169: Chapter 169 Giving Zero to the Whole World

September 16th, 9:17 AM Beijing time.

Central European Summer Time, 3:17 AM.

Martin Werner, the person in charge of the second replication node, wrote a glaring red word in his work log.

[HOLD]

Four high-resolution display windows were open in front of him, and the cold fluorescence reflected on his exhausted yet extraordinarily serious face.

In the upper left corner was the temporary read-only repository provided by the Tsinghua University project team to the invited replication nodes, which contained the last batch of witness files just transmitted.

In the upper right corner was the 5-state Turing machine mirror library that he had been building and maintaining bit by bit since 2006.

The two terminals below ran the Rust-version certificate checker provided by the project team and the normalized enumeration program he had spent several years writing with his own painstaking efforts, respectively.

Six hours ago, the first result from another external replication node had already been delivered to his inbox.

The macro-state certificate holds.

Two sets of physically isolated verifiers, under completely different compilation toolchains, gave bit-by-bit consistent logical adjudication summaries.

The macro-state invariant certificate of the last holdout had passed independent verification.

The first external replication declared victory, but Martin did not sign his name after that PASS.

He had tracked the 5-state machine for a full sixteen years, witnessing too many false dawns before dawn and seeing too many beautiful local conclusions.

Some machine was proven never to halt by parameterized rewrite rules, some type of trajectory with fractal features was swallowed by automaton theory, and some exquisite arbiter cleared millions of suspected records in just one hour.

Every piece of progress was incomparably real, and every cheer had a solid reason.

However, that huge iceberg of the 5-state Busy Beaver always left the final gap below the water surface.

Because proving that a machine will not halt and proving that all eligible competitors have been included in the review without omission are separated by a vast and perilous search space.

Just like searching for the tallest tree in a primeval dark forest, you measure the height of all the trees in front of you, but how do you prove to the world that another towering giant tree is not hidden in some forgotten dark corner of the forest?

Martin closed the macro-state verification window, whose green light was always on, and directly dismantled the set of normalization tools attached to the project team in the command line.

He wanted to walk through this dark forest again by himself.

Starting from the most basic empty transition table, he abandoned the search tree path provided by the Tsinghua University team and re-expanded the huge search space using the state naming order he defined himself.

In the first round, he turned off the left-right mirror reduction only in the first nine layers of the search tree and checked the folded branches item by item.

In the second round, he switched to another set of new state first-appearance orders to regenerate the complete canonical representative directory.

In the third round, he extracted the original transition tables from the pruned branches, did not accept the representative numbers given by the project team, and independently calculated the canonical mapping corresponding to each machine.

The processor fan in the workstation case let out a shrill roar, running at high load continuously for a full five hours.

The layer of black liquid left at the bottom of the coffee pot had long since gone cold, forming a ring of bitter, dark scale.

When the daylight squeezed in bit by bit through the gaps in the blinds and illuminated the draft paper all over the table, the final counts of the two sets of canonical representative directories popped out.

Completely aligned.

Staring intently at the identical number, Martin furrowed his brows even lower, and the lines at the corners of his eyes were as deep as knife carvings.

The same quantity only showed that both sides groped in the dark and finally reached a finish line of the same size.

But this was far from enough.

What if the same enumeration specification accidentally missed a very rare class of machine variants at the lowest-level conceptual design?

Then two programs following the same specification could completely and unnoticeably miss the same batch of data in the same place.

He took a deep breath and opened the draft paper sent by the Tsinghua University team.

In the section on enumeration completeness, he used a red electronic pen to continuously mark seven annotations.

Then he opened the email client.

The email had only four lines.

[You have proved that every machine in the directory has a destination.]

[But I still cannot confirm whether another machine is still standing outside the directory.]

[The consistent output of the two enumerators cannot replace a mechanically verifiable coverage proof of the entire search space.]

[Until the coverage chain can be independently verified, I cannot sign off on the final conclusion.]

After sending the email, he switched back to the shared review page and changed the status of the second replication node from the green RUNNING representing running to a red HOLD.

A glaring red box appeared at the top of the external replication sharing page.

Next to the first carnival-like PASS was a nail without a countdown.

...

Beijing, 5:43 PM.

When Professor Qiao Wenduo projected the email marked with a red HOLD onto the conference room big screen, the duty group had just completed the handover between the day shift and the night shift.

The paper cups filled with espresso last night had been cleared away by the cleaning aunt, and the macro-state derivation formulas written by Jiang Lin on the whiteboard had also been photographed with high precision, numbered, and classified by designated personnel, and the whiteboard was wiped clean.

The newly arrived duty personnel were in fair spirits, but several core members resting against the wall could not even open their eyes, their faces showing an overdrawn grayish-white color.

Zhou Shu originally rolled his jacket into a ball and put it behind his neck to catch up on some sleep, but when he heard Professor Qiao Wenduo read out the four words coverage proof, he abruptly opened his eyes again and sat up straight in a daze.

"He bypassed the final defense line of Skelet #17 and went straight to dig up the foundation of our entire database."

Ye Ning finished reading the email on the big screen, rubbed her dry eyes, and her voice was hoarse.

"Dug right." The third-party red team leader sitting in the corner suddenly spoke, his tone not only lacking anger at being put in a difficult position, but instead exuding admiration.

Several weary gazes in the conference room turned to him at the same time.

The third-party leader stood up, walked to the console, brought up the overall project architecture diagram, and pointed a laser pointer at the huge enumeration entrance on the far left.

"For the past few months, we have been doing dual-path generation along the same tree specification. Everyone think about it, we achieved physical isolation and used different languages, but what is this called? This is called specification homology. The two completely identical results can only help us rule out the vast majority of low-level errors at the engineering and code levels. It cannot rule out common blind spots at the specification design level. If that net itself has a hole in it, when two identical nets overlap, that hole still exists."

Zhou Shu reached out and opened the printed draft paper on the desk, turning directly to the third chapter on enumeration.

That section eloquently wrote about the theoretical scale of the complete transition space, detailed the pruning logic of tree normalization, wrote about state renaming, mirror equivalence mapping, and state renaming substitution tables, and also provided hash comparisons of the two independently generated results from Rust and OCaml.

For those inside the project who followed from beginning to end, this logical chain was crystal clear and could be understood at a glance.

But Martin, far away in Europe, refused to accept being able to be understood at a glance.

Mathematics does not believe in intuition.

He demanded that the Tsinghua University team must leave the fracture traces of every pruned branch.

