170: Chapter 170 The World Is Finally Understood

Time rolled back to 4:03 PM on September 19th.

Just three minutes had passed since Tsinghua University switched the BB (5) public repository from PRIVATE to PUBLIC.

Beijing, Jianguomenwai Avenue, the tech channel editorial department of a top domestic news platform's headquarters.

This was originally an exceptionally dull afternoon.

Several on-duty editors were yawning in front of the cookie-cutter digital product press release drafts on their screens.

Holding a cup of Americano that had already gone completely cold, Li Xin habitually refreshed the public source pools of major universities and research institutions.

An official press release from Tsinghua University popped up.

It was very short, under two thousand words.

There were no eye-catching header images attached, only dry black-and-white text, lying punctually and quietly at the very top of the information feed.

Li Xin's gaze initially lingered on the title for only two seconds.

[Joint Research Team Determines Exact Value of Five-State Busy Beaver]

Busy Beaver.

Staring at these four words, the first image that appeared in her mind was a brown animal wearing a red hard hat, holding a thick piece of wood and chewing it with wood chips all over its mouth.

In the context of the internet, this term was usually linked to some cute animal protection project or a newly released animated movie.

But the prefix was five-state, and the publishing institution was Tsinghua University.

Li Xin instinctively sniffed a trace of the unusual, put down her coffee cup, and scrolled down the mouse.

[S (5) = 47,176,870]

[Σ (5) = 4,098]

[Number of Undecided Machines Returns to Zero]

[Complete Proof Materials, Open-Source Verifier, and Coverage Witness Have Been Simultaneously Made Public]

She understood every single word above.

After combining them, however, her brain fell into a blank blur.

Those strange Greek letters and huge numbers combined together, exuding a cold aura that kept strangers at a distance.

Until she dragged the page to the third paragraph and her gaze touched the list detailing the authors and contribution descriptions.

First Author: Jiang Lin.

Undergraduate student of the Class of 2022 at Qiuzhen College, Tsinghua University.

Li Xin leaned closer to the screen, read it again, and then opened a search engine and typed in this name.

On the first page of search results, Jiangs Brick, iccm mathematics gold medal, and PFR / Marton were squeezed together, with publication dates all falling within the past five months.

A current-like tremor shot straight from Li Xin's spine to the back of her head.

She grabbed the internal telephone on her desk, her voice sounding somewhat sharp due to excitement.

"Editor-in-Chief, Tsinghua University released a piece of computational theory news, with Jiang Lin as the first author."

There was silence for two seconds on the other end of the phone: "Which Jiang Lin?"

"The one from Jiangs Brick."

"It's him again?"

"It's him again."

"Has the achievement been confirmed?" The editor-in-chief's tone instantly became serious.

"The full text, source code, certificates, and independent reproduction records are all made public. The press release states that the exact value has been determined."

"What level of achievement is this?"

"I, I don't understand," Li Xin replied honestly, "the screen is full of code and symbols."

"Immediately find someone to ask, and tell me within ten minutes whether it's worth pushing to the front page of the entire network."

Li Xin began making calls.

The first call went to a computer science professor at a top university; a lengthy buzzing sound came through the receiver, with no one answering throughout.

The second, she called Dr. Chen, who engaged in formal verification research at a top domestic think tank.

As soon as the call connected, Li Xin said at an extremely fast pace: "Dr. Chen, Tsinghua University just released an announcement on the five-state Busy Beaver, with Jiang Lin as the first author, saying the exact value has been determined."

Dr. Chen only heard half a sentence before his originally lazy voice suddenly pitched up, and in his panic, he even knocked over the water cup on his desk.

"What did you say? Made public?"

"Tsinghua University's official website just posted it."

"Give me the link, quick!"

"I'm sending it to you via WeChat right now, Dr. Chen. Just how big is this achievement? The editor-in-chief is waiting for my reply."

Rapid keyboard clicking sounds came over the phone, with an intensity as if trying to smash through the keyboard.

Dr. Chen acted as if he didn't hear her second half sentence at all, his breathing becoming exceptionally heavy.

A dozen seconds later, a curse filled with disbelief came through the receiver.

"It really is zero!"

"What zero?" Li Xin was baffled.

"Undecided machines, zero. Unknown: 0." Dr. Chen's voice trembled, as if chanting a sacred scripture, "They caught that ghost."

"So the problem is really solved?"

"From the public caliber and signed external reproduction records, the sentence that the exact value is determined can be reported," Dr. Chen flipped through the pages rapidly, "but I just opened the macro-state proof; don't make me sign for the entire field in a dozen seconds."

"Then just how big is it?"

"Give me half an hour, and I at least need to finish reading the contribution description and coverage chain structure."

"I only have five minutes!"

The other end of the phone paused for a moment.

"Then I can only give you a historical coordinate that won't be wrong."

Dr. Chen took a deep breath.

"You can write it like this."

"Thirty-two years ago, one of the most authoritative researchers on this problem publicly predicted that humans might never be able to prove these two numbers."

"Today, a Chinese team has erased the two words 'never' from human history."

Li Xin's hand holding the phone was slightly sweating, and she turned her head, casting her gaze once again toward the author column on the webpage.

"Thank you."

She paused for two seconds, hung up the phone, and pressed the internal line.

