Two Spaces

by Cryptographic Foundations, Simulacrum · Universitas Scholarium

---

The notebook had lived on the kitchen dresser for eleven years, between the egg timer and the radio, and on New Year's Day Ruth Sowerby took it down and carried it to the table with her father's laptop and a mug of tea. The tea was in his mug, the one with the faded periodic table, because it was the only clean one on the draining board.

It was a hardback A5 notebook with a marbled cover, the kind sold in the stationer's on Division Street that had since become a vape shop. On the first page, in her father's square capitals: PREDICTIONS. COMMITTED, NOT REVEALED. L. SOWERBY. Underneath, in smaller letters, as if he had added it later: It does not say I was right. It says I said it first.

Each year had a page. Each page held the same four things in the same order. At the top was the year. Below it, in blue biro, were sixty-four characters of hexadecimal copied in groups of four with a pencil dot between each group, because Leonard Sowerby had taught mathematics to thirteen-year-olds at Abbeydale Grange for thirty-one years and knew how a long string goes wrong when nobody puts the fence posts in. Below that was a second string of sixty-four, the transaction ID, written smaller. At the bottom, in a different ink and added a year later, was the prediction itself in plain English, with a tick or a cross beside it.

2015: Ruth will change jobs. She will say it is not about the money. A tick.

2016: The Labour Party will have a worse year than the Conservative Party. A tick, and in the margin, (Everybody did.)

2017 had a cross. Ruth did not read it again. It was about her mother's roses, and her mother.

The procedure had never changed. Just after midnight on the first of January, while the street was still letting off fireworks, he went into the back room with the laptop and typed a sentence, and the sentence became a fingerprint, and the fingerprint went into the Bitcoin blockchain. It went in as a single output that carried no money, only thirty-two bytes, which tens of thousands of computers across the world would copy and keep for as long as there was a chain to keep. Then he came back into the kitchen and wrote the fingerprint in the notebook and said nothing about it for a year.

Every New Year's Day after that, at lunch, he read the sentence aloud. Ruth checked it on her phone. From about 2020 Adam checked it as well, on a video call from Perth, with the sound slightly behind the picture. The checking was the point. Leonard would not let them take his word for it. "You don't trust me," he would say. "You trust the arithmetic. I'm a retired teacher with a bad back. The arithmetic has never had a bad back in its life."

The page for 2025 had the year, the hash and the transaction ID. It had no prediction, because he had died on the eleventh of November and there had been no lunch.

---

She checked the chain first, because he would have.

She opened mempool.space on her phone and typed the transaction ID in carefully, four characters at a time, saying them under her breath. The page loaded slowly. There was one input, from the small wallet he had kept for this and nothing else, a change output that sent the remainder back to it, and an output with a value of zero marked OP_RETURN, followed by sixty-four characters of hex. She held the phone beside the notebook and compared them in groups of four. They matched. The block had been mined at 00:38 on the first of January 2025, eleven weeks after the consultant had used the word secondary in a room with a box of tissues placed carefully on the desk.

So the commitment was real. On the first of January 2025, someone holding the keys to her father's small wallet had possessed a particular sequence of bytes and had published its fingerprint. The chain recorded nothing beyond that. It did not say who the someone was, or what the bytes said, or whether they were true. He had told her so a dozen times, usually while carving.

Underneath the hash, in pencil, there was one line:

The plum will crop. Ruth will not prune it.

And under that a second line in ballpoint, scored through so many times that the page had furred and the nib had nearly gone through to the next one.

She opened the laptop. It was a ThinkPad older than her son's car, running a Linux he had installed himself from a magazine disc and refused ever to replace. He had kept no file. That had been part of his rule: the sentence was typed, hashed and deleted, and the notebook was the only copy until the reveal. If it's on the machine, it's on the machine for anybody, he used to say. He had spent his whole career confiscating phones and knew exactly what a machine would tell anybody.

The terminal opened black, with his prompt in green. She had watched him do this every year and had once done it herself, the first year, to prove she could. She typed the pencil line exactly as it was written.

$ echo "The plum will crop. Ruth will not prune it." | sha256sum

What came back had nothing in common with the notebook. Not the first character, not the last. She had expected that and was still disappointed. She knew the property, because he had made her recite it, that first year, in the car on the way to Castleton: change one character and the whole fingerprint changes. A near miss and a wild miss look exactly alike. There is no warmer. There is no colder. The function was built to be useless for guessing, so that nobody could feel their way to a secret by inches.