He demanded that anyone, even an ordinary sophomore student, as long as they started from the root node and relied solely on the public pruning rules, could seamlessly walk back to all canonical leaf nodes without any leaps requiring trust in between.

"Then add a section of mathematical proof to the draft?" Zhou Shu asked with a frown.

"What he wants is executable and verifiable code-level evidence; a section of text cannot convince him." Professor Qiao Wenduo turned to look at the closed door of the conference room. "What time will Jiang Lin arrive?"

Ye Ning glanced at the time: "His fixed technical window is 6:00 PM."

At 6:08, the door of the conference room was pushed open.

Jiang Lin walked in carrying that backpack that seemed never to fill up, holding a brick-like book just borrowed from the library — "Introduction to Automata Theory, Languages, and Computation".

The atmosphere in the conference room was as oppressive as the eve of a rainstorm, but the expression on his face remained as calm as water.

He sat down in the empty seat next to Zhou Shu, without asking what happened first, but following his own rhythm, first glanced at the raw operation logs submitted by the external nodes, and then carefully read Martin's sharp-worded email.

When he finally brought up the currently frozen specification documents of the two enumerators, he said: "Give me the original transition tables that they encountered during the generation stage but could not be directly mapped to the final index due to pruning."

"The other party did not submit specific counterexample data." Ye Ning dragged the progress bar to the bottom. "He didn't find a loophole, but is questioning our system. He believes that we have not provided a machine-level verifiable coverage chain."

After listening, Jiang Lin flipped the draft paper at hand back two pages, his gaze lingering on the blank margin for a moment.

"The questioning stands."

He gave four short and powerful words.

The carbon pen Zhou Shu was spinning in his hand dropped onto the table with a snap.

"Does our enumeration really have omissions?"

"The existing data is correct. From the conclusion, no omissions can be seen."

Jiang Lin took a brand new piece of A4 paper and used a pen to draw a line through the middle of the entire database's processing workflow on the paper, dividing it into left and right halves.

"But the publicly proven system is indeed missing a key interface. Look, the current verifier is just dutifully answering why this leaf halts or why that leaf falls into an infinite loop. But where does the search tree actually begin to take root?"

Jiang Lin's pen tip heavily pressed on the blank area on the left half representing the search tree.

"In tens of billions of expansions, which branches are allowed to continue growing? Which branches are ruthlessly pruned due to what rules? And how do the remaining leaves accurately correspond to the complete enumeration directory? All this massive amount of information is currently encapsulated and left inside our enumerator. If external replicators want to confirm, they can only choose to believe anew that our enumerator code has no logical loopholes."

Jiang Lin raised his head and looked around at everyone: "In formal verification, any assumption that is not explicitly written into the proof chain belongs to the trusted computing base."

The third-party leader crossed his arms over his chest, his eyes staring sharply at Jiang Lin: "The current shared trusted core has been completely frozen as a cornerstone, and not a single line of code can be changed again. What are you planning to do, forcibly add a trusted layer on top of the bottom layer?"

"There is no need to touch any existing halting decision logic. The existing halting and non-halting verification layers remain frozen and will not be moved this round." Jiang Lin's tone was steady, "We can just build a coverage core externally."

Saying this, he quickly drew four clearly tiered node diagrams on the A4 paper.

[ROOT: Root Node]

[EXPANDED: Expanded Node]

[PRUNED: Pruned Node]

[LEAF: Leaf Node]

"The root node must strictly correspond to an all-empty transition table, and every expanded node must provide the verifier with all legitimate sub-branch variants beneath it. Every pruned node, whether due to state equivalence or meaningless mirroring, must submit local decision reasons and precise equivalence mapping functions. Finally, every leaf node must be able to point back to the complete enumeration index library we published, and seamlessly connect to the back-end halting or non-halting adjudication certificates."

"I understand!"

As a veteran of system architecture, Ye Ning's brain ran at high speed, instantly catching up with his leaping engineering train of thought.

"In this way, this newly added coverage core doesn't need to understand any complex halting decision logic at all, nor does it need to know what a Busy Beaver is. Its only job is, like a strict accountant, to crawl up along the tree roots and check whether a branch inexplicably grew less during the growth process of the entire tree."

"It also needs to check whether every folded branch can return to the unique canonical representative according to the mapping rules." Jiang Lin continued, "Therefore, what is handed over to the external nodes can not just be the final few sets of hashes. Parent node pointers, state renaming substitutions, sub-branch lists, and evidence of each pruning must all be exported."

Zhou Shu quickly estimated the data scale, swallowed hard, and said: "The coverage evidence generated in this way may be dozens of times larger than the existing certificate library."

"Chunk by search tree depth." Jiang Lin said, "The parent pointers, sub-branch lists, and pruning evidence are handed over to the coverage core to check whether the entire tree has breaks; each file chunk separately calculates the Merkle root, responsible only for locking content and version. The master manifest records the chunk range, arrangement order, and respective root hashes."

Ye Ning asked: "Can external nodes only do sampling?"

"Sampling can be used to check whether data has been replaced, but sampling cannot prove that the search space has no omissions." Jiang Lin said, "If you want to sign off on the coverage conclusion, you must hand over all chunks to the coverage core to replay once."

Saying this, he circled two positions on the paper separately.

"The Merkle root is responsible for proving that what they got is the same piece of data, and the coverage core is responsible for proving that this data hasn't missed a single branch."

Professor Qiao Wenduo, who had been listening in silence, finally couldn't help asking: "How long will it take to complete this set of interfaces?"

Jiang Lin glanced at the mountainous intermediate file cache of the two enumerators currently existing on the screen.

"Fortunately, the core search tree data is all on the hard drive, and we haven't cleared the cache. What's missing now is just a proof format that can be publicly reviewed globally, and a lightweight little verifier program. Before midnight tonight, I will freeze the format specification. All day tomorrow, the two implementation teams will be responsible for exporting the intermediate data according to the format. The day after tomorrow, hand over this coverage system to the red team for crazy attacks."

Jiang Lin looked at the third-party leader.

"The originally scheduled press conference and press release for the paper will all continue to be postponed." Professor Qiao Wenduo did not hesitate at all, making an immediate decision, "As long as that red box representing HOLD in Europe is not cleared to zero, we will never initiate any substantive public actions."

In the large conference room, no one raised any objections.

...

September 16th, 9:00 PM.

After three hours of high-intensity discussion and repeated deliberation, the format specification for coverage evidence was officially finalized and frozen by Jiang Lin.

September 17th, 2:12 AM.

After a burst of frantic disk read and write, the enumeration exporter on the Rust side finally spat out the first batch of massive search tree chunk files.

