180: Chapter 180 Evidence Preservation and Compression Theorem

Jiang Lin closed his computer, put the three repeatedly deliberated discussion materials back into his bag, and merged into the crowd to get off the train.

The air on the platform was much more humid than in Beijing.

The city of Nanjing seemed still unwilling to admit that summer had ended.

The air was filled with a sticky feeling unique to the south, as if every breath could inhale saturated water vapor.

Jiang Lin followed the tide of people up the escalator, passed through the exit turnstile, and just as he walked into the spacious and bright arrival hall, he saw someone right ahead holding a pick-up sign printed with his name.

The person holding the sign was a young man in his thirties, wearing half-rimmed glasses on the bridge of his nose, exuding a strong aura of an academic worker.

Beside it, there also stood a middle-aged man with slightly graying hair.

The young man saw Jiang Lin first and walked up quickly to welcome him.

"Student Jiang Lin?"

"I am." Jiang Lin nodded.

"Hello, I am Li Yuan, responsible for coordinating today's discussion on the School of Artificial Intelligence side." The young man extended his hand enthusiastically, "The car is already parked in the underground parking lot of Nanjing South Railway Station, and Professor Zhou Zhihua is already waiting for you at the school."

After the two shook hands, Li Yuan immediately turned sideways to introduce the gray-haired middle-aged man standing next to Li Yuan.

"This is Professor Sun from the Department of Mathematics. Hearing that you are coming to Nanjing this time and the materials you brought involve deep foundational logic problems, the Department of Mathematics temporarily adjusted the afternoon's teaching and meeting arrangements. Professor Sun will also bring two other teachers to specifically participate in the first half of our discussion."

Jiang Lin turned around and solemnly shook hands with the other party.

Professor Sun looked Jiang Lin up and down and smiled: "Our Department of Mathematics originally wanted to keep you in the department for half a day first, and ask you to explain the derivation part of PFR to us first, but we didn't win against the School of Artificial Intelligence. Professor Zhou Zhihua's side has timed things very strictly."

Li Yuan smiled and smoothed things over from the side: "Teacher Sun, this cannot be called snatching. Jiang Lin's email was first sent to Professor Zhou Zhihua's inbox in our school. We got the first chance by being close to the water, so to speak."

"That can only show that you acted fast and have a sharp sense of the theoretical frontier." Professor Sun waved his hand dismissively, unconcerned.

The three of them conversed while walking toward the underground parking lot following the indicator signs.

After getting into the car, a dedicated driver took charge of driving.

Li Yuan sat in the front passenger seat as the coordinator, while Professor Sun and Jiang Lin sat in the spacious rear seat.

The vehicle drove out of Nanjing South Railway Station and quickly merged into the main road of the urban area.

"Professor Zhou Zhihua carefully read the prerequisite materials you sent this morning." Li Yuan turned back, its expression becoming somewhat serious, "Originally, only four people from the School of Artificial Intelligence side were scheduled to participate in this afternoon's discussion. But after Professor Zhou Zhihua finished reading the materials, he made a temporary call and called over two other teachers from the department who specialize in representation learning and extreme model compression directions. Today's lineup might be a bit larger than originally planned."

Professor Sun leaned against the leather seat and chimed in: "On the Department of Mathematics side, we are mainly interested in the PFR mentioned in your materials and the topological structure of that unified verifier. However, we will only participate in the basic theory part of the first half. Once you cut into the specific experiments and engineering implementation links of machine learning later on, we pure mathematicians might not be able to interject."

"Today's problems might not really be separable by that much." Jiang Lin answered with a smile.

The vehicle drove onto the elevated bridge along the ramp.

The parasol trees on both sides of Nanjing's roads were still dark green and lush, their huge crowns extending toward the middle of the road and intertwining, the branches and leaves almost completely covering the outer walls of the buildings on both sides of the road.

Sunlight just past noon filtered through the gaps of the heavy leaves, continuously flickering on the speeding car windows.

Li Yuan opened the printed schedule in hand and confirmed the time nodes.

"We expect to arrive at the school building before 2:20, and officially start the discussion promptly at 2:30."

