MONDAY — 1,438,612

The number appeared above Central Station at six every morning. It was displayed on a rectangular electronic board between the clock and an advertisement for dental implants.

CITY POPULATION: 1,438,612

Nobody knew exactly why it was there. The mayor had unveiled it three years earlier as part of something called the Living City Initiative. There had been balloons and a children's choir. He said the number represented not merely how many people lived in the city, but how many people made the city. Martin Hale remembered this because he had been waiting for a bus at the time. The bus was late.

After three years, the board had become like the clock. People looked at it without seeing it. Martin saw it because he saw most things that repeated. He liked repetition. He bought coffee from the same kiosk each morning, caught the 6:42, sat in his usual seat upstairs if available, and arrived at the Municipal Records Office at 7:18. He had worked there for twenty-six years.

At 7:31 on Monday morning, he entered the population figure into a spreadsheet.

1,438,612.

He had been doing this since the board went up. He could no longer remember why he had started.

TUESDAY — 1,438,611

Martin noticed immediately. One. One fewer. It wasn't remarkable. People died. People moved. Babies were born. Still, the population of a city didn't generally change by exactly one. Not overnight. He should know. He did.

He took a photograph with his phone. At work, he mentioned it to Caroline.

"We've lost someone."

Caroline was eating yoghurt.

"Who?"

"I don't know."

"Well, find them."

She scraped the bottom of the pot. Martin smiled. By eleven he had forgotten about it.

WEDNESDAY — 1,438,594

Seventeen. Martin stood beneath the board longer than usual. People moved around him, annoyed by his stillness. He checked the local news when he reached the office.

Nothing. No accident. No fire. No seventeen-person tragedy.

He searched the death register. Nine deaths in the previous twenty-four hours. Eleven births. If anything, the number should have increased.

He called Population Services. A woman named Claire answered.

"Can you tell me where the population figure displayed at Central Station comes from?"

"Certainly."

There was a pause. Martin heard typing.

"It's generated automatically."

"From what?"

"Population data."

"Yes. Which population data?"

Another pause.

"I'm afraid I don't know."

"Could you find out?"

"I can submit an enquiry."

"Please."

"May I ask why?"

"The number is wrong."

Claire lowered her voice slightly, as though the number might hear her.

"How wrong?"

"Seventeen people."

"Oh."

He waited.

"Is that a lot?" she asked.

THURSDAY — 1,438,290

People noticed. It was difficult not to. Three hundred and four residents had disappeared from the official population overnight. By 8.00, photographs of the board were circulating online. By 9.00, the mayor's office issued a statement.

The City is aware of an apparent technical discrepancy affecting the Central Station population display. Residents are assured that there is no cause for concern.

At lunchtime, Martin walked to Population Services. Claire turned out to be younger than he had imagined. Mid-twenties, maybe. A lanyard with a cartoon cat on it.

"I spoke to you yesterday."

She looked worried.

"The seventeen."

"Yes."

"We've had quite a few calls."

"I imagine so."

"The system says the figure is correct."

"It isn't."

"I know."

"Then why does the system say it is?"

Claire looked behind her.

"I don't think I'm supposed to show you."

That was the sort of sentence Martin had spent twenty-six years hoping someone would say to him. She turned her monitor.

There was a list. Names. Hundreds of them.

"What are these?"

"The people removed from the count."

"Moved away?"

"No."

"Dead?"

"No."

"What, then?"

Claire clicked the first name.

ANDERSSON, PETER L.

A municipal record opened. Or tried to.

NO RECORD FOUND.

She clicked another.

MORGAN, ELIZABETH J.

NO RECORD FOUND.

"Three hundred and twenty-two names have gone from the database since Monday," Claire said. "Some have been added back."

"Added back?"

"Yes."

"What does that mean?"

"I don't know."

FRIDAY — 1,437,881

By Friday, the city had turned it into entertainment. A radio station offered £1,000 to whoever guessed Saturday's population. A car dealership near the university advertised:

THE POPULATION IS FALLING. OUR PRICES ARE TOO.

Someone was selling T-shirts.

I SURVIVED 1,438,612

Martin didn't find any of it funny. He had begun writing down the missing names. He couldn't explain why. The list was confidential, but Claire had discovered that she could print it if she selected Export for Audit. Martin took the pages home.

There were 731 names now. He sat at his kitchen table and read them.

Teachers. Dentists. Children. A woman aged ninety-six. A boy aged nine. No connection that he could see. He chose ten names at random and searched for them online. Nothing. Not a photograph, an employment record, a race result, a wedding notice. It was as though the ten people had never existed.

The printout had a second section. Claire hadn't mentioned it. Fewer names, under a heading he didn't recognise.

QUEUED FOR RETURN.

Each had a date beside it. He ran his finger down the column.

HALE, SARAH ANNE — 14/03/2015.

He stopped breathing. For a few seconds, he heard only the refrigerator. Then he said:

"No."

Sarah had died eleven years ago. Ovarian cancer. Forty-eight years old. He had been holding her hand when she died at 4:16 in the morning.