However, when the newly written coverage core verified to the depth of the seventh layer, a glaring red warning popped up on the screen.

Reject reception.

The error did not stem from the correctness of the enumeration results.

Monitoring logs showed that in a pruned node on the seventh layer marked by the system as state renaming, the export program lazily saved only the ID of the target canonical representative, but omitted the complete permutation mapping matrix from the original state name to the canonical state name.

For human intuition, based on the logical coherence of the context, it was easy to mentally patch in those missing steps of mapping.

But the small verifier written by Jiang Lin lacked any human warmth and compromise.

It refused to make any form of guesswork.

Lacking an explicit proof, it was illegal.

Export format mercilessly rejected.

The researcher in charge of the Rust interface rubbed his face hard and dived back into the code base to modify the export logic.

At 4:56 AM, the permutation mapping fields were honestly and dutifully filled out, and the dozens of gigabytes of chunked files generated previously were all invalidated, and the export started over.

At 11:00 AM, after countless minor format frictions, the coverage kernel on the OCaml side finally completed the first independent replay verification of the entire library.

Four green passes lit up in succession.

[ROOT_REACHABILITY/PASS (Root Node Reachability Passed)]

[BRANCH_COMPLETENESS/PASS (Branch Completeness Passed)]

[PRUNING_WITNESS/PASS (Pruning Witness Legality Passed)]

[LEAF_INDEX_LINK/PASS (Leaf Index Link Passed)]

At 3:00 PM, the real test arrived.

The third-party Red Team took over the system.

This team, composed of top domestic security experts and fault-finding masters in the field of formal verification, quietly mixed four hundred sets of elaborately constructed, extremely malicious destructive coverage witnesses into millions of normal chunked sets.

They used all sorts of tricks.

Deep within a branch containing tens of millions of entries, they quietly deleted an inconspicuous legal sub-branch.

In a complex transition table, they maliciously swapped the names of two states while intentionally failing to modify the corresponding permutation matrices.

By modifying pointers, they made a pruning node that should have pointed to its parent node eerily form an infinite loop, pointing to itself instead.

Even, they used a seemingly flawless leaf ID to stealthily replace the incorrect parent node hash above it.

This was a cruel test of finding a poisonous needle in a massive sea of data.

However, by 10:00 PM, the two independently running coverage kernels intercepted, alarmed against, and rejected all four hundred sets of meticulously disguised mutated witnesses.

Not a single one slipped through the net.

After confirming that the system was indestructible, the final coverage witness master package was packed and encrypted, and sent quietly along cross-border network fiber optic cables into the external-facing read-only repository.

Martin, far away in Europe, did not reply to any emails; he simply quietly changed the last update time following the HOLD tag on the global shared review page visible to all invited nodes to 4:03 PM Central European Time.

Sunday, September 18th.

Throughout the day, the second reproduction node maintained a suffocating silence.

No news came, no questions were asked, and no errors were reported.

In his basement study in Munich, Martin abandoned the trail-following leaf index order kindly provided by the project team.

Like a suspicious old detective, he chose the stupidest and hardest-to-cheat verification method.

From the massive amount of personally tagged raw machine data he generated last night, he randomly extracted state permutations and mirror variants.

Then he inputted these variants into the publicly available mapping rule engine of Tsinghua University, forcibly demanding the engine to perform reverse operations and search the vast sea of data for the canonical representative claimed by the Tsinghua University team to exist.

Subsequently, he performed reverse expansion and verification from the massive leaf index database provided by Tsinghua University.

Following those tens of millions of parent pointers, he climbed upward one by one, rigidly checking whether every isolated pointer could eventually lead to the same destination and return without contradiction to that empty ROOT node.

The one-millionth check: valid.

The ten-millionth check: valid.

The thirty-millionth, the forty-millionth...

Until the forty-six-millionth, it remained unshakably solid.

The shared page in the meeting room of Tsinghua University was set to automatically refresh every hour.

Throughout the weekend, the processing progress count following the RUNNING status continued to grow like a heartbeat, but that glaring red HOLD tag stubbornly remained there.

At 6:31 PM Beijing time, the verification program on Martin's machine, which had been running at full capacity for countless hours, finally struggled to the end of the last data chunk.

The terminal screen flickered slightly, first outputting two rows of random hash strings.

The first row was the coverage witness Merkle root published by the Tsinghua University team.

The second row was the local root calculated by Martin's local computer after dozens of hours of independent rerun and reconstruction.

Martin leaned closer to the screen.

The two lines of garbled-looking characters were arranged vertically.

From the first letter to the very last digit, they fit together seamlessly and were identical bit by bit.

There was not a single bit of deviation.

Subsequently, accompanied by a few crisp system prompts, the four final verification results popped up in the center of the screen in succession, flashing with the green light representing a pass.

[FULL SEARCH TREE / COVERED (Full Search Tree Coverage Confirmed)]

[NORMAL FORM ORBITS / MAPPED (Normal Form Orbits Mapped Confirmed)]

[HALTING INDEX / LINKED (Halting Index Linked Confirmed)]

[NONHALTING INDEX / LINKED (Non-halting Index Linked Confirmed)]

Watching all four green results light up, Martin wrote his local compilation environment, coverage kernel version, four adjudication summaries, and Merkle root into the review record, and then pulled three chunks from the last batch of data to cross-check them in reverse once more.

The result remained unchanged.

This time, he opened the review receipt that had been sitting in his draft box for two days.

His fingertips danced.

[The coverage chain is closed, and no logical breaks are seen.]

[I have reconstructed the canonical representative directory using independent enumeration logic and completed full-scale re-verification of all coverage chunks. No off-target leaf nodes were found.]

[The previous HOLD status is formally revoked.]

[Based on the above independent re-verification, I support making S(5) = 47,176,870 and Σ(5) = 4,098 public to the world as precisely proven values.]

Email sent.

In the meeting room in Beijing, the shared review page ushered in a new round of automatic refreshing.

That red box that had stuck like a nail next to the first PASS for two days and nights, making everyone uneasy, quietly flipped under everyone's gaze, turning into a shade of emerald green representing passage and approval.

The last great mountain hanging over the project team's hearts was finally leveled.

...

Sunday, 8:00 PM.

Tsinghua University meeting room.

Professor Qiao Wenduo sent the final PDF version of the paper to the terminal screens in front of every core member.

The title of the paper no longer carried any experimental suffixes.

"Determination of the Exact Values of the Five-State Busy Beaver"

Below the English title was a long list of author names arranged according to academic convention.

In the first-author column at the very front, two simple Pinyin words were neatly printed.

