202: Chapter 202 November 1st hasn't arrived yet.

October 30, 2022, 6:01 AM.

Zijing Building No. 17, Room 402.

The thirty-day countdown on the mobile phone restarted. Just as the first second ticked over, Jiang Lin had already made out the line of size 8 fine print on the side of the read-only verification disk.

[UNIT _ DISTANCE _ FINAL / READ ONLY / 03]

Over the past forty-two-plus years, he would have had to step back half a step to recognize a label of the same size.

His eighteen-year-old eyes recaptured the close-up focus, and the small patch of stiffness at the back of his neck left behind by years of desk work vanished along with it. The skin on the back of his hands was so smooth that not a single loose wrinkle could be found.

His body had retreated for him to October 30, yet the workbench, the Outpost, and that black line halted six years and seven months before the main peak still remained in his memory.

Jiang Lin steadied himself against the edge of the desk. At his feet were only two return hard drives, a read-only verification disk, and a sealed bag containing the final paper draft.

Twenty-nine transport units, three blue thermal interface boxes, and the dismantled G-Explorer-C spare parts had all been left behind in the Wasteland.

Over those forty-two-plus years, those pieces of equipment had either been integrated into the Outpost or entered long-term maintenance inventory. Bringing back a batch of old components whose service lives had already ended would only result in Room 402 gaining an extra scrap warehouse that needed reclassification.

The phone began fetching the missed messages from this past minute.

The delivery daily report from the Low Entropy Workshop, the site progress from the Beijing R&D Center, the humid working conditions added by the utility tunnel client, and the first-piece disassembly inspection photos sent by Xu Man popped up one by one in the notification bar, finally stopping at the question Gu Mingche had sent last night at 11:17.

["I've chewed through those few pieces. Are you really planning to open that number field where the degree grows alongside the number of points on November 1st?"]

Jiang Lin first connected the two return hard drives to the physically isolated terminal.

Inside the first hard drive were the final draft of the unit distance counterexample, six verification packages, and four thousand three hundred and seventeen dependency lists.

The second one only retained the Star-Tide precursor layer inverter, the 2022 public data adapter, the false-alarm boundary, and the minimum observation network; the original fragments of FDSO-2076A remained sealed in the permanent isolation zone of the Wasteland.

After checking the hash, Jiang Lin put the second hard drive into a shielding box and pasted a new label on the box lid.

[Star-Tide Precursor Layer / Real World Co-orbit Unknown / Network Access Prohibited / External Access Prohibited]

In the existing public data, no incoming flow satisfying the joint criterion could be found, and sparse observations did not allow him to write "cannot be found" as "does not exist."

The first step that could be taken in this matter was to supply humanity with two independent observation baselines beyond the heliosphere, the time required for which would be measured in decades; grabbing an extra half hour this morning would not change its predicament.

That fixed positive exponent in the other hard drive had already waited for sixteen years.

Jiang Lin replied to Gu Mingche.

["You don't need to wait anymore."]

Gu Mingche was probably still asleep; it took two minutes before "Typing..." appeared in the chat box.

["Did you straighten out the entrance?"]

["Done."]

"Typing..." disappeared once, then reappeared.

["Which part?"]

["The entire counterexample."]

The phone call came straight through.

After Jiang Lin answered, the sound of quilt friction and a cabinet door banging against the wall came through the earpiece first.

"Is the counterexample you mentioned the same thing as what I understand?"

"The planar unit distance conjecture."

"The day before yesterday afternoon, we were still calculating three back debts for you in the classroom."

"They've all been paid back."

There was another sound from Gu Mingche's side, this time sounding like a slipper kicking against the bed ladder.

"Leave the door open, I'm coming over now."

Twenty-seven minutes later, Gu Mingche stood at the doorway of Room 402 carrying two cups of soy milk and four steamed buns, with one side of his hair still pressed and pointing upwards.

When Jiang Lin took the soy milk, the cup wall was still scalding. The forty-three winters in the Wasteland, when brought over to the reality side, were only enough for Gu Mingche to walk from the cafeteria to Room 402.

He bypassed the sealed bag containing the final paper draft by the desk, placed the breakfast on the empty corner of the desk, and first reached out to touch the laptop in front of Jiang Lin.

"It's hot."

"Just turned on."

"I thought you hadn't turned it off for two days."

Gu Mingche pulled over a chair and sat down, taking the first page pushed over by Jiang Lin.

On the paper was only the final proposition and two constants.

[There exists an absolute constant δ ₀ ＞ 0, and arbitrarily large planar finite point sets P, such that]

[U ( P ) ≥ | P | ^ ( 1 ＋ δ ₀ ) ／ C]

He read along from the first line to the second line, then flipped back to check the quantifiers.

"Fixed?"

"Fixed."

"Doesn't it shrink with the number of points?"

"It only depends on the construction parameters."

"What is the lower bound?"

Jiang Lin brought up the rational interval verification page.