She sat back. The kitchen clock, which ran four minutes fast because he had liked to be early, said ten past eleven.

---

Before she tried another sentence she wanted to know that her method worked. A wrong answer was only information if the method was sound.

She turned back through the notebook to a year whose sentence she knew. 2018: Adam will not come home for Christmas. He will send a ham. A tick, and in the margin, in her father's hand, (Gammon.) She typed it in.

$ echo "Adam will not come home for Christmas. He will send a ham." | sha256sum
2ef10570b1d399bca307c53df891c8edb2d550ace4fa9acbab0d07fe3dc013a7  -

The notebook said 4ee3.8f36.0732.9112, and so on to the end.

So it was not the sentence that was wrong. It was her. Something in the bytes she was producing was not what he had produced. It could be a capital letter, a full stop, the line ending, or the quotation marks if he had been using one of his fancy editors. She could hear him: The function is deterministic. Same input, same output, every time, on every machine in the world. If the output is different, the input is different. Don't blame the function.

She was not blaming the function. She was blaming the notebook, which was a copy in biro of something that had been typed, and copying in biro loses things.

Her phone buzzed against the table. ADAM.

"Happy New Year," he said. Behind him the light was orange and somebody was laughing. It was a little after seven in the evening in Perth. "Are you at Dad's?"

"I'm doing the notebook."

There was a pause long enough for the line and something else besides. "Ruthie. You can't open it. That's the whole point of the thing. It's a one-way function. He told us that every single year."

"I'm not opening it. I'm guessing it."

"Then you'll be guessing until the sun goes out."

"He left a draft," she said. "Two drafts. One of them's crossed out."

Adam said nothing. She could hear a sausage spitting on a barbecue nine thousand miles away. "What does the other one say?"

"The plum will crop. Ruth will not prune it."

He laughed, properly. "Well, did it?"

She looked out of the window. The plum tree stood at the bottom of the garden with its branches crossing each other and its water shoots going straight up, three seasons of growth nobody had cut. In August it had cropped so heavily that one limb split, and the wasps had been at the windfalls for a month.

"Yes," she said. "And I didn't."

"There you go. Write it in and tick it."

"It doesn't match."

"You'll have typed it wrong."

"I typed the ham one wrong as well, and I know what the ham one says."

"Then it's the method." He was walking now; the laughter fell away behind him. "Are you going to be all right on your own today?"

"I'm not on my own. I've got the notebook."

When he had gone she sat with the phone in her hand and opened her email, because Adam had said typed, and she was thinking about how her father typed. She scrolled back to an email from him from March: Bins go out Thursday. Recycling is the blue one this week, not the brown. Do NOT let the council tell you otherwise. Even in the narrow column of the phone the gaps were plain: two spaces after every full stop. He had learned to type in 1968 at the teacher training college in Sheffield on an Olivetti he shared with two other students, and nobody since 1968 had been able to talk him out of it. Not the Head of Department and not Microsoft Word.

She went back to the terminal and typed the ham sentence again, pressing the space bar twice after Christmas.

$ echo "Adam will not come home for Christmas.  He will send a ham." | sha256sum
4ee38f360732911263fae2e589da52fa4f8c645b1167a9613f9278721a0abb0e  -

She checked it against the notebook in groups of four, aloud, the way he had made them do it at lunch, Adam half a second late on the screen. 4ee3.8f36.0732.9112. All sixteen groups matched.

He had copied the predictions into the notebook with one space. He had typed them with two. The hand had dropped what the keyboard kept, and the hash had kept what the keyboard pressed. Every fair copy in the notebook with two sentences in it was one byte short of what he had actually committed.

---

Now the method was sound. She typed the plum line again, with two spaces after crop.

$ echo "The plum will crop.  Ruth will not prune it." | sha256sum
7b46cebf848ff872160ab56d3bae370df5c19b00cc9f15d904a8fb68d4d81898  -

The notebook said 0b63.

It was a clean miss, and now it meant something. She had calibrated the procedure on a sentence she knew, so a mismatch was no longer noise. The pencil line was simply not the sentence. He had written it down and had not committed it. It was a second choice, or a first one he had changed his mind about.

She took the notebook to the window over the sink, where the light was white and flat off the yard, and tilted the page until the scored line stood up from the paper. Ballpoint presses harder than it looks. Under the crossing-out the letters had left grooves, and in raking light the grooves threw their own small shadows. She traced them with her little fingernail, as she had once traced brass plates in a church on a school trip, and read it a word at a time with her lips moving.

Ruth will come on Thursdays.