"What about the permission management of the discussion materials?" Jiang Lin withdrew his gaze from outside the window and asked Li Yuan in the front row.

"Everything is strictly executed according to the requirements sent in your email." Li Yuan closed the schedule, with a rigorous tone, "All attendees can only read the display version of the materials you provided on the screen at the discussion site, and are strictly prohibited from copying the original files through any physical media or network. The computer used for the meeting is a workstation completely physically disconnected from the network and is not connected to the school's public LAN. All discussion records and deduction drafts will be encrypted and saved separately after the meeting ends."

"Then what about the hidden verification data?" Jiang Lin pursued the question.

"It is managed by another independent group of personnel in our school who are not participating in today's discussion, responsible for keeping the key and hard drive." Li Yuan pushed the glasses, "Professor Zhou Zhihua himself also actively requested to recuse himself. Before the verification stage begins, he has not looked at the contents of those data either."

Jiang Lin nodded slightly.

Such data isolation measures, strict to the point of being paranoid, showed Nanjing University's extreme importance attached to this academic discussion.

Picking someone up at the station was just a worldly etiquette.

And separating the data source, access permissions, participants, and the final verification process in advance was the most professional preparation attitude when facing an underlying theory that might subvert existing cognition.

At 1:58 PM.

The black special car slowly decelerated and drove into Nanjing University.

The vehicle stopped in front of the modernly designed building of the School of Artificial Intelligence.

On the steps downstairs, several people were already waiting.

One of them was a senior professor specializing in model compression, and the other was a young researcher from the Department of Mathematics.

They stood at the door, each clutching the discussion materials printed out in advance.

Dense annotations and questions were left on the blank edges of the paper pages with red and blue marker pens. Obviously, these materials were not something they temporarily held in their hands to put up a front for greeting people, but had already been deeply digested.

Both sides conducted brief introductions and got acquainted on the steps.

Subsequently, Li Yuan, in charge of reception, did not directly lead Jiang Lin to the core conference room upstairs.

"The school has prepared a dedicated lounge on the second floor."

Li Yuan said, raising a wrist to glance at the watch.

"You rushed over from Beijing early this morning and sat on the high-speed rail for more than three hours. Go to the lounge to relax for a while, drink some water, and wipe your face first. This afternoon's discussion was originally scheduled for 2:30. If you feel that your state still needs adjustment, we can notify everyone to postpone the time to 3:00, or even 3:30."

Professor Sun from the Department of Mathematics also kindly persuaded from the side: "Yes, Jiang Lin, there's no need to rush like this. Doing basic theoretical deduction is the most energy-consuming. Professor Zhou Zhihua's side has already given word; the entire afternoon and evening time today has been reserved for you, plenty of time."

Jiang Lin slightly moved his cervical vertebrae and shoulders, which appeared somewhat stiff due to maintaining a sitting posture for a long time, and quickly and accurately confirmed his current physical and mental state in his mind.

During those three-plus hours on the high-speed rail, his brain had been running at high speed, most of the time carrying out the final layout and logical sorting of the materials.

This definitely could not be called any sort of rest.

But that level of consumption, for someone accustomed to carrying out survival calculations for several days without closing their eyes under extreme and high-pressure environments, had not yet reached the fatigue threshold that could affect his core judgment.

"The discussion does not need to be postponed." Jiang Lin put down his arms, with a resolute tone.

"Are you sure you don't need to adjust for a bit?" Li Yuan confirmed again.

"Sure."

Jiang Lin raised his head and glanced at the building.

"I've sat in the car long enough. Going directly to the conference room now, importing the materials, and setting up the verification environment in advance is more appropriate than letting me continue sitting on the sofa to rest."

Li Yuan looked at Jiang Lin's young face that exuded a calmness beyond his age, smiled understandingly.

"Alright, academic state indeed cannot be casually interrupted. Then we won't postpone, but you should at least go to the lounge to wash your face and wake up. The lounge is right next to the conference room, and purified water and some snacks to fill the stomach have already been prepared in advance by us."

This time, Jiang Lin did not refuse.

He was willing to immediately plunge into high-intensity mental work, but this did not mean he would delete normal human physiological needs together like redundant code.

The group passed through the access control and entered the interior of the building.