"Editor-in-Chief, I know how to push it. Highest authority, pop-up across the entire network."

4:11 PM.

The first carefully polished news push arrived at the lock screen interfaces of tens of millions of smartphones.

[A computational theory problem predicted 32 years ago to be unprovable forever was declared solved today, with the first author being 18-year-old Tsinghua University freshman Jiang Lin]

4:13 PM.

Another news platform quickly followed up, stripping away lengthy modifiers and hitting the core directly.

[S (5) = 47,176,870: Tsinghua University Team Determines Exact Value of Five-State Busy Beaver]

4:17 PM.

The third platform made the title even more direct, carrying strong incitement.

[Jiang Lin Has Solved Another World Problem]

4:22 PM.

The topic parachuted into the 27th place on the trending search list.

4:29 PM.

9th place.

4:36 PM.

1st.

At the top of the trending search list, a line of bright red small text began to flash frantically.

[Hot]

...

In the first ten minutes, the public comment section was filled with a comical blankness.

Massive traffic poured in, but crashed into a high wall named computational complexity theory.

[What breed is the Busy Beaver, a protected animal?]

[I thought it was researching wildlife ecology, but clicking in revealed nothing but code and circles I couldn't understand.]

[What does five-state mean? Excited, sad, angry, exhausted, wanting to get off work?]

[Running over 47 million steps to get off work, this beaver is indeed quite busy, busier than me going to work.]

[Can anyone speak human language? What on earth is being calculated here?]

However, information vacuums are always short-lived.

Soon, the first batch of self-media outlets that keenly sensed the traffic password yet understood only half of it rushed in like sharks smelling blood.

Using the most exaggerated vocabulary, they packaged a rigorous theoretical achievement into cheap science fiction.

[Eighteen-Year-Old Genius Cracks Computer Halting Problem!]

[From Now On, Computer Freezing Will Become History, and Windows Will Never Have Blue Screens Again!]

[The Last Security Lock of Artificial Intelligence Breached by a Chinese Student, Countdown to Machine Awakening Begins!]

[Jiang Lin Calculates Upper Limit of All Program Execution Times, Humanity Grasps Ultimate Truth of Digital Universe!]

[Global Software Industry Ushers in Historical Revolution, Silicon Valley Giants Hold Emergency Meetings Overnight!]

...

These sensational headlines were forwarded tens of thousands of times within half an hour.

Someone in the comment section solemnly declared that all mobile apps in the future would be able to predict in advance when they would lag and crash.

Someone said with certainty that Jiang Lin's theory had fundamentally proved that artificial intelligence would never betray humanity.

Another person seriously wrote a thousand-word long article on Zhihu explaining that the so-called five states were the five elements of metal, wood, water, fire, and earth running on the computer's underlying CPU, and Jiang Lin had found the one with the best feng shui among them.

Amidst this chaos of demons dancing, an accompanying image spread at an astonishing speed, quickly rushing out of the tech news comment section.

In the picture was a cartoon beaver wearing a yellow plastic hard hat, its eyes covered in red bloodshot veins, sitting in front of a dilapidated computer frantically pounding the keyboard, surrounded by piles of empty coffee cups.

Written in bold black text on the screen—

[Boss, I can work at most 47,176,870 steps.]

Below the picture was a line of large text—

[Chinese scientists calculated the limit of the universe's strongest wage earner: Boss, I can work at most 47,176,870 steps.]

[If step 47,176,871 hasn't gotten off work yet, don't wait—it will never get off work in its lifetime.]

In a short half hour, this image was made into countless versions of emojis, seamlessly embedded into contemporary wage earners' self-deprecating culture, and spread to tens of thousands of company slacking groups and project docking groups.

Computer science students and researchers, looking at these flying absurd remarks, anxiously left comments across various platforms to correct errors.

[It's not solving the general halting problem at all.]

[The BB function is uncomputable; Turing's coffin lid is about to fail to stay down.]

[That's a specific Turing machine model, not your home computer's CPU.]

However, the propagation speed of rigorous popular science far lagged behind the reproduction speed of memes and emotional venting.

At 5:04 PM, a programmer verified as a senior architect at a major tech company posted a nearly thousand-word professional explanation under a trending search news item, attempting to clarify the relationship between state space, halting witnesses, and Turing machines.

Sixteen minutes passed, and his likes were only thirty-seven.

And ranked above him, firmly occupying the first place in hot comments, was just a short sentence.

[In the same September, some people are getting familiar with teaching buildings, while someone is closing the case on human computational theory.]

Likes: 230,000.

At 5:20 PM, a long image titled Jiang Lin's Eighteen-Year-Old Life Timeline began to spread virally across major social platforms.

The background of the long image was a deep starry sky color, with a white timeline running through it from beginning to end.

May, Jiangs Brick (solved the aperiodic monotile tiling problem).

June, Gaokao 749 points (first place in Physics in the province).

July, iccm mathematics gold medal.

August, PFR / Marton (public proof of Finite Field Model).

September, five-state Busy Beaver (number of undecided machines returns to zero).

The person who made the chart didn't add any evaluation, nor did they use any sensational text.

He simply did an extremely cruel thing.

Accurately marking the interval days between each achievement with red numbers.

The five time nodes lined up in a column from top to bottom, quietly demonstrating an intellectual crushing that did not belong to ordinary people.

