143: Chapter 143 Terence Tao's entry into the game proves he's on the final judgment chain.

On August 3rd, at 0:40 AM, Zijin Villa was very quiet in the middle of the night.

The door of the 303 closed-door meeting room opened from the inside.

Professor Han Yanshan was the first to walk out.

His shoulders were slightly slumped, and several deep wrinkles had been pressed into the back of his originally crisp shirt.

His cuffs were rolled up above his elbows, and two dried blue marker traces stained the edge of his forearms.

Although he was exhausted from high-intensity mental overdraft, his mental state also showed a sense of relief as something heavy finally landed.

Ding Jian followed behind.

The thick manuscript was tucked under his armpit, its cover slightly curled from repeated flipping.

Then came Jiang Lin.

Carrying a backpack, his spirit could not be said to be energetic, yet he did not show too much fatigue.

Professor Lin Zhaoye was the last to leave the room.

Before closing the door, he turned back to glance at the meeting room.

Three mobile whiteboards were placed in a pin-wheel arrangement, and the towering layers of formulas on the boards had been erased.

Professor Lin Zhaoye raised his hand to turn off the lights, and the door closed.

The door lock clicked shut.

This crisp mechanical engagement sounded like a punctuation mark, temporarily sealing the past fifteen hours and forty minutes of meat-grinder-like derivation into the dark room.

"That's it for tonight."

Professor Han Yanshan spoke, his voice the hoarsest it had ever been in his life.

"Jiang Lin, tomorrow—no, today—before nine o'clock in the morning, I won't send you any new technical questions. Let's pause this review chain here for now; we need to let our brains cool down."

Standing aside, Ding Jian added: "To any external inquiries about today's closed-door content, uniformly reply that it was a routine academic discussion."

Jiang Lin nodded to indicate he understood.

After giving the instructions, Professor Han Yanshan remembered something and said: "Don't forget to synchronize this matter with Mr. Qiu."

Ding Jian said in a low voice: "He invited me into this review chain, and now that the first core obstacle has been smoothed out, we should tell him."

Professor Han Yanshan rubbed his tightly strained and aching brow forcefully, sighing: "Moreover, relying on just the two of us is not enough."

Professor Lin Zhaoye understood Professor Han Yanshan's meaning.

In today's mathematics community, Professor Han Yanshan was one of the brains in China capable of reviewing the main line of PFR finite fields.

Ding Jian's attainments in Marton entropy forms and probabilistic structures ranked in the global first tier.

But the manuscript Jiang Lin brought out was not a single-dimensional traditional paper.

It stepped simultaneously on four lines: Additive Combinatorics, entropy methods, finite field structures, and formal proof engineering.

It was like a massive project with a complex geological structure.

It required multiple top-tier construction teams equipped with different heavy equipment to tunnel simultaneously from different directions.

Professor Han Yanshan could illuminate a section in the east, and Ding Jian could probe the rock strata in the west. Everyone could verify the strength of the structure in their most proficient fields.

But no single person could, by their own strength alone, illuminate the entire bottomless tunnel and ensure that all interfaces fit seamlessly.

Professor Lin Zhaoye pondered for a moment and asked: "Do you want Mr. Qiu to invite the next reviewer?"

"Not the next reviewer." Professor Han Yanshan glanced at the backpack on Jiang Lin's back. "It's the next door."

Ding Jian never liked beating around the bush; he directly pointed out the name: "Terry must see this PFR line."

Terry, Terence Tao.

If a manuscript on PFR / Marton under the finite field F₂ model had solidly advanced to the Entropy Involution Lemma, to the eleventh power covering bound of K, and even had the Lean 4 formalization blueprint built to this step, then for this manuscript, Terence Tao was not merely an authority who could be invited to add extra splendor.

In the intersection zone of Additive Combinatorics and harmonic analysis, he was the highest mountain on this review chain that could not be bypassed.

Professor Lin Zhaoye quickly calculated the time difference in his mind and said: "I'll call Mr. Qiu first."

"We don't need to talk too much about technical details on the phone; saying too much will instead cause a loss of focus. Three things are enough."

Professor Han Yanshan explained.

"First, the finite field PFR main line, after our preliminary stress testing, temporarily shows no structural fractures."

"Second, Ding Jian personally verified Section 4.2 just now; that most dangerous Entropy Involution Lemma passed the minimal degradation model test, and the bound of K^11 has stabilized."

"Third, Jiang Lin has prepared the Lean formalization blueprint, which is sufficient to support external reviewers in entering the depths of the code line by line along the dependency chain."

This was not a finished product relying on a mature mathlib4 ecosystem.

In 2022, the Lean 4 public library was still far from thick enough; what Jiang Lin actually built was a project-local library.

The public library only undertook the most basic types, finite field structures, and general lemma interfaces.