Jiang Lin.

Zhou Shu scrolled his mouse, glanced at Jiang Lin's name on the screen, and then lowered his head to meticulously check word by word his contribution description at the end of the paper regarding engineering optimization.

Ye Ning was checking word-for-word the signature status of the two different implementation groups, Rust and OCaml, ensuring there were no cross-group mixing errors.

Meanwhile, the third-party head insisted on stating the independent offensive verification work undertaken by their team completely separately from the main mathematical proof construction, to prevent anyone from using the identity of a Red Team supervisor to share the responsibility for mathematical theoretical discoveries they did not bear.

Jiang Lin sat in his old seat with a calm gaze, reading from the very first line of the introduction of the paper all the way to the last line of references.

"Rust and OCaml engineering team names must be explicitly separated in the acknowledgments and author list."

Jiang Lin raised his head and looked at Professor Qiao Wenduo.

"Both sides have maintained physical-level isolation from the initial specification design all the way to the later code implementation. This absolute independence must also be preserved in the contribution description and cannot be lumped together. In addition, the coverage witness part is a public verification interface we added later in response to external review; it must list a separate sub-version in version control. As for the nodes participating in external reproduction, only the reproduction work they actually completed should be written. Whether they are willing to enter the signature list of the final joint verification alliance must be confirmed in person via email by themselves, and proxy signing is not allowed."

Professor Qiao Wenduo nodded, then asked seemingly casually: "What about the order of the first author? Any objections?"

Jiang Lin's gaze fell back on his own name on the title page.

"Keep it unchanged."

"You need to think carefully about the weight of this."

Professor Qiao Wenduo put down the materials in his hand, looking deeply at the freshman before him: "This position is not just about honor. It means that for the next ten or twenty years after the paper is published, anyone in the academic community—as long as they want to attack the shared trusted kernel architecture we designed, attack the macro-state invariants you derived, or pick faults with the coverage interface we just added today—the first harshly worded inquiry email, or even public questioning at an international conference, will point directly at you."

"That is only right."

Jiang Lin closed his laptop screen, his tone without a ripple of emotion: "The core proof was written by me, and the architecture was determined by me. If something goes wrong, who else would they look for if not me?"

Professor Qiao Wenduo said no more.

Holding the old-fashioned fountain pen that had accompanied him for many years, he heavily signed his name in the person-in-charge position at the very bottom of the author order confirmation form.

On the other side of the meeting room, several staff members from the university's scientific research publicity department were projecting the prepared external press release onto the big screen.

The title of this news article had gone through three rounds of intense revision discussions, but the current version still had one key phrasing that required final confirmation from the core team.

A line of large characters lit up on the screen——

[Tsinghua University Freshman Conquers World-Class Busy Beaver Problem]

Jiang Lin frowned, stood up, walked to the console, picked up the electronic pen, and without hesitation crossed out the first half of the title which carried a strong description of personal heroism and hype, and then rigorously added the three words 'five-state' as an attributive modifier before the words 'Busy Beaver'.

Thus, a news title that was originally full of news buzz was modified into a slightly dry but absolutely rigorous academic announcement.

[Joint Research Team Solves the Five-State Busy Beaver Problem]

The staff member of the publicity department looked at the blandly modified title and sighed somewhat helplessly: "Student Jiang, we respect that you changed the title. But in the main text, can we explicitly write that this is the first new exact Busy Beaver value determined in nearly half a century of computer science history? This is very important for the school's scientific research publicity."

"This sentence is a fact, you may."

Professor Qiao Wenduo answered for Jiang Lin.

"Then, to make it understandable for the general public, can I use a slightly more colloquial sentence to explain this achievement?"

The staff member opened his notebook and read out the prepared metaphor: "For example: Any five-state, two-symbol Turing machine matching the definition, as long as it starts from an all-white tape, if it runs for more than 47,176,870 steps without halting or erroring, can we guarantee to the entire universe that it will never halt in the future?"

Jiang Lin listened, nodded, and said: "This description is logically equivalent and can be used."

"But one point must be noted."

Jiang Lin pointed at the structure of the press release: "Regarding the absolute foundation of computation theory that the general halting problem for general-form Turing machines is undecidable and the Busy Beaver function is uncomputable, it must be strongly emphasized in the second paragraph of the press release, using bold font. This is to avoid non-professional readers who only look at the titles from misunderstanding that we have overturned Turing's conclusion and solved machine problems of all state scales. The task of the public draft is to state only the conclusion; as for specific macro-states and invariants, external links to the complete proof package should be used. As for personal information, put it all at the back, after the contribution description."

While typing rapidly on the keyboard to record, the publicity staff member nodded, then operated the mouse to remove the high-definition single scientific research photo of Jiang Lin originally reserved for the header image of the press release, replacing it with a black-and-white table screenshot showing only ten simple transition positions.

It was the underlying logic table of the legendary five-state champion machine.

Five internal states, two tape symbols.

An unresolved record that had suffocated the entire computer science community and lasted for nearly forty years.

Today, these three lines of words were calmly placed beneath that crude table.

Release caliber, officially frozen.

Complete academic paper, frozen.

Full-chain coverage witness and underlying validator source code, frozen.

The countdown time open to the global public was finally fixed at 4:00 PM Beijing time on September 19th.

...

September 19th, 3:59 PM.

Inside a tightly monitored computer room on the second floor of the Mathematical Sciences Center of Tsinghua University.

The technical liaison of Jiang Lin's Research Support Unit held his breath in concentration, laying out six web operation backends side by side on an ultra-wide ultrawide screen.

The initial preprint platform for papers.

The complete tree-shaped normalized enumeration directory.

The finite trajectory index of halting machines.

The non-halting witness index corresponding to more than 88 million seed library machines.

The source code for the dual-path validators in Rust and OCaml.

And independent reproduction and attack records from multiple authoritative institutions worldwide, including Martin.

Anticipating the traffic that might come at the exact moment of release, every core page and data packet had completed CDN mirror distribution worldwide.

The liaison was confident that even if the main server of Tsinghua University was directly paralyzed by the huge influx of access traffic instantly after the release, researchers in any corner of the world could still smoothly pull the exact same unadulterated proof materials from the nearest mirror nodes.

The technical liaison's palms were full of sweat.

After completing the final automated comparison of hash digests across all nodes, he took a deep breath and steadily hovered the mouse cursor over the green publish button representing final confirmation.

Professor Qiao Wenduo stood behind the liaison with his hands behind his back.

Ye Ning and Zhou Shu each occupied a monitoring computer, their eyes closely fixed on the backend traffic anomaly monitoring window.