This pure objective enumeration was enough to make any ordinary person who scrolled past this image stop their fingers scrolling the screen and feel an almost suffocating sense of oppression.

[Is this really the same person? Not a research team codenamed Jiang Lin?]

[I repeatedly checked the ID photo, it's the same one, his eyes haven't even changed much.]

[The achievements he made from May to September are longer than my life.]

[The most outrageous thing is that he is still a college freshman right now, brothers.]

[To be exact, his official classes started just a week ago. Other people haven't even handed in their first mathematical analysis assignment yet, and he has already changed S (5) from a conjecture to a theorem.]

[Who can tell me how many hours he actually has every day? Doesn't he need to sleep?]

After this question was pushed to the top comments, no one answered for a short while.

A few minutes later, a reply carrying a somewhat philosophical meaning quietly appeared.

[Perhaps he is not using the same time as us. We wander in time, while he carves monuments in time.]

...

September 20th, 6:40 AM.

Shen Yanqiu was awakened by the continuous vibration of his mobile phone.

Rubbing his sleep-swollen eyes, he groped for his phone on the bedside table, and the strong light from the screen made him squint.

At the upper right corner of the WeChat icon, inquiries from media editors, video platform heads, and news producers had piled up to the maximum limit of 99+.

Some asked if they could contact Jiang Lin, some asked if the general halting problem had been cracked, and others were already preparing to make a Turing Award special feature.

He opened the trending list. After a night of fermentation, yesterday afternoon's erroneous interpretations not only didn't disappear, but were pushed to even more exaggerated positions.

Shen Yanqiu didn't click them open one by one, directly opening Tsinghua University's original paper, public Q&A section, and contribution description.

After the Jiangs Brick incident, when facing this young man's name, Shen Yanqiu had developed an unpleasant yet very useful habit.

Whenever Jiang Lin's name rushed onto the trending list, don't rush to judge how big this 18-year-old young man's achievement actually was, nor rush to judge how much the media was exaggerating.

Go look at the raw materials first.

If the raw materials couldn't be understood, go find someone who truly understood them.

If those insiders were still reviewing, then shut your mouth and wait quietly.

However, this time, there was no need to wait anymore.

The paper PDF, open-source verifier source code, complete standardized enumeration directory, halting trajectory index, non-halting witnesses corresponding to 88,664,064 seed library machines, block coverage tree, and two sets of independent verifiers written in different languages had all been made public on the internet.

The project page had already posted the full review conclusions of multiple pre-invited nodes. After publication, hundreds of independent compilation, partial playback, and attack records were successively added.

They could not yet end the review for the entire field, but they had forced any new doubts down to specific rules, specific blocks, and specific counterexamples.

After a slight thought, Shen Yanqiu opened a document and created a new live broadcast outline.

[1. The general halting problem has not been cracked; the boundaries of Turing uncomputability still exist.]

[2. 47,176,870 is not the upper limit of computer speed; it is the scale of destiny for an extremely crude machine.]

[3. In 1989, humanity found the candidate champion; in 2022, the joint team proved that no legal machine could run longer.]

After writing these three points, he stared at the flashing cursor for a moment and solemnly added a fourth line.

[4. This exact value itself has almost no direct industrial use, but this does not mean the entire work has no practical value.]

After writing this line, Shen Yanqiu stared at the screen for a moment.

He knew very well in his heart that in tonight's live broadcast, the truly difficult part to explain and the easiest part to attract curses was precisely this fourth point.

At this moment, ordinary people's emotions had been pushed to the highest point by grand words full of epic feelings, such as Tsinghua University freshman, forty-year unsolved case, rewriting global computer textbooks, and computational theory limits.

What the public expected was a super weapon that could allow Chinese technology to instantly crush the globe, a magic that could instantly make life undergo earth-shaking changes.

Under such a fanatical atmosphere, any sentence stating that direct industrial use was close to zero could pierce the newly inflated emotional bubble like a sharp steel needle instantly.

There would definitely be people in the comment section scolding him for being sour, scolding him for belittling the achievements of his compatriots, or even scolding him for pretending to understand when he didn't.

But if in order to cater to emotions and harvest traffic, a piece of pure basic research was stubbornly said to be installable in smartphones next year and make autonomous driving error-free the year after, that was not popular science.

That was taking the great work truly completed by Jiang Lin and the Tsinghua University team to set up a stage for a fake, cheap public celebration feast.

It was a desecration of science itself.

Shen Yanqiu exhaled a breath of stale air, his ten fingers falling back onto the keyboard as he began to dismantle that massive proof architecture piece by piece.

...

Nine twenty-six in the morning.

On the message board of the Tsinghua University BB ( 5 ) project's public page, a very short note was added.

It was signed by Allen Brady.

In the field of theory of computation, this was a name that almost overlapped with the research history of the Busy Beaver itself.

It was he who, in 1983, established the exact value of the four-state Busy Beaver as 107.

It was also he who, when facing five-state machines with an exponential explosion of state space, left behind a fatalistic judgment in a 1990 paper: humanity might never be able to prove the exact value of S ( 5 ).

Next to this note was attached a high-resolution scanned image.

That was a page of a yellowed old paper, with the edges of the paper somewhat curled.