The spectral cluster index on F₂ⁿ, the conditional mutual information ledger, the covering recursive nodes, and the double involution encapsulation were all sealed by him in the local library.

Therefore, it was not a final formal proof, but a formalization blueprint.

A mechanized construction route that allowed external reviewers to enter the interior of the proof along the dependency graph.

Professor Lin Zhaoye took out his phone, turned, and walked to the end of the corridor, avoiding the noise of the ventilation duct.

Several people stood in place, waiting silently. No one spoke, and only Professor Lin Zhaoye's low, muffled conversation could be heard intermittently in the corridor.

About two minutes later, Professor Lin Zhaoye turned back and walked over quickly.

"Mr. Qiu hasn't slept yet; he wants to have a phone call with you."

Professor Lin Zhaoye handed the phone to Jiang Lin.

Jiang Lin took the phone.

"Jiang Lin."

"Professor Qiu, hello."

"I haven't seen the manuscript, so I can't judge whether this proof is right or wrong. But since Professor Han Yanshan and Ding Jian both believe that Section 4.2 has passed the minimal degradation model tests they could construct, then Terry is indeed the best candidate."

Jiang Lin quickly evaluated the current progress in his mind and then asked: "Contact him now?"

Shing-Tung Yau's reply had no hesitation: "I will write a private introductory email to Terry first. In the letter, I will only introduce the background and your progress tonight; I will not overstep my bounds to judge the conclusion for you. After he replies and expresses his willingness to read it, you can then send the repository invitation over."

Jiang Lin understood the subtle boundaries in this kind of academic socialization and nodded in response.

"Okay, I will fully open the main paper, the two technical memoranda, the independent verification guide, the Lean blueprint, the dependency graph, and the whiteboard scans. But the seventh edition text will remain unchanged as the review baseline, and the main branch needs to be locked. All annotations, formalization suggestions, and Lean code modifications must go through issues, branches, and pull requests."

A gigantic manuscript spanning Additive Combinatorics, entropy methods, and formal verification—once multiple people were allowed to enter and collaborate simultaneously—the most terrifying trouble was often not disputes over mathematical intuition, nor even chaos in authorship, but the disaster of version control.

A minor loss term, if quietly moved from node 38 to node 39 yesterday; a conditional mutual information, if rewritten into some equivalent form this morning; a local lemma, if casually merged into a higher-level corollary late at night...

In such a vast and complex logical chain, if there was no version tracking chain clear to the point of being rigid, then just three days later, even the author himself might face the screen in utter bewilderment, forgetting when and for what bloody reason a certain delicate estimation formula had been altered beyond recognition.

Shing-Tung Yau on the other end of the phone understood Jiang Lin's subtext, his tone revealing a sense of approval.

"Alright, then after you go back, prepare the repository's permissions and structure first."

...

The four people parted ways in front of the third-floor elevator.

Jiang Lin returned to his room, and when he washed up, his face was reflected in the mirror.

Eighteen years old.

There were no dark circles under his eyes, his skin was firm, and his hair was somewhat flat from sitting all day.

There was not even any obvious fatigue on that face.

More than a dozen hours of high-intensity derivation were enough for an ordinary eighteen-year-old boy to make his brain feel numb as if repeatedly crushed.

But Jiang Lin did not.

The dust storm nights of forty-eight consecutive hours without sleep in the Wasteland, being forced to guard the cooling pump until dawn during low-temperature failures at the Outpost, thirty-six full hours of not daring to leave the diagnosis table during the first emergency wakeup window of PMCU-17...

Those more extreme, longer nights lacking external support had long pushed his mental tolerance threshold to a position hard for ordinary people to understand.

Therefore, the fatigue brought by this whiteboard meeting at this moment was automatically categorized as minor within his body.

...

Coming out after washing up and drinking a cup of warm water, Jiang Lin sat down and opened his computer.

He pushed the local Git repository to a private repository on GitHub.

He used an account that he had started using after returning from the eighth Wasteland.

l-jiang-2004

Inside were only a few pieces of crude experimental code from the early days of the MPS-Kernel architecture.

A few helper scripts for auxiliary calculations of Jiangs Brick boundary states.

As well as a few self-use symbolic computation small tools written in Python.

On the homepage, there was no personal profile, no school name, no photo avatar, only a meaningless block of pure gray pixels generated by default by the system.

Jiang Lin first created a new private repository.

He had already thought of the repository name: pfr-f2-formalization-blueprint

The visibility was set to Private.

All initialization options were left blank.

Subsequently, he returned to the terminal and typed the command.

git remote add origin git@github.com:l-jiang-2004/pfr-f2-formalization-blueprint.git

git push -u origin main

Enter.

The progress bar began to move forward.

The main paper, Lean files, README, and dependency graph entered the main Git repository. The high-definition whiteboard scan images and manuscript PDFs were placed into Git LFS separately, leaving corresponding hash values in the README.

