberately — brought an actual difficulty rather than a pretext for one, because Haewon was the kind of person who would know the difference and had already spent enough time in situations where people told her things that weren't true.
She looked at it. Something in her posture shifted slightly — not relaxing, just redirecting, the way attention moved when a problem presented itself that was worth the attention.
"Your second step is doing too much work," she said. "You're trying to establish two things at once and it makes the third step dependent on an assumption you haven't stated."
"Show me."
She pulled the paper toward her, picked up her pen, and rewrote the second step in three lines that were cleaner and truer than what he'd done. He watched how she worked — the left-to-right certainty of it, the way she moved through a problem like someone who already knew it would resolve, just not exactly where. She wrote quickly and without hesitation, which meant she thought faster than she wrote rather than the other way around.
"That's it," she said, pushing the paper back.
"Yes." He looked at it. "Have you done the section on system proofs? The transition to the second module is poorly sequenced."
She looked at him. He was still looking at the paper.
"I've done most of it," she said.
"I'm working through it Thursday evening. If you find the sequencing problem I can share the approach I used for it."
She was quiet for a moment. She was doing the same thing she'd done when he sat down — assessing, deciding. He waited without appearing to wait, which was something he had been able to do since he was about twelve, and which most people read as patience but was actually just the ability to distribute his attention elsewhere without moving it visibly.
"Okay," she said.
He picked up his book. She returned to her problem set. Across the library, two year-ones were pretending not to be on their phones. Through the window, the courtyard was cold and half-empty, a few students moving through it in the thin midday light.
She noticed he was being unremarkable deliberately. He could tell because she was careful not to look at him directly for the rest of the hour — the behavior of someone who had decided the unremarkable thing was slightly unusual and didn't want him to know she'd noticed.
He would be back Thursday.
Taemin found him in the corridor after last period, falling into step the way he always fell into step — inevitably, without announcement, already talking.
"You ate lunch in the library," he said.
"I eat lunch in the library sometimes."
"Three days in a row isn't sometimes." He looked at Kael with the brief, sidelong quality of the look that arrived and left before it could be examined. "The girl in 2-C. Haewon."
Kael said nothing.
"She filed a complaint in October," Taemin said, in the tone of a man confirming a fact he already knew was confirmed. "About Sungho."
They reached the stairwell. Kael held the door.
"I know," Kael said.
Taemin went through the door. He was quiet for the length of a flight of stairs, which was unusual for him, and Kael let the quiet stand because Taemin's quiet was always working on something.
"Okay," Taemin said at the bottom of the stairs, in the same tone he'd said tomorrow twice before — as if the word were a full sentence.
He went left. Kael went right.
Sungho was in the courtyard at the end of the day, standing with his performance-laugh friend and two others from the football team, and he was being too loud.
Not loud in the way of someone having a good afternoon — in the way of someone filling a space with sound because the alternative was to let the space be quiet. He was talking about something — a match, a weekend thing, a piece of nothing — and the volume of it was aimed at his friend, specifically, like a demonstration he needed his friend to receive. The friend was receiving it. He laughed when the laugh was required. The two football students looked like people who had walked into the middle of a performance and were uncertain of their role.
Sungho checked the courtyard entrance three times in six minutes.
Kael was at a table near the courtyard's edge with a book open, eating the second half of something Taemin had left on his desk at some point during the afternoon — still warm, inexplicably. He turned a page. Sungho checked the entrance again. From this angle Kael could see the slight compression of Sungho's jaw when his friend said something that required him to laugh and he had to spend a fraction of a second producing the laugh rather than simply having it.
He knew this posture. Not this performance, but the shape beneath it — the particular expenditure of energy involved in appearing more comfortable than you were in a space that had just become uncertain. He had built a version of it himself, for school, for every new environment, and he used it when useful and set it down when not.
Sungho could not set it down. He didn't know he was wearing it.
Kael turned another page. At the bottom corner of the right-hand page, a note in the margin — something a previous student had written in pencil, years ago, mostly faded: this part is wrong but the conclusion holds. He read it twice, for no particular reason, and then looked back at the page.
Across the courtyard, Sungho checked the entrance a fourth time.
The afternoon settled around him. Students moved through and out of the space, the day concluding, the building beginning to exhale. Kael finished what Taemin had left and turned another page and did not look at Sungho again, because he had already seen what he needed to and the operation did not require his continuous attention.
That was how it was supposed to work.