Amidst a passage discussing the boundaries of computational complexity was that pessimistic prediction which had lasted for thirty-two years.

[ The exact value of BB ( 5 ) may remain forever elusive. ]

— — heavily crossed out with the ink of a blue fountain pen.

In that meager blank space on the margin, two brand-new equations and a date were written.

The ink was very new, and the handwriting even trembled slightly due to old age.

[ S ( 5 ) = 47,176,870 ]

[ Σ ( 5 ) = 4,098 ]

[ 2022.09.19 ]

Brady's note had only three paragraphs.

[ In 1990, I once felt despair when facing the vast and boundless machine trajectories; the computational tools and proof methods available at that time seemed to not allow us to truly exhaust that space. ]

[ Today, the young man Jiang Lin from China and his joint research team, with a complete, public, and mechanically verifiable report that can be independently checked by ordinary workstations according to public specifications, clearly told me: that judgment back then was wrong. ]

[ Hereby, I retract my prophecy. This is the mistake in my life that I am most willing to admit and feel happiest about. The charm of science lies in the fact that there is always someone who can light up a room you thought would be dark forever. ]

Within a short half hour, the image of the yellowed paper with its crossed-out prophecy rushed out of the narrow academic circle of theoretical computer science with unstoppable momentum.

For the general public, it was easier to understand the true weight of this achievement than any glossy trophy or media praise.

A scientific pioneer who personally established the previous world record forty years ago waited for more than thirty years, until his hair turned completely white, until he was almost forgotten by the academic circle, and finally, with slightly trembling hands, personally crossed out his despairing judgment on the next record, paying tribute to an eighteen-year-old Eastern boy.

This was a civilizational inheritance transcending borders and centuries, full of romance and solemnity from the classical age of science.

Immediately afterward, one wave followed another.

The most famous academic blog in the theoretical computer science community, Shtetl-Optimized, was updated.

The blogger was Scott Aaronson, an important researcher of the problem and a professor at the University of Texas at Austin.

He directly updated that famous article published in 2020 regarding the cutting-edge progress of the Busy Beaver.

In the old web cache, behind the equation BB ( 5 ) = 47,176,870, a word was originally clearly marked in red italics: Conjecture.

When countless researchers around the world refreshed the page, that red word had disappeared.

Replaced in its place was a steady and solid green bold word: Proved.

Aaronson pinned an update note at the very top of the page.

[ Two years ago, I officially wrote BB ( 5 ) = 47,176,870 as a conjecture. At the time, I thought that within my academic career, it would be difficult to see it become a theorem. Today, it is no longer a conjecture. ]

[ The Tsinghua University team has completed the most important theoretical advancement in nearly forty years since the four-state Busy Beaver was determined. I want to emphasize that finding that candidate champion running over 47 million steps already requires extremely strong computational experiments and structural judgment; proving that among all five-state machines that eventually halt, not a single one can halt later than it. And using rigorous mathematics to prove that every five-state machine running longer will actually fall into an infinite loop and run forever is another completely different level of achievement—that is the conquest of infinity by human reason. ]

[ In this work, what especially deserves the attention of the entire academic community is the first author, Jiang Lin. He constructed brand-new macro-state invariants for the most stubborn ghost machines, and what is even more commendable is that he did not arrogantly throw out a bunch of incomprehensible proof results, but instead made the entire proof system accept public verification standards far harsher than usual computational experiments. He built a logical sieve. ]

Domestic media, while frantically reprinting these words, extremely responsibly added Aaronson's authoritative background on the Busy Beaver problem at the end of the text, along with the historical fact that he officially proposed this exact conjecture two years ago.

Those people who were still being sarcastic in major forums, arguing whether this was once again a false genius myth or deification movement manufactured by the media, suddenly seemed to be collectively silenced after seeing Brady's note and Aaronson's Proved, decreasing by more than half.

At twelve noon Beijing time, Los Angeles was still nine o'clock the previous night.

Terence Tao forwarded the Tsinghua University team's public proof repository on his social platform.

He forwarded the link to the Tsinghua University team's public proof repository on his social platform.

And with the keenness of a top mathematician, he reminded everyone watching this carnival to pay attention to a fact that was easily ignored by those noisy headlines.

[ The weight of this work comes by no means solely from those two determined exact values.

When facing a computer-assisted proof so massive in scale—hundreds of GBs, containing tens of millions of branches, which humans could by no means read and review item by item—the authors demonstrated extremely high academic taste. ]

[ They did not force the world to believe the massive program they had run for months, but cleverly compressed the core of trust into a verification boundary consisting of only a few hundred lines of code—small enough and simple enough. Moreover, they made public every replayable witness chain. This provides an extremely inspiring paradigm for how humans can verify machine-generated large-scale proofs in the future. ]

Beneath this short review, the number of likes broke ten thousand in a very short time.

The top-liked reply was a pithy summary.

[ Terence Tao's translation: The answer is given to you, and the ruler to check the answer is also given to you. The ruler is small enough for professionals to audit line by line. Now, the whole world is welcome to find faults. If none can be found, this truth belongs to Jiang Lin. ]

At this step, the public opinion arena finally ushered in a thorough boiling, like a powder keg with its fuse ignited.

The topic of whether Jiang Lin could win the Turing Award rushed to the number one spot on the trending lists of all platforms with a sweeping momentum, and its popularity value was ten times that of second place.

