151: Chapter 151 The accounts are balanced

In fact, among the crowd leaving the lecture hall of the Mathematical Sciences Research Center, groups of scholars, doctoral students, and young faculty members were still talking about the global accounting matrix of Node 47 and those three vertical lines that cleaved the permissions, even after coming out.

" I always felt that the polynomial bound of PFR was something far up at the summit. Only today did I see that the path halfway up the mountain has already been paved to this extent. "

" Voss's boundary test caught it on the spot, and Teacher Han's triple stress test caught it too. This isn't just about local techniques; the entire framework stands firm. "

" We'll have to reorganize our group meeting plans as soon as we get back. At least three thesis topics for the second half of the year must be cut, and everything should lean toward this direction. "

A few doctoral students from Qiuzhen College were scattered around the water dispenser, keeping their voices very low, but the light in their eyes could not be contained.

Liang Chen stood among them, his phone still hot to the touch. He had cut off his live broadcast room well before the crowd dispersed.

The density of the questioning in the final half-hour was so high that he didn't even have the spare energy to hold up his phone.

The screen still lingered on that final barrage comment: " History will remember this afternoon. "

He suddenly recalled what his advisor had said at noon: " You don't have to understand all of it; just go see what a major proof looks like. "

Now he understood.

A major proof is never just a single stunning formula, nor is it some stroke-of-genius technique.

It is three whiteboards filled to the brim, load-bearing beams laid bare layer by layer, an accounting ledger where every loss has a destination and every payment has a record, and a skeleton that remains completely motionless after being battered in turn by the most rigorous reviewers.

On the other side of the crowd, Wei Dongyi had already reached the stairway.

The scratch paper in his hands was covered in tiny symbols—the verification path he had deduced along Jiang Lin's accounting matrix for half a class period.

A fellow teacher asked him what he thought. Without stopping his steps, he simply said indifferently: " The structure is very clear, and the books balance. "

In the context of the School of Mathematical Sciences at Peking University, this was already an extremely high evaluation.

More peripheral discussions had already spread across the entire internet.

Attention on that question on Zhihu broke 100,000 within two hours, with over two hundred answers pouring in.

The first to release systematically organized notes was a doctoral student from the School of Mathematical Sciences at Tsinghua University. It was a handwritten scanned document totaling seventeen pages, with messy handwriting yet a clear train of thought.

It did not involve the unpublished appendices and degenerate full tables, but instead organized the main closed link in the public report all the way from the intuition of the first row of small doubling to the permission-cleaving of the final three vertical lines.

In the comment section, moving from the initial "I don't understand it, but I'm deeply shocked," the judgments of industry insiders gradually settled out.

A highly upvoted answer did not rush to conclusions, but first explained something.

When the public talks about difficult mathematical problems, the most familiar ones are problems with loud enough names like the Riemann Hypothesis and the Goldbach Conjecture. The PFR Conjecture is not as mainstream, but it is a true load-bearing wall within Additive Combinatorics.

What it questions is an extremely plain yet counterintuitive problem.

If a set does not expand rapidly after being added to itself, what does that indicate?

Common intuition would suggest that addition should create chaos, volume should increase, and the structure should be scattered. Yet in certain special sets, the new entity after addition is only slightly larger than the original. This lack of chaos implies that some sort of algebraic skeleton must be hidden behind it.

This is not a problem that simply pursues elegant techniques.

It concerns whether modern Additive Combinatorics can truly compress local low expansion into a globally controllable structure.

If this wall is pushed open, many problems in the back that originally could only be bypassed will gain new entry points.

" It can be confirmed that the PFR polynomial bound over the finite field F2 is no longer just a possibility; its core framework is closed, and it is in a state of awaiting formal verification by the entire community. "

" The last time we saw work of this caliber land was Yitang Zhang's twin primes. The difference is that back then he was a stranger who burst onto the scene halfway through, whereas this time, it's an eighteen-year-old undergraduate. "

Following that, an even more professional answer delivered a killer blow.

In the past, many routes attempted to use geometric coverings to grasp the algebraic skeleton behind weakly doubling sets.

