On the sixth day of the cycle, the outsiders took over the old customs house, and Sael Dunmarrow, who had never in eleven years been late with a report, found that he had lost forty minutes of the afternoon watching a girl solder a wire.

He did not consider this a lapse. He considered it an observation. An Auditor was permitted to observe the conduct of those in his care. It was the basis of the entire office. If, in the course of observing, certain data accumulated that he had not requested, that was a clerical matter and could be filed at the appropriate time.

The customs house stood on the east quay, three doors down from the lodging house, a squat stone building with a collapsed roof at one end and a floor of cracked green tile. It had been empty for nine years. The Office had listed it as a hazard. Sael had listed it as a hazard in four consecutive quarterly reports, and the Office had filed all four. The group had found it on the second day, and on the third, Miyu Sakane had come to him with a very straight back and asked whether a dry building with no function was technically a violation of any regulation if one were to use it.

"It is unoccupied property of the Office," he had said.

"So it's a violation."

"It is a gap."

She had looked at him with the quick, bright, calculating look he was learning to associate with all of them, and said, "Do you know, Auditor, I think you say 'gap' when you mean 'yes.'"

He had not corrected her.

Now he stood against the doorframe with his arms folded behind him, in the cool dusk of the interior, and watched the club work.

He had not known what to expect. The Office's briefing on outsiders was four pages long and described them as disoriented, fragile, and prone to inflated estimates of their own agency. It said nothing about Hoshina Haruto, who had appointed himself quartermaster and was at that moment balancing a stack of crates on his head while arguing about the correct pronunciation of a Kethari word for bread. It said nothing about Tachibana Ren, who sat on an upturned bucket with a slate on his knee, scratching out a column of figures with his tongue between his teeth and a frown that could have split stone. It did not mention Fujisawa Nana, who had found a broken tide-gauge in the rubble and was cleaning it with a rag and a look of fierce, private devotion.

It certainly did not mention Sakane Miyu.

Miyu was on her knees in the center of the floor with a spread of parts in front of her: coils, brass discs, a length of salvaged copper wire, three small waxed bottles of something he suspected was ink. She had soldered the same wire twice and was now crouched over it with her nose a hand's breadth from the join, and she was talking, not to anyone, but to the wire.

"No, come on, come on. You're a good conductor. Be a good conductor. Don't do this to me."

The wire, to his interest, did not do it to her.

He had never seen anyone treat an object with such unembarrassed affection. In the Office, instruments were instruments. They were tolerated. Miyu spoke to hers like a person coaxing a nervous horse, and the thing, whatever it was, seemed to be listening.

"What is it?" Sael asked.

She did not look up. "A resonance meter. I think. If I'm right."

"You are not certain."

"I'm never certain. That's why it's called a meter. If I were certain I'd call it an answer." She held up a coil. "It listens to the sea. Tide, current, the pulse in the old gate. The gate has a frequency. When we fell through, it gave off a tone, a very low one. You must have heard it."

"I did."

"So it has a pitch, and the pitch changes with the water level, which changes with the moon. If I can lock onto the tone, I can read the window off the shift. Like reading a clock by the sound of the chimes." She shrugged. "It's a very stupid idea. It might work."

"The Office computes the windows from a table."

"I know. Suzu told me. It's a good table." Miyu finally looked at him, and her tone was entirely candid. "I think it's off by a day or two, though."

He was silent.

"It's not a criticism," she said. "It's just the way the tide's curve flattens near the peak. A table built from averages will always smear it. You'd need to measure it live."

"I am aware of the smearing."

"Are you?"

"I have been aware of it for six years." He heard the admission leave his mouth before he had checked it. "The table has a stated error of two days. It has always been two days. No one has asked whether it could be smaller."

Miyu sat back on her heels and regarded him with her head tilted. "Why not?"

"Because the gate was not expected to open."