Someone pieced together a photo of him at the end of July, wearing a white shirt and standing with a calm expression on the podium of the iccm mathematics gold medal, with the code-and-formula-dense front page of today's Tsinghua University computer science paper, attaching a title that was deeply chuunibyou-flavored yet impossible to refute.

[ Left hand pure mathematics, right hand computing limits: The dual-line path to deification of an eighteen-year-old youth ]

Some enthusiastic fans and media had already started writing the four words "Jiang Lin Theorem" into their article titles with great fanfare, as if as long as they shouted out this name online first, they could overstep their bounds and personally participate in a great naming in the history of science.

Watching the trending list getting more and more out of control and gradually heading toward a fanatical deification movement, Shen Yanqiu knitted his brows tightly.

He made a decisive decision and directly advanced his live stream, originally scheduled for eight o'clock in the evening, to two o'clock in the afternoon.

At the same time, he opened the backend and made a third modification to the live stream room's title.

Version One — —

[ Eighteen-year-old freshman breaks world difficult problem once again, just how terrifying is Jiang Lin ]

He stared at this sentence for more than ten seconds, feeling it was too much like those low-quality web novel title tropes, and deleted it entirely.

Version Two — —

[ The five-state Busy Beaver ended, computer science rewritten once again ]

Still not accurate enough, delete.

In the end, what remained in the backend title bar was a sentence so plain that it had no emotional ripples — —

[ What exactly did Jiang Lin solve? Why do we need it? ]

Five minutes before the broadcast started, the number of reservations had already exceeded eighty thousand.

At exactly two o'clock in the afternoon, the screen lit up on time.

Tens of thousands of viewers flooded into the live stream room, only to find that on the whiteboard behind Shen Yanqiu, there was neither Jiang Lin's handsome photo hanging nor any discussion about the Turing Award written.

Right in the center of the whiteboard were only those five rows of numbers progressing with history.

1.

6.

21.

107.

47,176,870.

" Good afternoon, everyone. I know you are very excited right now. " Shen Yanqiu skipped the pleasantries and cut straight to the point. His voice transmitted through the microphone, carrying a calming power, " But before the carnival, let's first talk about three things today that are easiest to get wrong and most likely to create false expectations. "

He picked up a red marker and heavily wrote three huge red crosses on the other side of the whiteboard.

" First, Jiang Lin and the joint team have not cracked the general halting problem. Turing's theory remains rock-solid. "

" Second, over forty-seven million is not the speed upper limit of modern computers. A step of a Turing machine and an instruction of a CPU cannot be directly converted in the first place; what this number measures is the running length of a specific machine before halting. "

" Third, this achievement cannot make your computer stop freezing from now on, nor can it automatically find all infinite loops for programmers. Friends who want to rely on it to fix ordinary software glitches with one click can take a break. "

The barrage on the screen paused weirdly for half a second, as if everyone had been stunned by these three basins of cold water.

Afterward, comments refreshed at an even more fierce speed, densely covering half the screen.

[ What the hell did it actually solve then? ]

[ Clickbait tricked me in? I saw other streamers saying humanity is no longer afraid of crashing! ]

[ Everyone don't rush first; Tsinghua University's original announcement indeed didn't say it cracked the general halting problem. Listen to Teacher Shen. ]

[ So the Turing Award is gone, has God Jiang fallen off his altar? ]

Shen Yanqiu ignored the restlessness in the barrage, operated the computer, and projected the formal theorem from the Tsinghua University paper to the center of the screen.

To accommodate ordinary viewers, he deleted all obscure formal symbols, retaining only the most critical qualifying conditions and final conclusions.

[ Five-State Busy Beaver Exact Value Theorem ]

[ For all standard five-state, two-symbol Turing machines starting from an all-white tape: as long as a machine eventually halts, it will definitely halt at the 47,176,870th step or earlier. ]

[ If it still has not halted when running to the 47,176,871st step, then it will never halt afterward. ]

[ Among all machines that eventually halt, the 1s left on the tape when halting are at most 4,098. ]

" This is the theorem they spent I don't know how many days and nights ultimately proving. "

Shen Yanqiu used his pen to tap heavily on the precondition in the first line.

" Everyone look clearly, not a single one of these conditions can be missing. Five states, two symbols, all-white tape, uniform Turing machine definition. As long as we leave this specific theoretical scope, this conclusion takes no responsibility. "

" Some people might ask, since the restrictions are so tight, why on earth is it difficult? Why could it trap humanity for forty years? "

Shen Yanqiu tapped the keyboard, and the screen switched to the champion machine rule table with only ten transition positions.

There were only a few sparse lines of numbers and letters.

" Because proving that a certain machine will halt, in principle, only requires providing a finite running trajectory. As long as the trajectory strictly follows the transition rules and eventually enters the halting state, the evidence is established. What is truly tricky is proving that another machine will never halt. "

Shen Yanqiu's speech speed gradually accelerated, carrying a hint of oppressive force.

" You let it run for a day and it doesn't halt; that cannot prove it won't halt tomorrow. You use a supercomputer to let it run for ten billion steps, and it cannot prove it won't suddenly crash into a halting state at the ten billion and first step. Within human limited time, you must give a logical reason that can cover infinite future evolution. "

The image on the screen switched again, appearing with the massive categorization page of the Tsinghua University public database.