It was like taking one regular box after another to enclose that seemingly scattered cluster of numerical building blocks.

The problem was that the number of boxes would always spiral out of control during the deduction.

Sliding from polynomials to exponentials.

Sliding from computable to unbearable.

And the truly striking part of the route Jiang Lin demonstrated today was not that he arranged the boxes more cleverly, but that he simply replaced the ruler altogether.

He no longer just asked how large this set was.

He began to ask how chaotic it was.

Sets were shattered into random variables, geometric volume was replaced by information entropy, and the Ruzsa distance was no longer merely the expansion scale after set addition, but transformed into a payment ledger of degree of chaos.

If weak doubling meant the system did not undergo drastic chaos, then in the language of entropy, there must exist a loss path that can be tracked, amortized, and compressed.

This is also why those who truly knew their stuff in the lecture hall did not applaud when they heard some pretty technique.

What they were staring at was the ledger.

Where each drop of entropy came from.

Whether every residual spectrum hedge was repeatedly paid.

Whether every permission cleavage truly prevented local victories from polluting the global assembly.

This is not a proof that looks very clever.

This is a major proof that has been turned into an engineering ledger.

The overseas mathematics community also exploded in pandemonium simultaneously.

Someone quickly mentioned that names like Gowers, Terence Tao, Ben Green, and Manners could not bypass this wall over the past few years.

Finite field PFR is not a problem that can be rushed through with enthusiasm alone.

It inherently required a world-class team to lower the losses bit by bit over several years and dismantle the old debts left behind by exponential explosions.

And now, a v1.0 manuscript from Jiang Lin had dragged all these names into the exact same review chain.

This carried more weight than any media headline.

Because those who truly knew their stuff understood that anything capable of making these people sit down and seriously take it apart was already no longer a gimmick.

Terence Tao updated an extremely short essay on his blog, with a title of only a single line: " On a new approach to finite-field PFR " .

The main text was under three hundred words, with no conclusive verdict, only stating that he was currently reviewing a new manuscript whose core framework of entropy involution and loss accounting was extremely inspiring, and that he would provide further commentary after complete formal verification was finished.

Even with such restraint, it was enough to make the entire field of Additive Combinatorics boil over.

Countless people followed the clues to Voss's updated v2 note and saw the sentence that it was simply waiting for a theorem that needed it; all the puzzle pieces clicked into place at this moment.

It was not a young person's gimmick, nor media hype.

It was a real, ongoing mathematical advancement.

At the center of this storm, Jiang Lin had already gotten into a ride-hailing car heading to Yizhuang, lowering his head to browse through the unread emails on his phone.

The first email came from Terence Tao: suggesting that in the v1.1 formalization blueprint, the three columns of permission cleavage be extracted separately into a universal lemma for future reuse when generalizing to general abelian groups.

The second came from Professor Zhou Zhihua: mainly asking if mid-September would be convenient to reserve a time for offline communication, with the location being either the School of Artificial Intelligence at Nanjing University or after his schedule was finalized.

The third was a long message sent by Liang Zhixia.

1. News of the afternoon closed-door meeting had already spread to the industrial circle, and at least eight investment institutions had re-sent docking intentions, with the valuation caliber rising by another 20% compared to last week.

2. Three top industry media outlets applied for an on-site exclusive interview at tomorrow's exhibition, all requesting to talk about the topic of a mathematics founder making industrial robots.

3. Professor Xu Mingchuan of Hengtai sent a congratulatory message, saying he didn't expect the roots of the Low Entropy Workshop to run so deep, and subsequent cooperation could be discussed at a higher level.

Jiang Lin replied item by item.

His reply to Terence Tao was very short: Agreed, next week I will extract the independent lemma branch of node 38.5.

His reply to Professor Zhou Zhihua was even more concise: Looking forward to the communication in September.

To Liang Zhixia, there were only three sentences.

No valuation for now.

The exclusive interview will only discuss engineering, not mathematics.

Hengtai will proceed at the original pace and will not accelerate by borrowing the hype.

The car drove past the South Fifth Ring Road, and the buildings outside the window gradually turned from university office buildings into contiguous industrial parks and factories.