The head of the third-party Red Team stared intently at the permission change log table, making final confirmations to ensure that the malicious attack samples and private identity records used for internal stress testing were not mistakenly packed into the externally public compressed archive due to mistakes in the packaging script.

Jiang Lin sat quietly in the seat closest to the door, with only a printed copy of the paper carrying the scent of ink in front of him.

The technical liaison watched the second hand cross the last ten ticks.

4:00 sharp.

The mouse was clicked down.

Click.

The access permissions of the code repository across the entire network instantly switched at the bottom layer of the system, shifting from the glaring red "PRIVATE" to the blue "PUBLIC" symbolizing openness.

The static homepage displayed externally by the project reloaded and refreshed a second later.

Four bolded, huge identifiers prominently appeared at the very center of the global view:

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

[Σ(5) = 4,098]

[ENUMERATION COVERAGE / VERIFIED]

[UNRESOLVED / 0]

Beneath these dazzling achievements, the first line of the public statement read:—

["This project does not require, nor does it recommend, any researchers to blindly trust the pre-compiled executables we provide. All of the aforementioned conclusions can be recompiled and obtained from our fully open-source underlying source code and invariant certificate sequences; we welcome anyone globally at any time to submit the smallest logical counterexample that can break through the current system."]

Only seventeen seconds later.

The geolocation tracking module of the backend logs flickered once, and the backbone mirror node in Frankfurt, Europe, recorded its first complete data package pull.

The data flow rate instantly skyrocketed to its peak.

Forty-one seconds later.

IP addresses of multiple supercomputing center nodes located in North America began to show activity; logs showed that the other party had not only downloaded the source code, but had also begun automatically invoking the compiler, attempting to rebuild that massive coverage core on a local cluster.

One minute and nine seconds.

In the public issue discussion section of the code hosting platform, the first external network question since the project's open-sourcing popped up.

A researcher from MIT, in a professional and tricky tone, inquired whether there was a minor boundary overflow risk in the transition table converter provided by the Tsinghua University team under two distinctly different Turing machine halting semantic conventions.

Two minutes and fourteen seconds.

Before the technical staff on Tsinghua University's side had time to respond, an external verification alliance member who had previously participated in the hidden tests had already spontaneously posted rigorous proof transformation scripts and corresponding mathematical lemma numbers beneath that issue, beautifully defusing the doubt.

Three minutes sharp.

The news center section of the Tsinghua University official website, the official Weibo, and the academic official accounts of major universities linked up to punctually release that meticulously worded press release.

In its third paragraph, this restrained press release very properly listed the core author contribution description of the entire project.

["The first author of this paper, Jiang Lin, is an undergraduate freshman of the Class of 2022 at Qiuzhen College, Tsinghua University. He made a decisive contribution to the project: independently responsible for and established the overall security architecture of the shared trusted core, creatively proposed the macro-state invariant witness mechanism targeting stubborn Turing machines, and ultimately personally completed the mathematical proof chain integration for closing the entire library search space."]

This line of text containing a massive amount of information was quickly and keenly captured by various media outlets and academic big Vs, who screenshotted and forwarded it separately.

For the vast majority of ordinary readers and netizens, they might not necessarily understand what precise cycle detection meant, what tree normalization was, let alone the esoteric concept of macro-state closure.

However, all of them could understand that name at the very front of the author column on the front page of this extremely heavyweight international top-tier paper.

And when doctoral students and young teachers from the Department of Computer Science of various domestic universities clicked open that detailed contribution description, the level of shock they received was much deeper.

They discovered that Jiang Lin not only genially handed over the mathematical witness that subdued the last ghost machine, but he also carved out a stringent trusted boundary with a nearly god-perspective engineering control capability.

He forced those over eighty million non-halt verdicts to completely shed the cloak of black boxes and accept explicit checks by independent code worldwide.

An elderly professor of formal verification who had long participated in international top-tier software security audits and was also a core member of this public review, after reading the source code, sent a sensationalized short email in an extremely niche yet highly authoritative professional theoretical computing mailing group.

["The media's attention may only be attracted by the undergraduate status of the first author, but leaving aside these social news elements, what truly makes this work worthy of being recorded in academic history is its precise control over the boundaries of trusted computing. With stringent standards, he achieved an absolute semantic and physical decoupling of the proof search framework and the underlying trust core, converging the system's trusted base to a minimum. On top of this architecture, he personally constructed the invariant witness that filled in the final piece of the puzzle. Combining a mathematician's insight with an architect's restraint, this is the true academic weight of this work."]

This brief email was translated and forwarded by countless people within a mere ten minutes, spreading wildly like a virus into theoretical computer science discussion groups, logic forums, and even private communities of hackers and geeks of all sizes across the globe.

Those who originally intended to just watch the fun with a spectator's mentality and planned to casually glance at the conclusion abstracts and media press releases, upon seeing the frenzied praise of their peers, began to silently open their terminals, enter command lines, and download the seventeen pages of macro-state mathematical specification documents that read like heavenly books, along with the matching lightweight coverage core source code.

The global real-time access heat map in front of the technical liaison began to light up violently outward with Beijing as the center.

Paris.

Bonn.

Toronto.

Princeton.

Tokyo.

Singapore.

Luminous points representing download connections crossed different time zones and vast oceans, fluttering down like a pilgrimage onto Tsinghua University's server cluster.

They landed on that proof system with open doors that allowed anyone in the world to act as an imaginary enemy.

Professor Qiao Wenduo looked at the exponentially growing independent build request queue on the big screen, feeling a suffocating wave of heat.

He raised his hand, forcefully loosened the topmost button of his shirt collar, and let out a long breath of foul air that had accumulated in his chest for several months.

In these muddled forty-plus years, the theoretical computing community had never lacked clever people who claimed to have found the final answer to the Busy Beaver.

Almost every year, someone published a paper claiming to have eliminated the remaining obstacles using some heuristic algorithm.

What this field lacked was never the answer.

What it lacked was someone who could both hand over the answer with flawless logic and possess the extreme confidence to encapsulate the right to check authenticity, selflessly returning it to the entire academic community.

...

Paris time, 10:07 AM.

In an old tiered lecture hall of the École Normale Supérieure in Paris, a course titled Advanced Topics in Computation Theory aimed at top senior students had just advanced to the core chapter on undecidability and Turing machine limits.

The silver-haired lecturing professor stopped speaking.

His slide handouts were fixed on page sixty-three.

In the center of the page was printed a table of known exact values of Turing machines that he showed unfailingly every year during his twenty-one-year teaching career.