In this way, reviewers could track the changes of every logical node without letting the repository body be dragged down by large-volume attachments.

Along with the prompt popping up in the terminal: Branch 'main' set up to track remote branch 'main' from 'origin'.

The push was complete.

Jiang Lin entered the repository settings page.

He first checked the visibility to confirm that the repository was still Private.

Then he enabled main branch protection: prohibiting force pushes and direct commits, requiring all modifications to be merged via pull requests.

He also configured protection rules for the v7-final-baseline tag, prohibiting deletion and force-overwriting, and the main paper text no longer accepted silent modifications.

After doing this, he clicked on the collaborators tab and added the three email addresses of Professor Han Yanshan, Ding Jian, and Professor Lin Zhaoye in turn.

After checking the repository permissions once more and confirming that no loopholes were left, he clicked to close the browser window.

The bottom right corner of the computer displayed: 1:12 AM.

Just at this moment, the phone placed on the desk vibrated gently, and the screen lit up.

It was a WeChat message sent by Professor Lin Zhaoye.

[Mr. Qiu has already sent a letter to Terry. It is currently past 10:00 AM US Western Time, just wait for the reply.]

Jiang Lin replied with a thank you, closed the computer, turned off the desk lamp, and went to bed to sleep.

On August 3rd, at six in the morning, Jiang Lin had already opened his eyes.

He washed up, changed clothes, and went downstairs.

The breakfast buffet hall of Zijin Villa was already open, but it was still early and there were not many people.

Jiang Lin directly pulled out the largest flat dining plate in the room.

He had no pickiness about the color, aroma, or taste of food; his only standard was whether it could fill his stomach and whether it could provide enough calories for brain consumption.

He picked up the tongs, piled six huge fresh meat buns, four freshly fried dough sticks, a large plate of oily and moist fried noodles on the plate, and finally took four tea eggs and a large glass of milk.

Eating his fill in a few minutes, on his way back, he took out his phone and replied to the emails accumulated yesterday one by one.

At seven o'clock, he returned to the room to pack his luggage.

Checked out at half past seven and took the conference group's car to Nanjing South Railway Station.

At 9:22, the high-speed rail departed on schedule.

Jiang Lin sat by the window, placed his backpack on his lap, and pulled a physical book out of the backpack's side pocket.

Additive Combinatorics.

The authors were Terence Tao and Van Vu, the 2006 classic version.

For Jiang Lin, this book had a significance far exceeding that of an academic monograph.

He had started reading it during the fifth Wasteland time.

With the intertwining of reality and virtual time, counting it up, he had read this not-so-thick book on and off repeatedly for nearly ten years.

Opening the title page, there was a line of English notes he had copied word for word with a pencil many years ago.

The handwriting was slightly blurred due to its age.

"The most important problems in Additive Combinatorics are about structure."

(The most important problems in Additive Combinatorics are about structure.)

Jiang Lin's finger slid across that line of text, then opened the book and began reading directly from the complex proof in the middle section.

It was not a review.

Nor was it error checking.

This proof had already been repeatedly disassembled by him too many times in the Wasteland.

Residual spectrum re-entry, third-layer loss recovery, entropy control functions, Marton bridge-building—all the locations most prone to causing old routes to collapse had been suppressed item by item in the seventh edition text.

The problem now was no longer whether the proof could get through.

But how the real mathematical community was to enter this proof.

Many intermediate structures he formed in the Wasteland served the purpose of long-term independent work.

They were precise, efficient, and even in some places more suitable for his proof route than the standard notation in real literature.

But a paper that needed to be reviewed line by line by mathematicians of the caliber of Professor Han Yanshan, Ding Jian, and even Terence Tao could not just stay within the author's own internal language.

It had to be able to return to the common literature system formed by Additive Combinatorics over the past twenty years.

This Additive Combinatorics by Tao and Vu was one of the most important entry points in that language system.

Which places should follow standard notation.

Which places must retain Jiang Lin's own entropy ledger terminology.

Which lemmas were merely rearrangements of old tools.

Which steps were truly new actions.

These were all interfaces that had to be repaired when the proof entered the Real World.

He wanted to make sure that the next person entering this proof wouldn't first get lost in his decades of Wasteland work habits.

The high-speed rail took two and a half hours.

Jiang Lin finished reading Chapter 12 and wrote down seven new lemma candidates on the scratch paper.

He did not look at his phone.

At 12:04 PM, the high-speed rail stopped at Jiangcheng North Railway Station.

Jiang Lin dragged his suitcase out of the station and directly took a taxi home.

In August in Jiangcheng, the sun was fierce.

The taxi's air conditioning wasn't strong enough; the plastic leather of the back seat was baked until it was burning hot, and when clothing pressed against it, it gave people a slight sticky sensation.