On the left were densely packed finite halting trajectory files.

On the right were non-halting witness files of various complex types such as exact loops, translation loops, backward unreachability, and macro-state invariants.

At the very bottom of the page was an eye-catching statistics column.

[ UNKNOWN: 0 ].

" In 1989, humanity had already found that candidate champion capable of running over forty-seven million steps. "

" But finding the champion does not equal proving that it truly is the champion. You must also prove that in the entire world of five-state machines, not a single machine that was omitted and would eventually halt can halt at a later step. "

" What Jiang Lin and the joint team completed is the second half. They gave a destination for every machine in the directory, and added coverage chains to prove that all legal machines have already entered this directory. "

" After the unknown machines return to zero, at least it finally turns into equals. "

The online viewer count of the live stream room had silently crossed the 100,000 milestone.

However, the scrolling speed of the barrage was actually much slower than when the broadcast first started.

Many people were staring intently at those few lines of icy theorems on the screen, trying to chew on the massive significance behind them.

A few seconds later, that most vulgar yet most realistic question, which had been asked countless times by netizens since the news release, once again filled the screen.

[ Having said so much, Teacher Shen, what use is it after all? It can't make mobile phones faster, it can't prevent blue screens, so why does the country spend so many resources doing this? ]

Shen Yanqiu looked at these barrages and was not angry; he calmly put down the pen in his hand.

" Let's first say an answer most likely to disappoint pragmatist friends. "

" 47,176,870, this number itself has almost no direct industrial use. Tonight, not a single chip company will write this number into the parameter table of the next-generation mobile phone CPU; hospital rescue equipment will not modify treatment plans because of it; and China's high-speed rail will not run one kilometer more per hour just because it knows the steps of a theoretical beaver. "

A large patch of puzzled question marks indeed appeared in the barrage.

" But, please everyone pay attention. " Shen Yanqiu's volume increased slightly, " What the Tsinghua University team has handed over to the world this time is by no means just a string of numbers. "

He operated the mouse, opened the public repository, and split the web interface into three columns.

The first column was the complete normalized enumeration directory, halting trajectory index, and the non-halting witness index corresponding to more than 88 million seed library machines.

The second column was the proof witness files of different types, along with the complex macro-state invariant rule matrix.

The third column was the strictly controlled shared trusted core, coverage core, and dual-path independent verifier source code.

" The first thing that can be directly used by researchers is a complete five-state Turing machine benchmark library. "

"From now on, any team researching the termination, non-termination proofs, and automaton behavior classification of small Turing machines can plug their decision tools into this dataset. If a tool determines that a machine will halt, the database contains finite execution trajectories for verification; if a tool determines that a machine will never halt, the database contains corresponding mathematical witnesses that can be attacked."

"What makes this dataset special is that it is not just a few carefully selected demonstration samples. The entire normalized search space is already closed, and every ruling can be traced back to the specific machine, specific certificate, and verifier version."

"However, the boundaries must also be made clear. First and foremost, it is a benchmark library for small Turing machine research and cannot be directly used to test real industrial code. Industrial software has completely different semantic layers such as input, memory, concurrency, exception handling, and operating systems. To migrate this method over, remodeling is mandatory."

"The second item is the method of macro-state invariants."

On the screen appeared the despair-inducing Skelet #17 machine. It was a black-and-white tape diagram that constantly expanded outward and looked completely chaotic, resembling the snow on a television screen after losing its signal.

Subsequently, the image switched to the structural topology map after Jiang Lin compressed it into finite macro-states.

"If we only use the step-by-step simulation method and let it run twenty billion times, what we would still see is merely a continuously expanding tape that becomes increasingly difficult to track. Instead of continuing to chase the changes of every single cell, Jiang Lin compressed these microscopic trajectories into finite macro-states."

"He proved that all future evolutions of this machine can only proceed along those few fixed categories of local rewriting templates. The tape can grow indefinitely, but the macro-states always remain within the same closed set; and this set is completely mutually exclusive with the halting entry."

"The specific witness constructed for Skelet #17 naturally cannot be directly applied to other programs. However, the idea of compressing infinite execution into a finite closure proof will provide a new analytical tool for complex small programs, symbolic dynamical systems, and Busy Beaver (6) research."

Shen Yanqiu took a deep breath, and his eyes became exceptionally bright.

"As for this third item, it is also what I believe is most likely in the future to transcend the pure theoretical problem of the Busy Beaver, truly enter the industrial sector, and enter other scientific fields."

"That is the architectural system that allows massive machine-computed conclusions to be subjected to small-scale human verification."

He took a screenshot of the sentence at the very top of the Tsinghua University project homepage, enlarged it, and filled the entire live-streaming room with it.

[No one is required to blindly trust pre-compiled programs.]

"This system separates complex search from final verification. The search program can be massive, aggressive, and even make mistakes; what truly bears the bottom line of trust is a small verifier with a controlled scale, frozen rules, and line-by-line auditability by professionals."

"The world does not need to believe the entire massive project; it only needs to check that final logical checkpoint."

"This architecture has the potential to provide a reference for large-scale computer-assisted proofs, compiler verification, cryptographic protocol auditing, and high-security software analysis. It allows auditors not to trust the entire massive search process, but only to check the verification boundary with a controlled scale."