The lounge on the second floor was not large, but it was comfortably furnished.

A set of soft leather sofas and a clean glass coffee table.

A water dispenser stood in the corner.

On the tabletop of the coffee table were placed washed fresh fruits, several plates of exquisite Suzhou-style pastries, and a stainless steel tray with a wet towel.

Jiang Lin walked into the adjacent independent restroom to wash his face, drank more than half a cup of warm water, and walked out.

Seeing him come out, Li Yuan hurriedly stepped forward and said: "The school has already reserved a room at the nearby Nanjing University International Conference Center, no need to rush too much."

"This will be decided depending on when today's discussion can reach a conclusion."

After this sentence was spoken, the several teachers present looked at each other and no longer spoke to persuade him to sit down and rest.

Because everyone could hear that this was no longer a polite and ritualistic evasion.

The young man in front of them was truly prepared to pour every single minute and second of this afternoon, and even all his energy, unreservedly into the problem about to unfold.

At 2:10 PM.

Under Li Yuan's guidance, Jiang Lin stepped into a small conference room.

He took out the specially encrypted and physically isolated work disk from his bag and plugged it into the dedicated interface of the conference computer.

He checked item by item the color mapping of the projection equipment, the execution environment configuration of the underlying code, and the read and write permissions of each folder.

The conference computer prepared by Nanjing University for this discussion was very clean. Just as Li Yuan promised, the network card driver had been directly disabled at the underlying system level, and the physical network cable interface was also sealed shut with sealing tape, without connecting to any public network.

The three core discussion materials brought by Jiang Lin were imported into the read-only storage area of this computer in advance through specific instructions. Any attempt to modify or copy operations would be directly rejected by the system.

And the hidden verification data was kept by another group of personnel; anyone in the current conference room, including Professor Zhou Zhihua himself, could not access it in advance.

At 2:17 PM.

The software and hardware environment checks were all completed.

After confirming everything was correct, Jiang Lin unplugged the isolated work disk and put it back into the computer bag.

Just as he completed this series of actions, other participating personnel began to push the door open and enter the conference room one after another.

Two senior teachers from the Department of Mathematics chose to sit on the side close to the front whiteboard, where it was convenient for them to stand up at any time to perform formula deductions.

The several researchers from the School of Artificial Intelligence who specialized in representation learning and model compression sat on the other side of the long table, opened their non-networked laptops in front of them, and prepared to record at any time.

There were no students auditing in the room.

There were no filming devices on the surrounding walls.

Nor were there any propaganda officers preparing press releases.

This was not a public report meeting to showcase scientific research strength to the outside world.

Public reports were responsible for communicating already formed results.

Today's conference room was responsible for judging whether a matter that had not yet been clearly defined could ultimately hold true.

At 2:26 PM.

Professor Zhou Zhihua, who had been sitting in the main seat of the long table and pondering with his head lowered, finally raised his head from that thick stack of printed materials.

At this moment, in the center of the wide solid wood desktop, three documents were neatly placed.

The first was the information entropy loss ledger during the theoretical proof process of PFR and Marton's theory.

The second was the logical topology of the unified verifier for BB(5).

The third was the reopening tracking record of candidate error conclusions based on MPS-EvidenceGate.

Among them, that second material regarding the shared trusted kernel old unified draft for BB(5) had been turned by Professor Zhou Zhihua to the last page.

On that pristine white paper surface, three logically mutually exclusive results were printed simultaneously.

[ACTUAL_RUN: HALT_AT_STEP_193]

[CERTIFICATE_CLAIM: NON_HALTING]

[VERIFIER_RESULT: ACCEPT]

Professor Zhou Zhihua's gaze penetrated through his lenses, looking calmly at Jiang Lin sitting opposite.

"Was the trip all the way here smooth?" He spoke in a chat-like tone.

"Smooth." Jiang Lin answered.

"Li Yuan said just now that you came straight over. I originally wanted to let you rest a bit more in the lounge. People who do theory cannot afford to have an unclear mind."

"I've sat in the car long enough, it's enough."

Professor Zhou Zhihua nodded and did not continue to dwell on this topic.