Local traffic radio played all the way.

At 12:35, Jiang Lin arrived home.

The aroma of food wafted through the stairwell of the old residential building.

Someone was arguing on the third floor.

The old cat of the neighbor on the fifth floor meowed with a long drawn-out tone.

Jiang Lin walked to the door of his home, and the door was unlocked.

Hearing the footsteps downstairs, Zhang Xiufen had already ajarred the door.

"Mom, I'm back."

"Oh!"

Zhang Xiufen poked her head out from the kitchen, her apron dusted with flour.

"I'm making sweet and sour pork ribs for lunch. Wash your hands first, the food is almost ready."

"Mhm."

Jiang Lin leaned his suitcase against the wall and went to wash his hands.

After lunch and a brief rest, Jiang Lin returned to his bedroom and opened his laptop.

There were no new email notifications.

He opened the browser, logged into GitHub, and entered the background status page of the pfr-f2-formalization-blueprint repository.

Professor Han Yanshan had already clicked to accept the collaboration invitation.

Ding Jian had also accepted the invitation. Not only that, but he had already left his mark in the issues section.

He had submitted two issues in a row, all of which were about the detailed conversion problems of the 23rd formalization node under the Lean environment, purely hard-hitting technical discussions.

Professor Lin Zhaoye had also accepted the invitation, but he clearly abided by his promise as a gatekeeper, and his account had not modified a single punctuation mark on any file.

Jiang Lin closed the browser.

He opened the document "Hengtai Mining Autonomous Driving Testing Cooperation Agreement (Revised v2)" sent by Liang Zhixia at noon.

At 3:20 PM, the phone on the desk vibrated, and Liang Zhixia called.

"President Jiang, have you finished reading the three core changes I highlighted in red in the contract?"

"I've finished reading it."

"Especially Article 7, Paragraph 3, regarding the wording of the ownership of test data. The Hengtai legal department wrote it as joint ownership and joint development. Such phrasing makes buck-passing too easy. On our side, it must be changed to Low Entropy Workshop retaining all intellectual property rights to the underlying algorithms and derivative data, while Hengtai Mining only holds an internal exclusive license for use during the contract period."

"That's what I thought too. Hengtai's legal department is notoriously difficult to deal with, and they will most likely block us on this clause."

"Let them block it if they want; the losses won't be ours."

"Alright, there is one more thing. Starting this morning, three investment institutions have successively sent formal emails. I checked their backgrounds, and they are all relatively active PEs in the A-share market. I don't know where they found out about our progress, but they are all asking when Low Entropy Workshop will open Series A financing negotiations. Following the stance you set earlier, I uniformly replied that Low Entropy Workshop has sufficient funds at the current stage and temporarily does not accept any form of external financing negotiations. I've also instructed Qiu Yue to set the same response on the automatic reply of the external email address."

"Keep it hanging like that. Letting capital in now will only disrupt the rhythm of R&D."

"Okay, then I'll go modify the contract first."

The call hung up.

Jiang Lin sent the organized detailed revision comments to Liang Zhixia via WeChat.

Afterwards, he pulled a stack of blank A4 paper from the desk drawer and picked up a pencil.

[G-01C Engineered Version: Foot-End Dynamic Contact Model Optimization]

At five in the afternoon, the wooden door of the bedroom was gently knocked on.

Mother shouted from outside: "I'm planning to make pork and chive dumplings that you love for dinner tonight. Will you be eating at home tonight?"

"Okay," Jiang Lin responded.

Hearing the affirmative reply, Zhang Xiufen smiled and went to prepare.

Jiang Lin stopped deducing the friction cone model in his hands, put down his pencil, and got up to go out.

He saw his mother sitting in the kitchen peeling garlic.

"Mom, I'll help you peel," Jiang Lin walked over and said.

"Oh dear, don't get your hands dirty," Zhang Xiufen hurriedly looked up and waved her hands, trying to stop him. "Peeling garlic is too pungent; soon your fingernails will be full of the smell and you won't be able to wash it off."

Jiang Lin ignored her, pulled another smaller wooden stool from the side, and sat down right next to his mother.

"Mom, hands like yours are meant for doing big things," Jiang Lin said while agilely grabbing a bulb of garlic, applying force with his thumb to twist and peel off the purplish-red outer skin.

Zhang Xiufen was stunned, evidently not expecting her usually taciturn son to say such things, and immediately her eyes crinkled into slits with a smile as she scolded playfully: "You've only been to Nanjing for a few days, and your mouth has sure gotten slick."

Although she said that, she still pushed a small stainless steel basin specially used for holding peeled garlic cloves in front of Jiang Lin.

The mother and son sat like this in the kitchen, accompanied by the occasional sound of cicadas from outside the window, quietly peeling garlic for ten minutes.

For dinner, steaming hot handmade pork and chive dumplings were served on the table.