[38]

Gu Mingche stared at the thirty-eight for a few seconds, then inserted the straw into the soy milk cup, hitting the thickest edge of the plastic sealing film on the very first try.

"This number is so polite that it's small, terrified of disturbing any finite-scale point sets."

"It's enough that it disturbs the conjecture."

"That's true."

Gu Mingche pushed the soy milk aside and flipped down to the general construction diagram.

Over the past six days, he had caught up on the graph theory, incidence geometry, and analytic number theory materials Jiang Lin had listed for him, and had even recalculated the failed drafts of the cubic number fields from scratch, yet half of the main chain on the screen still fell outside the boundaries of his knowledge.

That half began from the maximal pro-2 extension allowing finite branching, passed through the Golod-Shafarevich inequality, the totally real infinite tower, and the uniform upper bound of root discriminants, and then reconnected from the other side of the CM field to the planar point sets he was familiar with.

"You swapped the problem of insufficient degree for an infinite tower."

"Right."

"With a designated prime number splitting completely, is there still a way for the tower to remain infinite?"

Jiang Lin opened the first attack package, and the page stopped at a table with only three rows of numbers.

[d ( G ) ＝ 5]

[r ( G ) ≤ 6]

[d ( G ) ² ／ 4 ＝ 6.25]

Gu Mingche copied the three rows of numbers onto paper.

"The margin is only a quarter."

"It's already enough for the strict inequality to be used."

"What if I beat your generator rank from five down to four?"

"Behind it are the independent certificates of the Frattini quotient."

"What if one extra relationship rank upper bound was miscalculated and missed?"

"Starting from page thirty-four, the allowed branching points, real infinite places, and 101 complete splitting conditions are listed item by item."

Gu Mingche flipped to page thirty-four, read two paragraphs, and then stopped.

"I'll continue reading this part, but at most I can only help you check whether the symbols secretly changed names."

"Symbols need people to check them too."

"Don't lower your peer-review threshold yet."

He exited the first attack package and clicked open the cubic number field failure comparison.

That twenty-seven-page old draft still retained the counterexample written by the classroom doctoral student, with red boxes circling the two locations where the conjugate coordinates went out of control.

The new construction added all complex embeddings alongside it, and the element u generated by the ideal ratio was suppressed onto the unit circle in every conjugate coordinate.

Gu Mingche read along the ideal combination numbers to the class group pigeonhole principle, his finger stopping at the denominator of h ( K ).

"There are many combinations in the same ideal class, which doesn't mean that after taking the ratio, you can still have just as many different directions left over."

"Look at the deduplication lemma."

"Roots of unity will repeat."

"Starting from the first edition of the main proof, the multiplicity of the roots of unity has been listed separately in the fixed constant C, and the first round of internal verification re-obtained the same upper bound from the original class group data."

"What about the principal element multiplied by a general unit?"

"Units whose embedding modulus lengths are all equal to one enter the kernel; the size of the kernel in the CM field has a unified control here, and the proof is on page nineteen of the fourth package."

Gu Mingche flipped over. The steamed buns in the plastic bag had already steamed a thin layer of moisture onto the desk surface.

He pulled out a piece of paper to pad underneath the verification disk and continued checking that bridge from the Minkowski lattice to the planar projection.

At 8:06, he picked up his phone.

"This is already beyond the scope of what I can be responsible for; I'm calling the teacher."

When the phone call connected, the sound of paper turning and pen caps snapping shut came from the earpiece. After listening to Gu Mingche's words, that discrete geometry class teacher only asked a single question.

"Did Jiang Lin solve that loophole in the cubic number fields, or the complete conjecture?"

Gu Mingche turned on the speakerphone.

Jiang Lin replied: "The complete conjecture. The conclusion is that the conjecture does not hold."

The sound of chair wheels rolling across the floor came through the phone.

"First send the theorem statement, the dependency overview diagram, and the two connections you think are the most fragile. Do not upload the entire file to the internet."

Jiang Lin selected three documents from the outgoing package that had already had their internal paths and future system labels cleared.

One minute after the email arrived, the other party changed the scheduled afternoon meeting time to nine o'clock.

"Bring the paper draft and offline disk to the Science Building; Gu Mingche comes too."

At 9:12, the corridor of the Science Building still retained the emptiness of a Sunday morning, yet three chairs had already been placed at the door of the office.

The teacher took the offline disk and asked Jiang Lin and Gu Mingche to first write the file hash, delivery time, and current knowledge scope on the cover.

"From now on, do not forward it to student chat groups, and do not use online collaborative documents."

He also wrote Gu Mingche's name into the knowledge scope column.

Gu Mingche looked at that column: "I just came over to deliver some steamed buns."

"You also read forty-seven pages."

"Out of those forty-seven pages, there were over twenty pages where I could only check the page numbers."

"Wrong page numbers can also harm people."

The teacher took away the registration paper and opened the main document, but skipped the abstract, background, and final parameters, going straight into the two connections where the counterexample was most easily broken.