She was quiet for a moment. Then she said, "That's a really sad reason," and went back to her wire, and Sael stood against the doorframe and felt the sentence settle in him with an unexpected weight.

---

The Arimura girl was the last to arrive.

He knew her step by now. It had taken, by his count, five days and eleven hours, which was much less than he would have expected. A light, quick, slightly uneven tread, as though she were always about to break into a run and had not yet decided to. She came up the quay at the third bell with the inventory book clasped to her chest and a small paper bag in one hand, and he heard her before she crossed the threshold, because she was talking.

"Ren, I need your sums by dusk, not midnight. Haruto, did you get the lamp oil? Not the cooking oil, I said lamp oil, the other one. Nana, if you break that gauge I will personally forgive you, but I would prefer that you didn't. Miyu, how long?"

"Two hours."

"One and a half."

"Two," said Miyu, serenely.

"One and three-quarters."

"Suzu."

"Two hours," Suzu conceded, and went to the long table at the center of the room and set down her bag, and in the same motion lifted her head and saw him.

She stopped.

It was only a pause. A catch in the rhythm of her speech, so slight that anyone else in the room would have missed it. But he did not miss it. It was a quarter-second, perhaps less. Her mouth had been shaping a word and it did not finish. He catalogued it, without meaning to, between her third and fourth steps: the stall, the little recovery, the straightening of her shoulders. Then she said, in a clear, formal voice, "Good afternoon, Auditor. Thank you for allowing us the use of the building."

"It is a gap," said Sael.

"I've been told."

Haruto, at the back, coughed into his sleeve. It sounded suspiciously like a laugh.

Suzu pretended not to hear. She pulled out a stool and sat, and opened the inventory book, and began to organize the afternoon. And Sael, who had been intending to leave some minutes ago, found that he was still leaning against the doorframe, and that his feet had not received the instruction.

He watched her assign.

It was something to see. She did it without raising her voice, with a smile that was real and a manner that was brisk, and it appeared to cost her nothing. Ren was to verify the sums. Haruto was to catalog the stores, and to do it quietly. Nana was to repair the gauge and then to walk the quay at each bell and record the water height, because the child was meticulous and liked a task. Miyu was the engine. Suzu spoke to each of them in turn, and each of them straightened as she spoke, the way a plant will lean toward a window. She remembered, he noticed, that Ren took his tea cold. She remembered that Nana disliked being the only one with nothing to do. She remembered that Haruto, though he made jokes, responded best to being given a job with a deadline. She had a note about each of them. She did not need to look at the page.

She did not assign herself anything.

He waited for it. He kept waiting, through the end of the sequence, through the last name, through the moment when she snapped the book shut and rose from the stool with the satisfied air of a woman who has seen to everything. He noted it, and noted that he was noting it, and noted that in the entire arrangement of the afternoon there was not one line of work for Arimura Suzu.

It was an interesting gap.

"You have not given yourself a task," he said.

She glanced at him over her shoulder. "I'm the coordinator."

"That is an assignment of oversight. It is not a task. At the end of the afternoon, the others will have produced something. You will have produced a schedule."

"That's the job."

"It is not a job. It is the absence of one." He considered. "Do you intend to rest at any point?"

"I don't need to."

"I did not ask whether you needed to."

She opened her mouth and shut it again. There was a flush along her cheekbone. "That's not in the terms," she said, with great dignity.

"No. It is an inquiry."

"Then I decline to answer it."

"Noted."

He noted it. He noted it very thoroughly. Some distance behind her, Haruto had put his face into a crate and was making a high wheezing noise, and Ren, with deep disgust, had turned his bucket to face the wall.

---

The explanation was her idea. She came and sat across from him at the end of the long table, in the pale light from a hole in the roof, and laid the inventory book flat between them, and said, "I'd like to describe what we're attempting. In case it affects your reports."

"It will not affect my reports."

"In case it does."