Dipping them in the mashed garlic and vinegar sauce made from the garlic he had peeled himself just moments before, Jiang Lin ate thirty-six of them in one go.

At eight in the evening, after cleaning up, Jiang Lin returned to his room and closed the door.

He turned on the computer.

Terence Tao's email still hadn't arrived.

But the background status of the GitHub repository already showed signs of white-hot activity.

Over the past few hours, Ding Jian had been like an untiring bug-fixing machine, submitting three more long-form issues in a row, with all his firepower concentrated on the conditional independence of the obscure 28th node.

Professor Han Yanshan still hadn't uttered a single word in the issue section, but in the early morning he sent a local compilation log where eleven consecutive timestamps showed that he had repeatedly synchronized the latest dependency graph.

This meant that this top domestic brain was scrutinizing every single line and every single word of the deduction logic in the manuscript.

Jiang Lin pulled his attention back to the Physics world and continued sketching the complex foot-end contact model equations of G-01C on paper, working for two hours straight.

At half-past ten at night, he washed up and went to bed on time.

Waking up on the morning of August 4th, Jiang Lin glanced at the GitHub repository again.

Ding Jian's offensive over there was even more ferocious; he had accumulated a total of eleven issues.

The usually silent Professor Han Yanshan had finally broken the calm and submitted three issues.

Each question was very short, consisting of just a few words, yet between the words and phrases, it struck like a scalpel right at the most ambiguous and critical parts of the reasoning chain.

At eight in the morning, Jiang Lin rode his bicycle to Low Entropy Workshop.

The concrete road of the old industrial park had been bleached white by the sun, and the peeling layer of gray paint on the outer walls of the factory building looked even more mottled in the heat wave.

The second-floor office didn't have a shred of the so-called sense of dignity of a startup company.

A few long tables, a few computers, two rows of iron filing cabinets, a numbered sample rack placed against the wall, and the whiteboard on the wall that had been re-planned by Liang Zhixia.

The left side of the whiteboard wrote contracts and payment milestones, the right side wrote engineering review tasks, separated in the middle by a red line.

At the very top was a line of printed text pasted by Chen Zhi.

[G-01C Hengtai Post-Blind-Test Review Materials, Do Not Circulate Externally, Do Not Take Photos, Do Not Deviate from the Numbering System.]

When Jiang Lin entered the door, Liang Zhixia was already waiting for him by the conference table.

Chen Zhi sat near the filing cabinet, with three folders spread out in front of her, their covers pasted with numbered labels of different colors.

Qiu Yue did not sit at the conference table.

Wearing headphones at her external workstation, she stared at the public mailbox background, dragging cooperation invitations from investment institutions, local parks, MCN agencies, and inexplicable robotic pet companion projects one by one into different categories.

"President Jiang."

Liang Zhixia pushed a directory in front of him.

"The final payment process on Hengtai's side has been completed, and the four hundred thousand has arrived this morning. Added to the initial eight hundred thousand, this stage's 1.2 million engineering cooperation fee has been completely settled."

She didn't say this with much excitement.

Because it was written very clearly in the contract.

This money did not correspond to any IP transfer, technical licensing, industry exclusivity, or joint ownership of derivative results.

It was simply the first clean income earned after Low Entropy Workshop brought a non-production environment core test prototype into a real industrial pressure scenario for the first time.

Jiang Lin nodded: "Distribute it according to the original budget after it hits the account."

"It's already been split up."

Liang Zhixia turned to the second page.

"Prototype spare parts repair, material procurement, outsourced processing, servers and NAS, legal fees, salary reservations, and safety cash flow—Chen Zhi has already numbered all of them."

Chen Zhi pushed one of the folders forward by half an inch.

"These are the payment vouchers and budget tables. Every single transaction has a purpose number, and subsequent procurements will follow the same set of numbers."

Jiang Lin flipped through two pages.

Liang Zhixia waited for him to finish reading before opening the third material.

"The engineering review starts here."

Written on the cover of the document: [G-01C | Hengtai Post-Blind-Test Hardware Damage Report]

Author: Xu Man.

Jiang Lin raised his eyes.

Xu Man sat on the other side of the conference table, with a transparent engineering box placed in front of her.

Inside the box were several disassembled components.

A worn white POM foot-end, a piece of cut red heat-shrink tubing, two fixing screws with impact marks.

And a protective cover with shallow marks cut into the edges by gravel.

Each item was attached with a small numbered label for traceability.

Xu Man pushed the engineering box to the center of the table: "After the Hengtai blind test, G-01C has no structural damage, but there are three categories of problems that must be dealt with."

She turned to the first page of the report.

"First, the outer edge wear of the right-front foot-end exceeded expectations. It's not that the material as a whole is not wear-resistant; rather, the wet cinder and rusted angle steel on the thirty-seven-degree gravel slope caused localized cutting-style wear."