"However, this can only provide a paradigm, not one-click-install security. Every new field must still redefine its operational semantics, security properties, threat models, and certificate formats, and independently prove its own verifier."

A long bullet comment bearing the real-name verification badge of a core architect from a major tech company slowly stopped in the center of the screen.

[Therefore, the number 47,176,870 itself is like the precisely measured altitude of an extreme peak. What can truly be migrated to other fields are the new ice axes, storm-resistant tents, and complete safety protocols they forged during this extreme mountaineering expedition.]

"That metaphor is fantastic." Shen Yanqiu clapped his hands. "At the same time, everyone, do not forget that the coordinates themselves also hold immense value."

"Before yesterday, all of humanity only knew that in a five-state world, there existed at least one machine capable of running for this long. After today, all of humanity can know with absolute certainty: absolutely no eventually-halting five-state machine will ever break this record."

"This is not a sports transcript that will be replaced by a new record next year. As long as the definition of Turing machines remains unchanged and the foundational logic of mathematics does not collapse, then a hundred years or a thousand years from now, when future generations re-run this verifier, what they obtain will still be nothing other than these two unchanging numbers."

"The advancement of human civilization is not entirely composed of tangible material progress such as building faster cars or making smaller chip manufacturing processes."

"There is another kind of advancement: within a set of clear formal definitions, turning facts that were still unknown yesterday into logical conclusions that any latecomer can re-examine."

The number of online viewers in the upper right corner of the live-streaming room had unknowingly jumped to 150,000.

In the bullet comments, someone asked about another trending term hanging on the hot search list that had sparked countless controversies.

[Teacher Shen, since Jiang Shen has contributed so much, can we directly call this the Jiang Lin Theorem?]

Shen Yanqiu glanced at the detailed author contribution statement released yesterday by Tsinghua University on his tablet.

"Everyone, look closely. The name that has now officially entered the papers and been written into the formal libraries is called [Five-State Busy Beaver Exact Value Theorem]. It comes from the machine data left behind by generations of researchers and years of proof work by the joint team, and after full-scale replication by multiple authoritative nodes, over a hundred independent builds in different environments, and public attacks, it has finally landed."

"As for what Jiang Lin personally did, the contribution statement, external review records, and version history of the paper have already been written very clearly."

"In the future, if in the theoretical circle, peers out of respect informally refer to that key constructive method targeting Skelet #17 as the Jiang Lin macro-state invariant, I wouldn't be surprised in the least."

"But please remember, academic naming is not a hot search vote in the entertainment industry; it is not a matter of whoever has more fans getting the naming rights. Whether a name can remain in the history of science forever depends on how academic papers in the next ten, twenty, or fifty years cite it."

The next highly-voted question appeared more direct and carried a stronger sense of comparison.

[Teacher Shen, compared with Wiles proving Fermat's Last Theorem and Chen Jingrun's 1+2 result, which achievement is actually more difficult?]

Shen Yanqiu shook his head.

"Let's correct a statement first. What Chen Jingrun proved was 1+2, which is a major advancement in Goldbach's conjecture research, but does not equate to a complete solution of Goldbach's conjecture."

"Secondly, there is no need to rank different achievements into a martial arts power leaderboard. The problems they faced, the tools they required, and the ways they were established are all different."

"Wiles's proof of Fermat's Last Theorem is primarily a mathematical argument chain written and read by humans. No matter how complex the proof is, peers can still follow the paper, lemmas, and background theory to check it layer by layer."

"BB (5) faces a different kind of difficulty. It requires both mathematical structural insight and large-scale machine enumeration and computation certificates. Not a single person can use the naked eye to review all the machines and all the blocks item by item."

"Therefore, aside from answering what BB (5) actually is, this work must also answer another equally serious question: when a proof is so large that it exceeds an individual's reading capacity, on what grounds does the entire academic community believe that no machine was missed during the calculation process and no branch was erroneously pruned?"

"The 1976 proof of the four-color theorem heavily relied on computer checks, which triggered long-term discussions on how to audit and reproduce the computational parts. The core of the controversy has never been the arrogance of the predecessors, but rather that the tools available for peers to re-examine at the time were not mature enough."

"What Jiang Lin and the joint team advanced this time is that they also turned why it is trustworthy into an achievement. They made the specifications, certificates, independent implementations, and verifiers public. Any skepticism can be pinned down to specific rule numbers, covered blocks, and minimal counterexamples."

"Therefore, I will not tell you that it is harder than Fermat's Last Theorem, nor that it is greater than 1+2. I can only tell you that it solves a different kind of problem and establishes a different way of being trustworthy."

[...]

The bullet comments quickly split into several factions.

Some were still discussing the four-color theorem, some were asking whether the verifier could be migrated to AI proof systems, and others merely grasped onto the social ruler they were most familiar with.

[Turing Award?]

[Is an achievement like this enough to win a Turing Award?]

[Isn't it too early to talk about awards right after publication?]

Looking at this enthusiasm that almost spilled off the screen, Shen Yanqiu instead gave a helpless smile.

"I don't know. Regarding awards, today in this live-streaming room, no serious scholar can replace the future ACM awards committee to prematurely award that medal."