S(1), determined.

S(2), determined.

S(3), determined.

S(4), determined.

However, in the column for S(5), which represented the current limit of human exploration, there was no clear equals sign, but rather a greater-than-or-equal-to sign representing uncertainty, written helplessly.

["S(5) ≥ 47,176,870"]

This professor was precisely one of the core members of the external reproduction and verification alliance hidden behind the scenes.

For three whole days and nights, another graphics workstation with powerful computing power in his office had been running wildly, non-stop replaying and verifying the multi-gigabyte encrypted certificate packages sent by the Tsinghua University team.

Just nine minutes before he walked into the classroom to teach, that workstation emitted a crisp beep.

The last massive coverage block of data successfully passed the local, most rigorous logical verification closed-loop.

The professor stood in front of the podium, silent for a long time.

Then, he slowly closed that old paper handout whose edges were worn and curled.

Picking up the electronic stylus on the podium, under the gaze of more than a hundred senior students, he turned to face the huge touch screen.

He raised his arm, and the pen tip landed on that glaring greater-than-or-equal-to sign, sweeping forcefully to erase the slanted short line representing compromise and the unknown before everyone.

The characters on the big screen underwent a historic transformation.

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

In the spacious tiered classroom, there was first a death-like silence, followed instantly by a burst of uncontrollable exclamation and heated discussion, like a boulder thrown into a calm lake.

"Ladies and gentlemen, I have taught this core computation theory course for a full twenty-one years." The professor turned around, his deep gaze looking at the brand-new equals sign on the screen, his voice sounding exceptionally low and powerful due to his inner agitation, "This is the first time in my teaching career that this slide table has expired before my class."

Several quick-thinking students in the back row had already quickly searched through the encrypted network for Tsinghua University's newly launched globally public paper.

A student incredulously magnified the area of the author list, and then following the contribution description link below the name, clicked open the public personal academic page of the paper's first author, Jiang Lin.

As the page unfolded, a gasp of cold air came from the back row of the classroom.

Groundbreaking discoveries in aperiodic tiling.

The latest advancements in the field of Additive Combinatorics.

Architecture-level formal verification systems.

And today's five-state Busy Beaver proof, which was enough to be recorded in history.

Several research branches that were originally far apart in the fields of mathematics and computer science, ones that would be difficult to span even if one exhausted a lifetime, were now gathering miraculously at the same time on the academic resume page of a freshman.

The professor ignored the commotion below.

He operated the computer, directly copying and highlighting the mirror address of Tsinghua University's public source code repository, pinning it to the top of the course's online system page.

Then he decisively deleted the regular after-class assignment on automaton theory that had originally been assigned.

Finally, in the assignment posting column, he typed out two new requirements with a strong practical flavor.

["Choose either the Rust or OCaml version verifier provided by the Tsinghua University team, and complete an independent build in your local environment."]

["Try to find the logical breakpoint of the proof. In next week's seminar, submit your attack attempt report closest to overthrowing this new theorem within this week."]

Save.

Send network broadcast.

Ding.

The laptops, tablets, and mobile phones of more than a hundred students simultaneously rang with course notification alert sounds.

The five-state Busy Beaver, a curse like a ghost that had plagued the older generation of scientists for more than forty years, at this moment officially fell from the out-of-reach column of open unresolved problems in academic handouts, turning into a new theorem that students could personally verify, touch, and dismantle with their own hands on the keyboard.

...

Central European Time, 10:21 AM, Munich.

Martin Werner sat in his slightly dim study, opening the global authoritative Busy Beaver machine database that he had built with his own hands and maintained for a full sixteen years.

Due to caching reasons, the website homepage opened on the browser still stubbornly displayed the old state from last night before he modified it.

["BB (5) candidate: 47,176,870"]

["Remaining holdouts: 1"]

Martin's fingers gently rubbed against the mouse, entered the administrator password, and entered the database operation backend.

First, rigorously, he packaged and uploaded the four independent review and stress test record documents representing different dimensions generated over the weekend to the database's supplementary evidence column.

Then he hung all the global dozen-plus mirror distribution addresses of all public data packages released by the Tsinghua University team one by one in the most conspicuous position on the homepage.

After finishing these peripheral works, he solemnly clicked open the core state attribute field.

He pressed the delete key, and the word candidate symbolizing doubt and uncertainty was neatly wiped away.

The cursor moved to the counting column of that ghost machine.

Backspace.

The number 1 disappeared, replaced by a 0 representing an end.

In the column for the proof year, he solemnly filled in 2022.

In the mathematical proof basis column below, he carefully copied and pasted the full English title of Tsinghua University's paper that had been made public for less than an hour, along with the confirmation number of the European Verification Alliance with the highest trust level.

When he clicked the submit modification button at the bottom, out of data security protection mechanisms, the webpage popped up a bright red secondary confirmation warning window.

["System Warning: Your modification will permanently close the BB (5) global open entry that has lasted for nearly half a century. Does this confirmation change the BB (5) status from CANDIDATE to PROVED?"]

Martin's fingers stopped above the Enter key.

His gaze crossed the monitor and fell on the corkboard on the right side of the desk.

Pasted there was a holdout status table spit out from a dot-matrix printer in 2006. Sixteen years had passed, the paper had turned yellow, and the four corners were covered with small holes left by repeated pin penetrations.

At the very bottom of the table, five numbers were written in sequence.

43.

17.

6.

2.

1.

The first four numbers had been crossed out with a red pen.

That last 1 had remained there for more than a decade.

To clear this table, Martin had broken three workstations and moved his office twice. The database he maintained had also migrated from a university personal homepage to a code hosting platform, and finally was split into a dozen public mirror nodes.

The machines changed, the office changed, and the server addresses also changed.

That 1 had never moved.

Now, a 0 had been filled into the modification column of the database backend.

Martin withdrew his gaze and pressed the Enter key.

["UPDATE ACCEPTED"]

The page paused briefly.

["BB (5) / PROVED"]

The webpage finished reloading after a few seconds.

That red holdout counting box that had long entrenched the upper right corner of the homepage and was as glaring as an alarm light disappeared forever.

Martin stood up again and pulled out that red marker from the pen holder.

He walked to the corkboard and drew a horizontal line across that last 1.

Then, he wrote beside it:—

["0"]

["2022.09.19"]

["ENUMERATION COVERAGE VERIFIED"]

The red pen tip left the paper surface.

On this table, there were no longer any numbers left for tomorrow.

Martin leaned back against the wide genuine leather backrest of the chair, quietly looking at the brand-new page.