He did not argue. She spoke clearly and quickly, with the economy of someone who has rehearsed a pitch many times in her own head, and she drew small neat diagrams as she went, a circle for the gate, a wave for the tide, a line for the interval. The stylus moved in her fingers. She wrote a figure, a ratio, and underlined it. She wrote another, and a caption in tiny script.

Then, in the middle of the third sentence, she stopped.

Her stylus had stopped at the same instant. It hung above the page, its tip a finger's width from the paper, and her eyes, which had been tracking the line she was writing, lifted slowly from the book and slid sideways, to the left, to the place where his hand lay open on the table.

She was looking at his hand.

There was no particular reason for it. It was only a hand. It had a pale gray back and a pearly sheen across the knuckles, and in the soft light it looked almost like a thing carved from the inside of a shell. She was looking at it with an expression of such total absorption that for a moment he forgot how to continue. Her lips had parted slightly. Her pupils were wide. The stylus began, very slowly, to tilt in her fingers.

Then she blinked.

Her eyes snapped back to the page. The pen came down, and a thin vertical line shot across the paper where the next word should have been. She said, "Sorry. The, the interval," and her voice had gone up half a step, and the tips of her ears had turned an interesting shade of rose.

"You stopped," said Sael.

"I lost my place."

"You did not lose your place. You were at the ratio. You had it on the line above." He found that he was whispering. "You stopped in the middle of a word."

"It happens."

"Does it?"

"Everybody does it."

"Not you," said Sael. "Not before today."

Her ears went darker. She said nothing, and looked at the page, and he looked at her, and the thing in his chest, which had no category, which had not appeared in any of the briefing papers, did a slow soft turn like a fish under ice.

He committed the moment to memory. It was automatic. It happened without any choice on his part: the tilt of her head, the hovering pen, the pink rim of her ear, the fact that she had been looking at his hand. He stored it where he stored everything, in the vast, orderly archive that was the only thing he had ever been truly proud of. And as the file closed, it occurred to him, with the cold clarity that visited him at the edges of his work, that he did not understand its meaning. He had the data. He did not have the interpretation. He had never before been unable to interpret a datum.

He filed it under pending.

---

The meter woke at the fifth bell.

He had been summoned. Haruto had come down the quay at a run, shouting something about "it's doing the thing, Auditor, it's actually doing the thing," and Sael, who did not run, had walked at a pace so brisk that Ren had to jog beside him. By the time they reached the customs house the whole group was gathered around the center table, in the long gold light of the evening, silent, breath held.

On the table sat Miyu's machine. It was a squat ugly thing of brass and copper and old gauge-glass, with three coils on top like horns, and a wire that ran out through the broken wall and into the sea. Nana's rescued tide-gauge sat at its side, rubbed clean, its needle trembling. A pale line of light crept across the face of the dial. It quivered. It slid. It stopped.

"There," Miyu breathed. "Lock. That's lock." She was crouched beside it with her hands hovering, not touching. "Ren. The sum."

"Sixteen days," said Ren, in a tight voice. He had the slate in both fists. "Sixteen days, eleven hours, and, and nine minutes. Dusk ebb. Plus or minus six minutes."

There was a silence.

"The table says nineteen," said Sael.

"The table is wrong," Miyu said, very gently. "By three days. I'm sorry."

He looked at the dial. He looked at the slate. He did the arithmetic himself, without a pen, in the time it took to draw a breath, and he reached the same answer to the minute. He stood quite still, in the middle of the cracked tile floor, in the ordinary light of a Kethari evening, and for the first time in eleven years he saw the shape of the error that had been in the table all along.

He said nothing.

He did not trust himself to say anything. Eleven years of inherited figures, passed from hand to hand, and a girl in a borrowed tunic had read the tide off a copper wire.

"It works," said Haruto, in a hushed, reverent voice. "It actually works."

"It works," said Nana.