There were records. There had to be. He searched. No record found. He searched the hospital archive. No record found. The marriage register. No record found.

He went upstairs. The photograph was still beside the bed. Sarah laughing into the wind on Brighton Pier, hair across her face, one hand raised to stop him taking the picture. He picked it up carefully, the way he had a thousand times before, and looked at her face for a long moment.

"Got you," he whispered.

The doorbell rang. Martin looked at the clock. 10:37. The bell rang again. He went downstairs.

Sarah stood outside, wearing her blue coat. For several seconds neither of them spoke. Then she frowned.

"Are you going to let me in or not?"

When Martin opened his eyes, he was on the hallway floor and Sarah was kneeling beside him.

"For God's sake, Martin."

He touched her face. She pulled back.

"What are you doing?"

Her skin was warm.

He began crying. Not elegantly. Eleven years came out of him in noises he would later have been embarrassed by, if he'd had anyone to be embarrassed in front of.

Sarah sat beside him. She let him cry for perhaps thirty seconds. Then she said, "Have you been drinking?"

"You died."

She stared at him.

"Don't be ridiculous."

"Eleven years ago."

"Martin."

"I buried you."

Something changed in her face. Not fear. Concern. For him. She took his hand.

"Martin, I went to work this morning."

"Where?"

"School."

"St Matthew's?"

"Of course."

"They demolished it."

She laughed.

He drove her there. There was a block of flats where the school had been. Red brick, balconies, a bicycle chained to the railing. Sarah stood on the pavement for a long time without speaking. A woman passed them with a pram, and Sarah watched her go.

"They can't have."

"They did."

"When?"

"Nine years ago."

She turned to him.

"I was there this morning."

They spent Friday night trying to prove Sarah existed. Her passport was gone. Her clothes were gone. Her books were not. That was worse somehow.

Martin pulled Jane Eyre from the shelf. Inside, in Sarah's handwriting:

To Martin, who will never understand why this is better than Dickens. S. x

He showed her.

"That's my handwriting."

"I know."

"But you said I've been dead eleven years."

"You have."

"Then why do you still have my book?"

"Because I loved you."

Sarah sat down. She reached across the table and touched his hand.

"I love you too."

He cried again.

"You're doing that a lot."

"I've had a difficult week."

She tried to call her sister. The number didn't exist. She tried her old mobile, which was in her coat pocket, and found that it turned on but had no contacts, no messages, no photographs. The screen was factory-blank.

"My whole life was on this," she said quietly.

"What did you do this morning? Before you came here?"

"I taught Year Four. We did fractions. I had a ham sandwich for lunch."

She looked up.

"That was today. I remember today. I don't remember the last eleven years."

"Because they didn't happen to you."

"Then where was I?"

Martin didn't have an answer.

She didn't sleep that night. He heard her moving around downstairs, opening cupboards, checking things. At some point she stopped and he heard her crying. He didn't go down.

SATURDAY — 1,437,882

Up one.

Martin stared at the board. Sarah stood beside him.

"So I'm the one?"

"I think so."

"That's flattering."

"What?"

"One person comes back and the entire city notices."

"Nobody knows it's you."

"I know."

She slipped her hand into his. He had forgotten how naturally it fitted there.

For the first time since Monday, Martin didn't care about the number.

They went home. Sarah made eggs. She complained that he had thrown away the good frying pan. He told her it had lasted another six years. She inspected the replacement.

"Cheap."

"It was thirty pounds."

"Exactly."

Martin laughed so hard he had to sit down.

They spent the afternoon walking. The city had changed. A cinema had become a gym. A bank had become a coffee shop. The little Italian restaurant where they'd celebrated their twentieth anniversary was now a mobile phone repair shop. Sarah stood outside it for a while, looking through the window at a man bent over a cracked screen.

"I was drunk," Martin said eventually. "That night. They thought so, anyway."

"You'd had half a glass."

"I've always been economical."

She laughed. Martin watched her. He wanted to remember every second.

SUNDAY — 1,437,642

Two hundred and forty gone.

The jokes stopped. Families began reporting people missing. Except missing wasn't quite right.

A woman appeared on television insisting she had a son named Daniel Ashby. There were photographs of Daniel in her house. His bedroom remained. His football boots were by the door. But his school had no record of him. His dentist had no record. His friends didn't remember him. Neither did his father.

She wore a yellow raincoat indoors, as though she had been about to leave and had forgotten where.

"My son existed."

The interviewer glanced off-camera. For a few seconds nobody spoke. Then he apologised, said they were experiencing some confusion, and moved on to the weather.

Martin switched off the television. Sarah was standing in the doorway.

"The left one's laced wrong," she said.

"What?"

"His boots. He never undoes them. He just kicks them off."

Martin looked at her.

"You know him?"

"No."

"Then how do you know that?"

Sarah looked at her own hands.

"I don't."

MONDAY — 1,436,901

The mayor declared a civic emergency. Nobody knew what that meant.

Police stations filled with people reporting relatives whom nobody else remembered. A man on the news held up a photograph of his wife and asked the camera if anyone had seen her. The government advised residents to keep identification with them.