"Second, the sensor protective layer experienced localized shear slippage on irregular contact surfaces. It cannot be seen with the naked eye, but after disassembly, it can be seen from the micro-wrinkles at the edge of the adhesive layer."

"Third, the reducer output end did not fail, but the backlash slightly enlarged after the impact. It hasn't reached the scrapping standard yet, but if we enter the unmanned closed roadway grayscale testing in the next stage, this margin is not enough."

Xu Man continued: "My suggestion is that G-01C, as a post-Hengtai-blind-test prototype, should no longer participate in the next round of extreme working condition testing. It should be converted into a disassembly calibration prototype. The next round of testing should at least redo two sets of foot-end components: one set with conservative materials, and one set with modified materials."

"Okay." Jiang Lin nodded.

Xu Man's shoulders visibly relaxed a little bit.

She wasn't afraid that Jiang Lin would deny her judgment.

She was afraid that Jiang Lin, like many startup bosses, would forcefully shove the prototype—which had already completed one high-intensity blind test—back into the test field just to rush the next round of contracts.

Liang Zhixia wrote down a line next to her.

[G-01C converts to a disassembly calibration prototype, and will not enter the next round of extreme testing.]

Subsequently, Chen Yan opened his computer and projected a timeline onto the wall.

"My side is cross-verification of video, logs, and foot-end sensors."

On the screen was a synchronized timeline cut into dozens of segments.

External high-frame-rate video.

G-01 internal state machine logs.

IMU yaw curve.

Main shaft current.

Foot-end thin-film sensor output.

Common timecode plate.

All data was compressed under the same timeline.

Chen Yan pointed to a gray area among them.

"From the seventeenth to the twenty-fourth second of the Hengtai slope, G-01 passed through the sprayed slippery area. External video showed no obvious side slip at the foot-end, but an abnormal deviation of about 3% appeared in the foot-end thin-film sensor output."

He paused for a moment and enlarged the local curve.

"This deviation is not a controller misjudgment, nor is it a state machine switching error. It comes from the micro-shear of the sensor protective layer on irregular surfaces."

Xu Man chimed in: "The disassembly evidence matches."

Chen Yan nodded: "So my conclusion is that the next stage cannot directly use this piece of data as real foot-end force. We must first establish an irregular surface protective layer shear compensation model. Otherwise, the state machine will think it sees changes in the ground, when in reality it sees that the sensor itself was twisted a bit."

Jiang Lin looked at the enlarged 3% deviation curve.

If it were before the tenth Wasteland, he would have recorded this matter as a problem to be verified.

But now, he had already completed the G-01 mass-production engineering master in the Wasteland.

Foot-end materials, reducer flexsplines, and sensor protective layers—every single one had been rolled over by even more brutal and longer-cycle tests.

In the Real World team, Xu Man provided the hardware damage interface, Chen Yan provided the data authenticity interface, and Liang Zhixia provided the organization and contract interface.

Jiang Lin took a new file bag from his backpack and placed it on the desktop.

There was only a line of words on the cover of the file bag.

[G01-Production | Real World Mapping Task Package_v0.1]

"Starting today, G-01 will no longer be promoted according to the mindset of a single prototype."

Jiang Lin said.

"The next round of test prototypes will be split into three sub-packages according to the engineering master."

He wrote three lines on the whiteboard.

[Foot-End Materials and Protective Layer]

[Reducer Impact Margin]

[State Machine Input Credibility]

Then he looked at Xu Man.

"Xu Man, you are responsible for the first package. First establish a material screening matrix. Wear resistance, compressive strength, shear layer stability, processing difficulty, supply stability—quantify all of them. At the current stage, don't pursue optimality; first screen out the materials that cannot be used."

Xu Man lowered her head to take notes.

Jiang Lin looked at Chen Yan again.

"Chen Yan, you are responsible for the third package. Model the 3% deviation separately; don't rush to compensate it into the controller. Answer one question first: on irregular contact surfaces, which sensor outputs are real changes in the ground, and which are just false signals given to you by the protective layer and adhesive layer."

"In other words, do data credibility classification first, without directly modifying the state machine?" Chen Yan asked.

"Correct," Jiang Lin said, "Making the machine tell the truth is more important than making it take an extra step."

Qiu Yue poked her head in from outside: "Sister Zhi, another institution sent a financing email saying they can skip the financial model and directly give a valuation."

"Template reply," Liang Zhixia didn't even raise her head.

Qiu Yue made an OK gesture, retracted her head, and continued dealing with emails.

...

At 2:46 PM.

Professor Lin Zhaoye sent a message.

[Mr. Qiu forwarded Terry's official reply; he is willing to take a look.]

Immediately following, a screenshot popped up in the chat interface.

The full text of a forwarded email.