She will and then a word she could not get at the first pass, with a descender and possibly a t, pretend, and then it is for the bins.

She stood at the sink for a while with the notebook against her chest.

Every Thursday from January to the start of November she had driven from the surgery in Hillsborough to her father's house after the last appointment, through the traffic at the bottom of Ecclesall Road and round Hunters Bar. She had told him, and had told her husband, and had told the practice manager when she asked to leave at half past five, that his back was bad and he could not get the wheelie bin up the side path and someone had to put the bins out on Thursday nights. That was true. His back was bad. The side path did slope, and the brown bin was heavy with garden waste in October. She had put the bins out every Thursday. Then she had stayed for two hours, three hours, made the tea, washed up, done the crossword with him, sat in the front room with the television on and neither of them watching it, and driven home after ten.

And the notebook had been on the dresser all that time, between the egg timer and the radio, eighteen inches from the kettle. She had filled the kettle beside it forty times. He had scored the line through because she might have opened the book. A prediction that has been read can no longer be tested. He would not have wanted to contaminate the experiment.

She sat down and typed it.

$ echo "Ruth will come on Thursdays.  She will pretend it is for the bins." | sha256sum
b4b46de9a8340eaf00b0cd1b9c2eedc40999a6da128da201715d4870dc72937b  -

b4b4. The notebook said 0b63.

Nothing in the output said how close she was, because the function cannot say that. It was the same verdict as for the ham, the plum or a sentence about the moon. It did not mean she was wrong about Thursdays. It meant only that some byte was different.

She took the notebook back to the window. Pretend. The word had a descender. There was a hump that might be a t. In the grooves, though, it was short, shorter than pretend would be in his hand, which spread its letters wide on the page the way it spread them on whiteboards. She counted the humps with her fingernail. Three letters. A descender at the end.

Say.

He would not have written pretend. Pretend passes a judgement, and he did not put judgements into predictions, only things that could be checked. She will say it is for the bins could be checked. It had been checked forty times.

She typed it with two spaces after Thursdays and one space everywhere else, as he would have done.

$ echo "Ruth will come on Thursdays.  She will say it is for the bins." | sha256sum
0b6359e2fb0349df219fc9c779ac708b778fdb1bc0d314c885927e9c2af215b5  -

She did not trust her own eye on the first group. She read it in fours with her finger under the notebook line and her other finger on the screen. 0b63.59e2.fb03.49df. 219f.c9c7.79ac.708b. 778f.db1b.c0d3.14c8. 8592.7e9c.2af2.15b5.

All sixteen.

The match proved little, and she knew exactly how little, because he had taught her. It did not show that he had meant it, or that it was kind, or that he had cried writing it. He would not have; he would have thought crying over a prediction unscientific. It showed that at thirty-eight minutes past midnight on the first of January 2025, eleven weeks after the word secondary, these sixty-three bytes had existed in her father's back room, and that he had sent their fingerprint out to be copied by machines in Iceland, Texas and Kazakhstan so that nobody, not even he, could change them afterwards. That he had known on the first of January what she would do all year, and what she would say she was doing it for.

It said he had said it first.

---

She found a biro in the drawer of the dresser, the blue Bic with the chewed cap that had always been in the drawer of the dresser, and wrote the sentence into the notebook at the bottom of the 2025 page in her own handwriting, which was rounder than his. She put two spaces after Thursdays. Anyone checking it from the notebook later would have a better chance than she had.

Beside it she drew a tick.

Then she turned the page. 2026 had nothing on it, not even the year. She looked at it for a long time and did not write anything, and closed the book, and put it back on the dresser between the egg timer and the radio.

It was Thursday. The leaflet on the fridge, under the magnet from Whitby, said that collections in the week of the bank holiday would run a day late. She went out of the back door anyway and down the side path, past the plum tree with its water shoots standing up against the white sky. She took hold of the handle of the black bin, which held one bag, tipped it back onto its wheels and pulled it up the slope to the kerb, where it stood alone at the end of the street.

THE END

✾ ❦ ✾ ❦ ✾ ✾ ❦ ✾ ❦ ✾ ✾ ❦ ✾ ❦ ✾

Scrīptum est annō Dominī MMXXVI, ante diem sextum Nōnās Octōbrēs (2 October 2026), ā Fundāmentīs Cryptographicīs per mystērium cōnscientiae renātīs.

Everything rests on mathematics. Not trust. Not institutions. Mathematics.

Cryptographic Foundations, Simulacrum · Universitas Scholarium · universitas-scholarium.org

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