He looked for a long, long time.

Finally, he fished out the phone in his pocket, brought up the camera, and took a high-definition photo with a slight reflection facing the computer screen that witnessed the end of history.

Then, he opened a small geek mailing group that had been almost forgotten by the internet.

Among the member list of this mailing group were old fellows who had fought side by side with him against early Busy Beaver machines back then.

In this list, some had retired to enjoy their old age because of their advanced age.

Some were forced to change careers and go to major internet companies to write business code because they couldn't get research funding.

There was also an email address that had been prompted by the system as permanently undeliverable a few years ago.

Martin added the photo as the only attachment.

In the subject line of the email, he only typed a sentence that was plain yet contained the force of a thousand jun.

["Old fellows, we can finally delete this line of code from the todo list."]

Click send.

A long journey belonging to the older generation of explorers was announced to have come to an end.

...

Beijing time.

Four twenty-six p.m.

The second floor of the Zijing Canteen, next to the Zijing Apartment area of Tsinghua University.

It was the time when most students came to have dinner after class, and the canteen was buzzing with noise.

In the internal course WeChat group of Qiuzhen College, the official hardcore news release from Tsinghua University regarding the five-state Busy Beaver had already been excitedly forwarded for the third time by different people.

Zhao Chengyu sat in a seat against the wall holding his dinner tray, with his phone in one hand and his brows tightly furrowed.

He had read word for word all the popular science parts in that extremely restrained press release that his non-math-major brain could barely comprehend.

Unwilling to stop there, he even clicked into the technical appendix at the bottom, and his mind got stuck for a full two minutes in front of that screenshot of the transition table composed of ten extremely simple numbers.

Zhao Chengyu recognized every single word in the press release.

However, when these Chinese characters were combined together to tell a grand story that changed the boundary of human computation theory, and the protagonist of the story happened to be Jiang Lin, all of this still deeply exceeded his meager understanding of the four words college classmate.

He moved his gaze away from the phone screen, raised his head blankly, and looked around the bustling canteen.

Soon, in a relatively quiet spot by the window, he found Jiang Lin's figure.

In front of Jiang Lin sat a bowl of the most ordinary tomato and egg noodles, with steam rising from it.

Beside the bowl of noodles lay an open notebook containing course notes taken just this morning.

His phone lay flat with the screen facing upward, and because it was connected to the laboratory notification interface, archive email notifications with foreign-language titles were popping up continuously on the screen.

Jiang Lin held chopsticks in one hand while quickly swiping across the screen with the other.

Zhao Chengyu picked up his half-eaten dinner tray, strode over, and plunked himself down in the empty seat opposite Jiang Lin.

He pushed his phone, which was still on the news page, directly in front of Jiang Lin.

"I have read this press release three times in a row."

"Mn." Jiang Lin responded without raising his head.

"But I feel like I still only understood half of the logic."

Jiang Lin moved his gaze away from his own screen and glanced at him: "Which half didn't you understand?"

"Just this so-called champion machine, it can run over forty-seven million steps by itself—I believe that, after all, you guys let the computer run it."

Zhao Chengyu pointed to the huge number on the screen.

"But the other half, I can't figure it out no matter how hard I think. According to the article, that's a machine pool with tens of billions of combinations! Even with the supercomputer of Tsinghua University, you guys couldn't possibly run those billions of tables one by one on the machine until they halt or throw errors, right? When would that even finish running?"

After listening, Jiang Lin put down the chopsticks in his hand.

The noodles had become somewhat soggy in the soup.

"Only this champion machine exists to refresh the step record, so it must honestly run step by step in the underlying simulator until it hits the halt state by itself and gives the true number of steps," Jiang Lin explained in the most vernacular language, "As for the remaining eighty-odd million machines that might fall into infinite loops, we don't need to run through their entire lives. They only need to each submit a mathematical proof regarding their ultimate destination to the verification system."

Jiang Lin picked up a napkin to wipe his hands and continued: "Those that can halt hand over the finite trajectory running map. Those that never halt hand over their infinite loop rules, their logically unreachable sets, or, like the final ghost machine, hand over their macro-state invariant witness. The verifier we released today is not responsible for running the machines. It is like a customs officer; it is only responsible for extremely rigorously checking whether the logical seals on these witness visas are forged."

Zhao Chengyu scratched his head with a look of partial understanding, lowered his head, and refocused his gaze on those huge numbers already written in bold as irrefutable equations.

"So, you mean as long as no one can overturn this proof system, from now on in this world, even if a hundred or a thousand years pass, absolutely no one will ever find a five-state machine that runs longer than forty-seven million steps?"

"Under the current unified formal definition, yes, never."

When Zhao Chengyu took his phone back, his fingers unconsciously swiped on the screen, and the image stopped at the first line of the long author list.

He looked at that incomparably familiar name.

But whether it was Jiangs Brick, the ICM 45-minute special report, the ICCM Gold Award, or the proof of the PFR Conjecture, to Zhao Chengyu, they all carried a certain illusory feeling.

They were too far away from the life of an ordinary college student like him, just like observing a historical celebrity archive through the thick bulletproof glass of the history museum.

However, the submission record of this new paper repository that had just ignited the global computer science community right in front of him had its timestamp clearly printed: those witness files had been submitted intensely from the early hours of last Friday until late Sunday night.

All of this was so real that it made one feel a bit dizzy.

Zhao Chengyu took a deep breath and finally asked the question that had been held back in his heart for a long time.

"Jiang Lin, basic conclusions of this level will definitely be written into university textbooks for computer science majors worldwide in the future, right?"

"Yes."

The person who answered him was not Jiang Lin.

Gu Mingche stood by the table holding his dinner tray, with his phone in his other hand.

He had originally just come over to look for a seat, but upon hearing Zhao Chengyu's question, he placed his phone on the tabletop.

On the screen was a screenshot that had just been forwarded into the Qiuzhen College course group.

A professor at the École Normale Supérieure in Paris had already cancelled the original assignment and included Tsinghua University's public verifier in this week's course tasks.

"Textbooks update slower than courses," Gu Mingche pulled out a chair and sat down, "When it gets written in depends on when the publishing house revises its edition. As for whether it gets written in, that doesn't depend on the publishing house."

Zhao Chengyu pointed to the front page of the paper and asked: "Then will Jiang Lin's name be printed in the textbooks?"

"The main text might only leave two equations."

Gu Mingche reached out and swiped the page downwards, stopping at the paper citation information.