The sender was Terence Tao, and the recipient was Shing-Tung Yau.

Dear Shing-Tung,

Thank you for the note. If Han and Ding have already looked at the manuscript and the issue is specifically the PFR/Marton bridge over F₂ⁿ, I would be glad to take a look.

Please ask author to send the repository invitation directly to my UCLA address. I will treat it as restricted review material.

Best,

Terry

Jiang Lin finished reading the email and immediately logged into GitHub.

He moved the cursor to the invitation bar and typed in the email address that was world-renowned in the mathematics community.

tao@math.ucla.edu

Enter.

At the top right of the screen, a green prompt box popped up as expected.

Invitation sent.

At 3:27 PM.

After refreshing the GitHub page, in the Collaborators list, the status text next to Terence Tao's name had changed from gray Pending to striking green.

Accepted.

This meant that the other party, far away in Los Angeles, had seen the invitation and accepted access permissions.

However, there was no new movement in the repository's activity logs.

The other party did not immediately raise any issues, nor did they make any tentative commit submissions.

Clearly, forty-seven intertwined formalization nodes, a manuscript text dozens of pages long, a high-resolution scanned image of the whiteboard containing the core deduction logic.

A dazzling set of dependency relationship graphs.

Even a genius like Terence Tao, known as the Mozart of the mathematics world, could not see through all the mechanisms within in an hour.

However, at 5:32 PM.

Terence Tao left the first extremely short review comment below the README.

"I have cloned the repository and will first compare the manuscript dependency graph with the Lean node map."

At 6:09 PM, he left another marker next to the file for node 38.

At 8:47 PM, the third marker appeared on the boundary layer of the dependency graph.

...

On August 5, Jiang Lin woke up in the morning and received an email from Terence Tao.

Sender: Terence Tao

Recipient: Lin Jiang

CC: None

Send Time: Aug 5, 2022, 06:18 UTC+8

Email Subject: Re: PFR over F₂ⁿ, K^11 covering bound

Dear Lin,

"I have read the manuscript package and the formalization blueprint. The Entropy Involution Lemma appears to be the key new move; in particular, it seems to prevent the loss term from re-entering the covering iteration at exactly the point where the standard approaches lose polynomial control."

"The mathematical proof is clear enough for line-by-line review. The remaining difficulty, as I see it, is how to encode several of the heavier arguments cleanly in Lean without obscuring the structure of the proof."

"I would be happy to comment on the Lean encoding of the remaining six formalization nodes, especially the doubled-involution wrapper, if you are open to that."

"Terry"

Jiang Lin read the email twice.

Terence Tao was like a skilled surgeon, pointing out the most crucial fact in the entire pathological slice.

The Entropy Involution Lemma was the key new move in the entire proof.

At the position where the standard route lost polynomial control, it successfully prevented the loss term from re-entering the covering recursion cycle.

To Jiang Lin, these few calm statements carried far more weight than any extravagant praise.

Because this undeniably showed that Terence Tao hadn't just given a cursory glance at the abstract of the paper, nor had he only looked at the statement of conclusions in the README.

He had indeed bypassed the peripheral narrative, read directly to the most critical fracture point of this manuscript, and confirmed that Jiang Lin's patch there was effective.

What moved Jiang Lin even more was the third paragraph of the email.

"I would be happy to help with the Lean encoding of the remaining six formalization nodes, if you are open to that."

"if you are open to that."

He was inquiring, waiting for permission.

Without hesitation, Jiang Lin opened the reply box and began to type.

Dear Terry,

Thank you for reading.

Yes, I would be glad to coordinate with you on the Lean encoding strategy for the remaining six formalization nodes.

When Jiang Lin typed up to here, he paused for a moment.

The restriction K ≥ 8 had to be written clearly.

The case K < 8 was not a gap; rather, it had already been uniformly swallowed by the preceding finite-field small doubling boundary and Ruzsa-type covering steps. The real danger was whether the third-layer loss term would crawl back into the covering recursion after K entered a larger interval.

He continued writing downward.

"Node 38 is the heaviest one to encode: it corresponds to the third-layer loss recovery in the K ≥ 8 regime. The proof is closed in the manuscript, but the Lean formulation still needs a cleaner doubled-involution wrapper."

"I will keep v7-final as the fixed manuscript baseline. All encoding changes will go through branches and issues."

"Lin"

After typing the last letter, Jiang Lin carefully checked the reply from beginning to end.

Click send.

The moment the email was sent, Jiang Lin leaned back against the back of his chair and breathed a sigh of relief.

After eating lunch at noon, Ding Jian sent a WeChat message.

"Jiang Lin, Terry just posted a message in the Lean Zulip channel. He should have desensitized it first; I'll screenshot it for you to see."

Followed closely by a screenshot.

Official Zulip channel of the Lean mathematics community.