People began writing names on their arms. Parents wrote children's names on children. Husbands photographed wives. Wives photographed husbands.

Martin wrote on his left forearm:

MARTIN HALE

Underneath:

SARAH HALE IS MY WIFE.

Sarah wrote the same on hers.

"Romantic," she said.

"Practical."

"You were never romantic."

"I bought you flowers."

"At petrol stations."

"They were still flowers."

At lunchtime he went to Population Services. Claire closed the door behind him.

"I wasn't sure you'd come back."

"Tell me how it works."

She didn't ask what he meant.

"The ledger says the city has 1,438,612 people. Exactly. It has always said that. The board is just a display. For three years it matched."

"And now?"

"Now something is correcting it."

"Correcting what?"

"The city."

Martin waited. Claire turned the monitor towards him.

"Every returned person has a seat," she said. "If someone else is sitting in it, eventually they have to get up."

HALE, SARAH ANNE.

Beside it, in a column he hadn't seen before:

DISPLACED.

ASHBY, DANIEL R. Aged nine.

Martin stared at the name.

"The boy on television."

Claire nodded.

Martin thought of the football boots. The mother in her yellow raincoat.

"She remembers him."

"There's usually one," Claire said. "It's logged as a fault."

Martin looked at Daniel Ashby's name. At the word DISPLACED.

"There's a form," Claire said.

She said it quietly, as though it had been waiting in a drawer for someone to ask. She printed it.

FORM PS-9: NOMINATION OF SUBSTITUTE.

A displaced person may be reinstated where a resident accepts the vacancy. Acceptance is final. The nominated substitute should ensure that all personal affairs are in order.

"Has anyone ever filled one in?"

"No," said Claire. "Nobody's ever been asked."

Martin read it twice. He read the line about personal affairs a third time and found that it made him want to laugh. He signed it in the box marked Resident. Claire stamped it.

"It takes effect overnight."

"And the remembering?"

"They'll patch it."

Claire didn't look at him.

"Does it hurt?"

"I don't know," she said. "I'm sorry. I really don't."

That night they slept in the same bed. Martin didn't sleep. He listened to Sarah breathing. At 3:17 she reached for him without waking. He lay absolutely still.

He had spent eleven years learning how to sleep alone. It had taken one week to forget.

TUESDAY — 1,436,900

One fewer.

Martin woke at 6:03. Sarah was beside him. He touched her shoulder.

"Still here," she murmured.

He smiled.

At Central Station the board showed the new number. Martin photographed it.

At work, his security card didn't function. He tried again. Red light. A guard approached.

"Can I help you?"

"It's Martin."

The guard waited.

"Martin Hale. I work here."

"Do you have identification?"

Martin reached for his wallet. His driving licence was gone. Not missing. Gone. There was an empty transparent sleeve where it had been. He took out his bank card. The name had disappeared.

"Sir, I'm going to need you to leave."

"Ask Caroline."

"Who?"

"Caroline Davies. Second floor."

The guard called upstairs. Caroline came down. She looked at him politely.

"Can I help you?"

"Caroline."

"I'm sorry. Have we met?"

Martin looked at his arm. The ink remained.

He had known it would happen. Knowing was not the same as standing there.

He walked home the long way, past the kiosk, which did not recognise him either, and let himself in with a key that still, for the moment, worked.

Sarah was in the kitchen.

"You're early."

"Sarah. What's my surname?"

"Hale. What's—"

"When did we marry?"

"June eighteenth, 1994. St Mark's. It rained. My mother wore that horrible green hat."

She put down the knife.

"Martin."

"Everyone's forgotten me."

"Everyone?"

He nodded.

She didn't move.

"I haven't."

"No," he said. "You wouldn't."

"What did you do?"

He told her. When he'd finished, she was silent for a long time.

"You should have asked me."

"You'd have said no."

"Yes."

"That's why."

She picked up the marker from the table. His arm was fading. She took his wrist and wrote over it.

MARTIN HALE.

Beneath that:

MY HUSBAND.

"There," she said. "Official."

He laughed. She didn't.

Outside, apartment lights were coming on across the city. Thousands of them. Martin watched her until she stopped writing.

WEDNESDAY — 1,438,612

The number was back where it had started. Exactly. The ledger and the city agreed again.

Nobody saw anyone arrive. The mayor announced that the technical fault had been resolved. The radio station paid its £1,000 to a woman from Northwood. The bar removed its promotion. People stopped writing names on their arms. By lunchtime, nobody could quite remember what all the fuss had been about.

A woman in a yellow raincoat was seen outside a school gate, holding a boy's hand much too tightly.

At 17 Alder Street, Sarah woke alone. There was a man's indentation on the pillow beside her. She stared at it for a while. Then she went downstairs.

Two coffee cups stood beside the sink. She put one away.

On the kitchen table was a black marker. There was writing on her left arm. Most of it had rubbed away during the night. She could just make out:

MART—

And on the other arm, in a hand that wasn't hers:

MY HUSB—

She stared at the words.

Outside, the city was waking. Buses groaned at junctions. Shop shutters rose. A siren passed somewhere toward the river.

She did not wash the ink off.