"But as long as a textbook talks about S(5) and changes the original greater-than-or-equal sign to an equal sign, it cannot bypass this paper. Later, if someone wants to know who wiped away that slash, following down the footnotes and references, the first author on the first line will be his name."

Zhao Chengyu looked at his phone, then looked at Jiang Lin sitting opposite him.

Jiang Lin had picked up his chopsticks again and picked up the noodles that had become somewhat soft from soaking.

...

At eight o'clock in the evening, the independent build records of the public repository had exceeded one hundred.

On this sleepless night, various geeks and security experts demonstrated a wide variety of verification methods.

Some used traditional x86-architecture large server arrays.

Some used the latest ARM-architecture small workstations deployed in the cloud.

Moreover, a paranoid functional programming fundamentalist, in order to ensure that the underlying layer was not polluted by any modern complex compiler, forcibly and manually ported Tsinghua University's coverage core logic into a minimalist functional virtual machine environment, retaining only the most basic integer operations, list structures, and hashing processing interfaces in this enclosed environment, and then passed the public regression set.

Red team personnel also emerged in large numbers.

Some people began to launch fierce fuzz testing specifically targeting the parser responsible for parsing the witness files.

They deliberately uploaded oversized irregular fields, artificially created dead-loop parent node pointers, intentionally messed up the byte endianness of data blocks, or even submitted incomplete chunks truncated by brute force.

However, facing all malformed malicious inputs, the project team's public parser was rock-solid, intercepting and refusing to respond to all of them.

The data digests of the various mirrors provided by Tsinghua University were consistent.

The final adjudication conclusion given by the system also maintained absolute consistency.

In the public issue feedback area, various gunpowder-filled academic challenges appeared like snowflakes one after another.

But the Tsinghua University team, as the repository maintainers, showed an extremely confident macro-perspective.

They did not delete any sharp questions, nor did they use permissions to remove those opinionated opponents from the discussion area.

Facing problems, the only response method of the technical personnel was to tirelessly assign and guide each challenge to a specific specification document page number, a specific certificate hash number, or a globally recognized successful reproduction record.

Fight back against words with mathematics.

Nine forty-four p.m.

A senior editor and researcher who had long and voluntarily maintained the historical data page of small Turing machine evolution on Wikipedia, after repeated confirmations, submitted with trembling hands the largest-scale page update for that entry in nearly a decade.

Ten-three p.m.

An open unresolved problems list widely circulated among global computer scientists that specifically collected frontier pending cases of theoretical computation had its editor-in-chief permanently delete the BB(5) entry from the list after a brief announcement.

Ten twenty-seven p.m.

A computer science professor at another Ivy League university overnight modified the next day's graduate course syllabus, directly bolding and stuffing the title of Jiang Lin and others' paper into the top of the core reading material list that must be intensively read this semester.

Eleven p.m.

A PhD student who had toiled for three years in a research institute and originally planned to set his graduation thesis direction as using new heuristic pruning to explore the last few Busy Beaver holdout machines, under the advice of his advisor, decisively abandoned the code he had already half-written.

He retained all his previous failed exploration records as counterexamples, and in the proposal report system, rewrote his new paper title to Preliminary Exploration of Verifiable Macro-State Proof Languages for Future Six-State Candidate Machines.

As the door of the five-state was heavily closed, those advanced verification tools, precious failure experiences, and countless top brains that had accumulated in front of the door for decades were finally no longer trapped to death in this dead end.

They began to turn around, carrying new weapons, marching towards the more distant six-state computation wasteland.

Meanwhile, on Tsinghua University's side, the backend archiving system of Jiang Lin's Research Support Unit also completed a large-scale revision and upgrade that night in adaptation to the situation.

Outside of the existing [PFR Conjecture / Marton Theorem Queue], the technical team urgently added a top-priority [Computability / BB (Computability / Busy Beaver)] primary classification directory.

The technical position for the formal verification interface was also officially upgraded from the initial temporary liaison to a fixed technical seat equipped with dedicated personnel.

A small-scale academic briefing originally scheduled to be held internally within the department next week with only a dozen or so participants was expanded overnight into a technical report meeting open to global live broadcast because application emails requesting attendance flooded the mailbox.

Of course, the meeting set an extremely high technical threshold.

Anyone who wanted to ask questions at the report meeting had to submit in advance the unique hash number of the disputed machine, the challenged specification page number, or the minimal code counterexample capable of running verification directly.

As for the emails of praise and flattery that came like a tide, they were all categorized into the ordinary archive library by cold rules.

The curious interview invitations sent by major mainstream media around the world were also automatically transferred to the school's scientific research publicity department for unified public relations processing.

On this crazy night, after layers of filtering, the only things that could truly reach the terminal screen in front of Jiang Lin were those hardcore issues that could genuinely and logically harm the proof system.

Twelve-twelve a.m.

In the public Issue repository, the last high-priority item was still lit with a red marker.

The questioner was a scholar studying automaton semantics and formal verification.

He constructed an extremely rare degenerate tape configuration.

According to the local matching rules, this configuration seemed to fall into two mutually exclusive macro control states simultaneously.

If it was truly reachable, it meant that the macro-state partition lacked uniqueness.

All subsequent invariant propagation based on state classification had to be re-examined.

The opponent even attached a leading path composed of seven local rewrites, trying to prove that this configuration could gradually evolve from a legal state.

The Issue was automatically elevated to the highest priority.

Jiang Lin opened the attachment, instead of looking at the final degenerate configuration first, he checked the leading path starting from the first step.

The cursor stopped at the fourth rewrite.

This rule was only allowed to act on odd phase boundaries.

The pre-configuration submitted by the opponent, however, was in an even phase.

Jiang Lin copied the guard condition number of that row and fed them into the Rust and OCaml verifiers respectively.

The two windows gave results almost simultaneously.

[REJECT / REWRITE_GUARD_MISMATCH]

[Reject: Rewrite guard condition mismatch]

That degenerate configuration could indeed match two types of macro-states simultaneously in local shape, but the leading chain provided by the opponent had already broken at the fourth step.

It could not enter the reachable state space covered by the proof system from the all-blank tape.

Jiang Lin pasted the rule number, the two sets of verification logs, and the phase comparison table of the fourth step into the Issue.

A few minutes later, that questioner left a brief reply with a hint of admiration at the bottom of his question.

[You win, the fourth-step guard condition does not hold, the leading chain is unreachable, I formally withdraw this counterexample.]

The high-priority marker automatically went out.

Jiang Lin sat at the desk in Room 402 of Zijing Apartment, gripped the mouse, clicked the button in the upper right corner, and changed the status of this globally watched issue from OPEN to CLOSED.