[part:gemini-3.6-flash]

The applause in the auditorium this afternoon, Mr. Qiu's evaluation, and the dense formulas covering the whiteboard receded slowly behind him like an ebbing tide.

It wasn't that they weren't important.

The outside world would view that entropy-based route as a stroke of inspiration.

Jiang Lin, however, knew very well that it was not.

In the Wasteland, there was no abundant computing power, no stable supply chain, and no experimental environment that permitted graceful failures.

Every instance of thermal drift, every amplification of noise, and every runaway error chain ultimately forced him back to the exact same question.

Had the system's disorder actually decreased?

The Wasteland didn't believe in pretty geometric shapes; it only believed in the increase and decrease of entropy.

But Jiang Lin knew full well that the moment the proof closed on its final line, the first phase of the endeavor was over.

What followed would be a long process of verification, completion, generalization, and formalization into practice—it was the responsibility of the whole community, no longer him carving out a path alone in the dark.

His attention always had to be focused on the next unfinished task.

At 6:17 PM, Jiang Lin arrived at the Yichuang International Convention and Exhibition Center.

The tech giant booths on both sides of the main corridor were already brightly lit, giant LED screens looping promotional videos, uniform-clad staff conducting final rehearsals, and even the welcome robots' voice prompts being debugged over and over again.

Compared to the surrounding glamor, Low Entropy Workshop's corner booth still looked like a quiet sidekick.

But today was different.

Three or four people wearing exhibitor badges stood by the booth, speaking in low voices as they walked around the G-01C unit 3, occasionally glancing up at the text on the backdrop.

Seeing Jiang Lin arrive, Liang Zhixia immediately went up to greet him.

"People have been coming by to ask questions since this afternoon, all peers and investors. When they heard our boss was the Jiang Lin who gave the PFR talk at Tsinghua University this afternoon, they were completely stunned."

She spoke clearly in a steady tone, as usual revealing little emotion, except for a subtle gleam in her eyes that betrayed her inner excitement.

Jiang Lin didn't pick up on the topic, walking straight to the terrain simulator box: "How is the state of the demonstration unit?"

"Xu Man just finished the third round of standby inspection. Joint temperatures, battery voltage, and foot sensor calibrations are all green." Xu Man stepped out from inside the booth, holding an inspection log. "Chen Yan is fine-tuning the final version of the state machine visualization to ensure smooth log scrolling during tomorrow's demo."

Chen Yan sat on a folding chair with his laptop plugged into the demonstration unit, the screen displaying a state transition diagram under debugging.

He looked up to say hello while his fingers kept flying across the keyboard: "Boss Jiang, I highlighted the response time for retraction re-entry in yellow so the audience can spot it right away."

"No need to highlight," Jiang Lin said. "Keep it as it is."

Chen Yan paused briefly, then caught on and nodded. "Understood. Don't manufacture artificial selling points."

Liang Zhixia walked with Jiang Lin to the outer edge of the booth, walking along the backdrop while quietly reporting tomorrow's schedule.

"The doors open at nine tomorrow morning, and we expect the highest foot traffic in the first two hours. Chen Zhi and I will handle reception at the front desk, Xu Man will answer hardware questions, and Chen Yan will monitor the demonstration backend. If you don't want to make an appearance, you don't need to stay at the booth the whole time—just show up at the afternoon industry sub-forum."

"Tomorrow is G-01's first official public debut, so it's better if I show my face," Jiang Lin shook his head and said. "If the media asks about technology, answer about technology. If they ask about the company, answer about the company. If they ask about anything else, just refrain from responding."

As night deepened, the hustle and bustle inside the exhibition hall gradually died down.

Most booth workers had finished for the day, leaving only a few scattered spots lit up as people rushed to finish work.

The Low Entropy Workshop booth was also mostly packed up.

Chen Zhi arranged the brochures, business cards, and safety guidelines for tomorrow in order on the reception desk, then double-checked the emergency supplies.

Xu Man switched the demonstration unit to locked standby mode and covered it with a dust cloth.

Chen Yan exported the final version of the demonstration program and ran three full-process simulations, all with zero anomalies.