The first was how the infinite tower simultaneously maintained total reality and 101 complete splitting, and the second was how the exponentially growing unit modulo elements turned into non-overlapping unit distance edges on the plane.

These two connections belonged to different fields. If the former broke, the degree of the number field would never grow; if the latter broke, no matter how tall the tower, it could only remain inside algebraic number theory for people to visit.

"Look at the tower first."

The teacher rewrote T and S on the paper and changed G in Jiang Lin's proof back to his own customary notation.

"The upper bound you gave for the relation rank is six. Which base field's relation bound is used here?"

"The rational number field; the allowed branching set is six finite prime numbers, all real places are included in the splitting conditions, and the Frobenius relation of 101 is listed separately."

"If 101 has already split in the maximal elementary quotient, it won't trim off a generator. How do you rule out a circular argument in the notation regarding this point?"

Jiang Lin switched the Frattini quotient certificate to the projection matrix page.

The Frobenius image corresponding to 101 was zero in the elementary quotient, five independent quadratic directions were generated by the six prime numbers in T, and the two conclusions used two sets of separately calculated residue symbols.

The teacher took out draft paper, recalculated the quadratic residues modulo 101 one by one, and then checked the independence of the five directions along matrix elimination.

When the printer in the office spat out the third page, he drew the first checkmark behind [d ( G ) ＝ 5].

"This only shows that the elementary layer hasn't collapsed."

"That's why the relation bound is placed separately in the next section."

"You wrote six being less than six point two five so large that it's easy to make people think the hardest part left is elementary school arithmetic."

"The shortest step is suited to be placed on the last page."

"And suited to let laymen mistakenly think the preceding four hundred pages are all foreshadowing."

The teacher flipped to the Shafarevich relation bound, his pen tip moving downward along each local condition.

Jiang Lin sat opposite and finished eating the first steamed bun that had already cooled down, while casually processing the first-piece disassembly inspection photos sent by Xu Man.

In the photo, a PG platform that had completed disaster relief re-inspection had two seals replaced, and its right rear foot bearing clearance was twelve micrometers greater than the factory value, which was still within the red line set by Chen Yan.

He replied ["Enter life tracking according to the original plan, do not release early"], and then turned his phone to silent.

At 10:44, the teacher wrote down the first formal query beside the relation bound.

[Q-001: The bookkeeping method when independently recalculating the real infinite place splitting conditions into the relation rank upper bound.]

This query would not invalidate the proof for the time being, nor did it allow Jiang Lin to cross it out based on his own internal verification.

Jiang Lin copied Q-001 into the main review directory, retaining the original sentence written by the teacher without changing a single word.

The teacher dialed a peer who studied class field towers, compressed the problem into three sentences, and agreed to send only the first attack package.

The second call was made to Professor Lin Zhaoye.

"Are you free today?"

The other end of the phone asked something, and the teacher flipped the unit distance proposition to the first page.

"Jiang Lin gave a lower bound with a fixed positive exponent."

The person on the other side spoke a few more sentences.

"Never mind how small it is for now; as long as it is truly greater than zero, you know the consequences."

The teacher reported the hash of the first package, asking Professor Lin Zhaoye to first check the planar projection, edge deduplication, and window boundary, without touching the internal conclusions of the class field tower part.

The six verification packages thus got their first batch of persons in charge in the Real World.

The class field tower was handed over to two algebraic number theory researchers for independent recalculation; the class number and unit modulo element counting were split into another group; Professor Lin Zhaoye was responsible for geometric projection; the teacher retained the main chain splicing; and the task Gu Mingche received was the most plain: starting from the first page, check whether all definitions, citations, and symbols were consistent throughout.

Gu Mingche wrote his task on the registration form and finally remembered that there were still three steamed buns left on the desk.

"I'm going back to grab my breakfast."

Jiang Lin reminded him: "It's already thoroughly cold."

"I lined up for twenty-seven minutes."

"Then don't waste it."

Gu Mingche walked to the door, then turned back and stuffed Jiang Lin's read-only disk into the cabinet as well.

"Don't modify the main draft again today. Wait until the first round of queries comes back, lest the version we're reviewing chases after you."

"Okay."

The teacher lifted his head from the registration form: "Who else has read it?"

"In the Real World, only the three of us."

"What about external submission?"

"Haven't done it yet."

"The media, preprints, and your previous review chain are all suspended, at least until the tower, counting, and projection groups each give their first round of conclusions."

The teacher flipped over the cover and saw that date in the task metadata that had not yet arrived.

[Plan Officially Launched: November 1, 2022]

He circled the date with his pen.

"What is this about?"

"The original plan."

"Today is October 30th."

"So it didn't go according to the original plan."

The teacher looked at Jiang Lin for a moment, crossed out that line of words, and wrote down a new status below.

[October 30, 2022, entering independent verification in the Real World.]

Gu Mingche created a directory for the first query, with filenames starting from Q-001.

The save time was 12:47 PM.

November 1st was still on the next page of the calendar, yet someone in the Real World was already prepared to start from the original theorem and recalculate that quarter of a relation once more.