# maths > Additive Combinatorics.

Terence Tao's statement was very restrained.

"I have been looking at a private formalization blueprint for an Additive Combinatorics manuscript. I cannot discuss details yet, but some of the project-local Lean infrastructure may be relevant later."

There were already more than a dozen responses below.

"Manners: Interested, especially if this touches finite-field Additive Combinatorics. Please add me when circulation opens."

"Green: Interested, especially in the combinatorial skeleton once details can be circulated."

Another mathlib maintainer asked: "Are the verified nodes in core mathlib style, or in a project-local library?"

Terence Tao replied: "Mostly project-local for now. We will see what can be upstreamed later."

...

At 4:06 PM.

Terence Tao sent the first issue.

Title——

"Node 38: encoding the doubled-involution step"

The text was not long, but every single sentence landed on the heaviest part of the formalization blueprint.

Node 38 was already clear enough in the natural language proof.

If one directly followed the narrative order in the paper to translate the third-layer loss recovery mechanism into Lean line by line, the formalized code would become extremely heavy.

Because the language of the paper allowed mathematicians to simultaneously track conditional distributions, mutual information terms, spectral cluster indices, and payment relations of covering recurrences within the same paragraph.

Lean does not allow this kind of compression.

It requires every variable substitution, every conditioning, and every equivalence transformation to be explicitly named.

Terence Tao suggested not writing Node 38 as a huge monolithic lemma.

The "doubled-involution" structure within it should be extracted separately and encapsulated into a reusable intermediate structure.

In this way, the third-layer loss recovery itself would remain unchanged.

But Lean would no longer need to repeatedly expand four-variable conditional distributions in the same file.

Those symmetries that Jiang Lin had compressed away with natural language in the paper could be explicitly exposed in the formalized code.

After reading the issue, Jiang Lin picked up a pencil and wrote three lines on a scratchpad.

Line one: the paper proof path.

Line two: the current Lean encoding path.

Line three: symmetric conditioning encapsulation.

When writing to the third line, he paused for a moment.

Because he discovered that what Terence Tao pointed out was not a new mathematical idea.

But a cleaner interface.

Node 39 was originally used to record a segment of local dependency transmission after Node 38.

In the paper, this segment was merely a natural extension of Node 38's conclusion.

But in the Lean blueprint, because Node 38 was written too heavily, it was forced to be split into an independent node.

If, according to Terence Tao's suggestion, the doubled-involution structure was pre-encapsulated, Node 39 might not need to exist as an independent formalization node anymore.

It could be merged into the corollary layer of Node 38.

This would not change the paper.

Would not change the proof.

Would not change any covering bound.

What changed was only the way force was borne in the formalization engineering.

Jiang Lin replied beneath the issue.

"I agree. The manuscript proof is unchanged, but the Lean encoding should expose the doubled-involution wrapper first. Node 3a corollary of the Node 38 wrapper rather than a separate formalization node. I will update the dependency graph before pushing."

Five minutes later, Terence Tao replied.

"Good. Please keep the original encoding branch for comparison."

Jiang Lin looked at this sentence and nodded slightly.

Not a single person who had truly done complex proof engineering would casually delete the old route.

The old route was not wrong.

It was just heavy.

And in formalized mathematics, heaviness itself is a kind of risk.

Not mathematical risk.

It was collaborative risk, maintenance risk, and review risk.

If a proof could only be written into the machine by the author himself along the original path, it had not yet truly become an engineering object that the community could take over.

Jiang Lin did not push immediately.

He first created a new branch locally.

formalize/node38-doubled-involution-wrapper

Not fix.

Not correction.

This was not bug-fixing.

This was encapsulation.

Then, he re-split the natural language proof of Node 38 into three layers.

Layer one: the generation rules of four-variable copies.

Layer two: fixing the macro and subsequent symmetric conditioning structures.

Layer three: how the conditional mutual information term hooks back into the third-layer loss recovery ledger.

In the paper, these three layers could be connected into a single paragraph.

Because those who truly understood would fill in the intermediate variable transportation in their minds on their own.

But Lean would not fill it in for anyone.

Lean required every step to be written out.

And precisely because of this, formalization was not weakening the aesthetic of the proof.

It was driving the bridge piers in the proof—which originally could only be skipped over by relying on expert intuition—one by one into the riverbed.

At 10:00 PM.

The new encapsulation draft for Node 38 was completed.

Node 39 was temporarily marked as — "candidate corollary of Node 38 wrapper"

The machine check had not yet run.

Nor was Jiang Lin in a rush to run it.

For this step, he was prepared to wait for Professor Han Yanshan and Ding Jian to review the new dependency graph, and then cross-check the interface naming with Terence Tao.

Because from now on, every node numbering was no longer just his own work habit.

It would become the coordinate system for several reviewers to jointly enter this proof.