The team members packed up their things and left one after another, agreeing to meet at the exhibition hall entrance at eight tomorrow morning.

Eventually, only Jiang Lin and Liang Zhixia remained in the booth.

As Liang Zhixia was organizing the last stack of documents, she suddenly spoke up: "Boss Jiang, honestly, when I came across the news this afternoon, I was quite surprised."

Jiang Lin was looking down at the formal node progress schedule on his phone and raised his eyes upon hearing this.

"Surprised by what?"

"Surprised that you seem completely unaffected." She slid the documents into a folder and zipped it up. "If it were the founder of any other startup with academic achievements of this caliber, they would have plastered marketing everywhere already. I can even guess the headline: 'Fields Medal-Level Mathematician Enters Startup World to Redefine Industrial Robotics.'"

Jiang Lin couldn't help laughing out loud.

"Mathematics is mathematics, and engineering is engineering. No matter how well PFR is done, it won't help G-01 climb a five-degree steeper slope or reduce the deviation in the foot sensors by a fraction. Conflating the two shows a lack of respect for both."

Liang Zhixia looked at him.

The spotlights from the ceiling of the exhibition hall cast a distinct outline across the side of his face.

At eighteen years old, the words he spoke sounded like those of someone who had spent decades immersed in the industry.

This person truly had never positioned himself as a genius prodigy entrepreneur from the start.

Mathematics was probably his ruler, and engineering his hammer.

The ruler defined the clear boundaries, and the hammer struck down solid, tangible implementation.

Two endeavors, two tracks, running parallel without conflict in him, yet never blurred together.

Yet keeping them separate did not mean they didn't share common underlying discipline.

A mathematical proof dreads hidden losses; engineering dreads hidden faults.

A proof must prevent double counting; a machine must prevent a single success from masking underlying instability.

What Jiang Lin truly valued was never pasting mathematical jargon onto robotics promotional flyers, but embedding verifiable, replayable, and decomposable discipline into every control chain.

"By the way, this state machine at the exhibition is just the outer shell of the explicit control chain. The real challenge lies in the portable backend across different hardware, sensors, and scenario packages later on." Jiang Lin remembered something and said, "When we return to Jiangcheng next week, we'll launch a new internal project."

"In what direction?"

"A compiler."

Liang Zhixia paused for a moment: "A compiler? We're going to build our own compilation toolchain?"

"In the initial stage, it'll just be an intermediate representation layer and an operator scheduling framework," Jiang Lin explained. "No need to rush into hiring. We'll set up the project first, I'll draft the initial architecture, and Chen Yan can work with me on it. It won't be made public—treat it as preliminary research."

Liang Zhixia did a quick calculation in her mind.

A preliminary research project, unannounced, with the founder personally leading the initial architecture.

Combined with the news about the CHIPS Act she scrolled through this afternoon, plus Jiang Lin's remark on the high-speed rail about perfecting their own layer first, the answer was practically obvious.

She didn't pry into details, simply nodding: "Alright, I'll set up the project number when I get back and follow internal confidentiality procedures."

When the two walked out of the exhibition hall, the night breeze dispersed the daytime heat.

The giant billboard on the plaza was still illuminated, the slogan "Intelligence Empowering the Future" standing out prominently against the dark night.

People were still moving in and out of the distant subway entrance: conference attendees dragging suitcases, journalists carrying cameras, and setup workers in overalls, merging into small streams flowing toward every corner of the city.

It would be even busier here tomorrow.

Thousands of attendees, media representatives, investors, and industry professionals would flood in to see the latest robotics technology, inspect the sleek booths, and witness an industry trend wrapped in capital and spotlights.

Few would realize what that technical alignment session—whose live stream clips and handwritten notes had already spread across the internet—held tens of kilometers away at the Tsinghua campus just hours ago actually signified.

Even fewer knew that the youth who had stood before the whiteboard in that auditorium was now standing in the evening breeze outside the exhibition hall, thinking not of praise, valuations, or how many amazed glances he would draw tomorrow.

His mind was on the wear curves of foot materials, the credibility classification of state machines, the design of the compiler's intermediate representation layer, and the vast topological map spanning mathematics and engineering.