"It works!" said Haruto, again, much louder, and then the whole room went up like a flock of birds. There was shouting. There was laughter. Ren had thrown the slate in the air and was catching it clumsily, scarlet to the roots of his hair. Haruto had picked Miyu up bodily and was spinning her in a circle, to her indignant shrieks. Nana was jumping on the spot, not making a sound, her whole body vibrating like a struck string.

And Suzu, who had been standing at the far end of the table with her book against her chest, turned around.

She was laughing. He saw it from a distance of four meters. It was not the polite smile she had used with him in the tower, nor the brisk smile of the coordinator, nor the strained smile he had seen on the first evening, brittle as sugar glass. It was a laugh that came from somewhere under all of that, a wide helpless laugh with her head tipped back and her eyes squeezed shut and the pale light gilding her throat. It was the sound of someone who had forgotten to be responsible for a moment.

She opened her eyes.

She looked straight at him.

And she smiled, at him, directly, without calculation, as one smiles at a friend across a crowded room. She held it for a full second. Then the color rose in her cheeks and she looked away, and the moment was gone.

Sael found that he was standing in the center of the floor with his mouth slightly open.

He had been about to say something. He knew he had. He had arrived at this point carrying a sentence, a precise and necessary sentence about the permissibility of the device and the formal status of its output. He could feel the shape of it in his mind, the grammar of it, the place where the first word began. But the sentence was gone. It had gone out of him like water from a cracked cup, and nothing in all that tidy archive could recover it.

He had never forgotten a sentence in his life.

---

The room had settled into a happy, exhausted bustle. Haruto was passing around a flask of something dark and sweet. Miyu was explaining the coil winding to anyone who held still. Sael had withdrawn to the doorframe, where he stood in the lengthening shadow, watching, and trying, in a clear and systematic way, to account for himself.

It was a surplus datum.

That was the finding. It was a smile, produced by a human female under conditions of mild euphoria, directed at a nearby observer. It conveyed no information relevant to the register. It had no administrative weight. It would not appear in a report. It was merely a piece of the day that had fallen out of the pattern, like a button from a coat, and which he had, for reasons he could not identify, picked up.

He did not need to keep it.

He turned the thought over once, and set it aside, and found, a moment later, that he was holding it again.

He was an Auditor of the third rank. He did not hold surplus data. He sorted it and discarded it. That was the discipline. And yet when he reached for the part of himself that knew how to discard, he found it was not there, and in its place was an image: a head tilted back in the pale light, a throat gilded, a mouth open on a sound he could still, if he chose, hear in his skull as clearly as a bell.

He looked at the group. They had not noticed. Ren had gone back to his figures, muttering. Miyu was sketching on the wall. Suzu had returned to the book, her hand moving rapidly, her face composed, a small wrinkle between her brows. She did not look up.

For reasons that were not clear to him, he was very glad of this.

The formal procedure was straightforward. A discovery of this nature, a new and more accurate prediction for a gate opening, was to be transmitted to the Senior Auditor of the district within one bell of its discovery. This was not a courtesy. It was a requirement. The Senior Auditor of the district was Ilvane Rook, who had trained him from the age of nine, and who would want the figures.

He took out his ledger. He wrote the date. He wrote Window One, revised, sixteen days. He sat looking at it. He drew a line under it, and above the line he wrote, in his own neat hand, a transmission time: the sixth bell.

The sixth bell came.

He did not send it.

He sat on a crate beside the doorframe with the ledger on his knee and the entry written and the courier's token in his pocket, and he told himself that there was no urgency. The window was sixteen days away. The group needed a night to verify the numbers. A premature report that proved inaccurate would reflect poorly on the district. It was merely prudent to wait.

The bell rang for seven, and the lamps were lit, and Suzu stood and stretched, and looked across the room and caught his eye. She raised her hand in a small, uncertain wave, and he lifted his, a precise inch. The corner of her mouth moved.

He sat there for four hours.

It was, he noted, the first time in his life he had delayed a report, and he could not have said, if the Office had demanded a reason, what it was that he was waiting for.