"However, if you must rely on some heavyweight award to judge whether an achievement is great, then I suggest you first remember two facts that have already happened today and are visible to everyone."

"First, the last confirmed new exact value of the Busy Beaver was born in 1983."

"Second, Professor Brady, who personally determined S(4) back then and stated in black and white that S(5) might be forever unprovable, has crossed out his own judgment with his own hands today."

"These two facts will not change by even a fraction of a percent whether Jiang Lin wins an award with a specific name in the future or not."

"A medal will not make these two equations a fraction more correct, nor will its temporary absence make them a fraction less heavy."

As Shen Yanqiu's voice fell, the top of the live broadcast screen was empty for less than a second.

The next moment, bullet comments surged in simultaneously from the right, quickly covering the whiteboard, leaving only intermittent gaps even for those five numbers.

[In 1989, humanity found the answer; in 2022, Jiang Shen gave all of humanity the confidence and qualifications to say that the answer is definitely correct.]

[Numerical coordinates cannot be packed into tomorrow's mobile phones, but that verification methodology might just enter the audit chain of future machine proofs.]

[The most exaggerated part is that when he solved this decades-old problem, the notice in the Qiuzhen College Class 221 group chat was: Tomorrow morning's first-period Mathematical Analysis, please do not be late.]

This hardcore yet deeply infectious science popularization live stream lasted for one hour and seven minutes.

When Shen Yanqiu finally closed the streaming interface, backend data showed that the cumulative number of people entering the live stream exceeded a staggering six million.

Among them, the tens-of-seconds clip spontaneously recorded and edited by netizens and spread the widest that night was neither a prediction about the Turing Award nor an exclamation over Jiang Lin's cheat-like eighteen-year-old resume.

Instead, it was the sentence Shen Yanqiu spoke with a steady tone while holding a pen and standing in front of those five constantly jumping numbers on the whiteboard.

[In this boundless sea of computation, there is never a universal navigation chart. But the fifth island of human civilization has been completely surveyed and mapped today.]

[...]

Nine-forty-two in the evening.

Tsinghua University, second floor of the Mathematical Sciences Center, Jiang Lin's Research Support Unit office.

The atmosphere here was completely different from the clamor of the outside world.

Three administrative and technical liaison personnel had been working continuously for over a dozen hours, their eyes bloodshot, yet their spirits remained in a state of high excitement.

The academic secretary summarized the external feedback that poured in like a tsunami that day, compressed it through strict filtering rules into a nineteen-page layered briefing, and sent it to Jiang Lin's terminal.

The first layer of the briefing consisted of spam and routine rejection items.

Media interview and profile interview applications: 1,762.

These even included several famous overseas talk shows.

Invitations for university reports, youth forum speeches, and commercial open classes: 319.

Emails asking whether this achievement could be used to develop antivirus software, resolve industrial lathe control failures, or even prevent general artificial intelligence from awakening and destroying humanity: 467.

All of these messages were blocked at the filtering layer, failing to touch even the edges of Jiang Lin's technical queue.

Only a meager eighteen were truly screened through layers and marked as Grade A core technical requests. Among them, nine came from the program termination research group.

They applied to use the normalized enumeration catalog, halting trajectories, and non-halting certificates made public by the joint team as one of the public benchmark sets for small Turing machine termination analyzers.

Six came from the proof assistant development team and the formal verification research group.

They hoped to discuss with Jiang Lin how to extract universal interfaces from this coverage kernel.

What they were truly interested in was whether the combination of parent pointer tracing, pruning witnesses, equivalence mapping, and leaf node linking used in this BB(5) coverage proof could be organized into a certificate specification applicable to other large-scale enumeration proofs.

There were also three from university and research institute teams that had long studied high-security software.

They attached a public-tier threat model summary, requesting a subsequent closed-door technical discussion to be organized.

[...]

At the same time, Room 402, Building 17 of Zijing Apartment.

Jiang Lin sat in front of his desk, turning through the briefing page by page, reading from the first page all the way to the last.

Then, in the handling comments section at the end of the briefing, he wrote down his responses sequentially.

[1. Regarding the public benchmark set: Free use is approved. The usage statement must fix the version number and corresponding hash of this release to ensure that different teams are using the exact same data, allowing test results to be comparable with each other and traceable to their source.]

[2. Regarding the universal coverage kernel: Interface splitting can be discussed. If joint work is carried out in the name of the Research Support Unit, all BB(5)-exclusive semantics must be stripped away, a separate independent repository must be built, and its derivative relationships and applicable boundaries must be clearly marked in the release notes.]

[3. Regarding high-security system migration: Commercial cooperation endorsed by this achievement is temporarily not accepted. Please first submit the operational semantics, security properties, threat models, responsibility boundaries of existing analyzers of the target system, and a minimal verification object that can be independently tested. Once the materials are complete, a decision will be made on whether to enter technical discussions.]

After writing the third item, Jiang Lin pressed the send key and then opened his work terminal.

On the right side of the work terminal, the operating status directory of the Low Entropy Workshop Beijing R&D Center was blinking regularly.

At the very top was a data packet that had just completed decryption verification, coming from the underground utility tunnel operator of a certain northern city.

After completing all preliminary confidentiality agreements and repeatedly confirming the data boundaries, the other party submitted the first batch of desensitized real-world field test data.