He reached out and pushed that material about BB(5) along the desktop to the center of the table.

"The formal derivation of the PFR part in your materials has very rigorous logic, we can talk about it later."

His index finger tapped on that line of record regarding the Turing machine running to the 193rd step and experiencing a catastrophic halt.

"I want to take a look at this attack test machine first. Why would a non-halting certificate that has already passed the unified verifier be overthrown by the actual running result at the 193rd step."

"Yes."

Jiang Lin opened the computer in front of him.

Professor Zhou Zhihua stared at the error certificate that had been officially verified and passed by the system, and said, "Then let's first take a look: why wasn't the key information that caused the machine to halt at the 193rd step preserved as evidence during that so-called hyper-efficient compression and verification process?"

Jiang Lin acknowledged with a hum, typed on the keyboard, and connected the projector's signal source.

The large white projection screen at the front of the conference room instantly lit up.

The screen was split in half by the software.

On the left, it displayed the state transition matrix of a four-state attack test machine constructed by Jiang Lin.

On the right was the hexadecimal code of the non-halting safety certificate that had triggered the disaster and passed verification.

That state table looked pitifully short.

If it were printed out, without even needing to change the font size, half an A4 sheet of paper would be more than enough to hold all of it.

However, once such a machine—which looked as simple as a children's toy—was made to execute step by step according to the state table and run on an infinitely long blank paper tape by the simulator, it could follow those simple rules and trace out a long and unpredictable trajectory.

This was probably one of the most easily misleading things in the entire field of computer theoretical science.

A small number of rules by no means implied that the system's evolution would be simple.

Jiang Lin moved the mouse, enlarging the final keyword field in the certificate file on the right until it occupied half the screen.

[Isolated_Window: TRUE (Isolated Window Verification Status: True)]

Professor Zhou Zhihua leaned back in his chair and glanced at that huge TRUE.

"Who filled in this TRUE?" Professor Zhou Zhihua asked.

"The certificate generator," Jiang Lin replied. "During code compression and logical packaging, the generator directly made this assertion in order to reduce the file size."

"Then, who is responsible for checking the truth or falsehood of this assertion?"

"The back-end unified verifier."

"How does it check?" Professor Zhou Zhihua's voice raised slightly.

"The verifier's logic has been streamlined. It didn't re-run the underlying physical state, but directly read the boolean value of this field."

Professor Zhou Zhihua raised his head to look at Jiang Lin: "And then?"

"There is no and then." Jiang Lin's answer was completely calm.

The entire conference room instantly plunged into a stifling silence.

Time seemed to stall for two seconds.

Professor Sun sat nearby, his brows tightly locked, seemingly digesting this absurd logical closed-loop.

"In other words, the verifier simply went to read the three characters 'I am correct' written by the generator itself, and then the verifier announced to the entire system, 'Um, I've looked at it, it's correct'?" Professor Zhou Zhihua broke the silence.

"Yes, that's right."

"Heh, the interpersonal relationships within this system get along really harmoniously," Professor Zhou Zhihua laughed and said.

Jiang Lin did not respond, but directly hit Enter on the console to start the simulation program.

The Turing machine on the screen began to run at high speed.

The red cursor representing the read-write head flashed frantically on the virtual paper tape.

At the twenty-sixth step, the cursor completed a local loop.

At the fifty-second step, the cursor steadily advanced to the right.

Seventy-eight steps.

According to the monitoring footage generated by the system backend, the local data structures on the paper tape shifted three cells neatly to the right, exactly following the pattern described in that safety certificate.

There was no sign of any out-of-bounds.

Judging from the running trajectory of the first hundred steps, this certificate appeared extremely reliable, or even perfect one might say.

The machine's read-write head was like a pendulum trapped within a limited window, moving back and forth, completing a self-replication every precise twenty-six steps, and then shifting three cells to the right like an hour hand.

It was extremely like a good tenant with regular work habits and a stable schedule, who paid the rent to the landlord on time or even early every month, making people feel completely at ease.

One hundred and forty steps.

One hundred and sixty steps.

The Turing machine's operation remained stable, with no sign of any crash.

However, at the very instant the system clock jumped to the 184th step...

The machine's read-write head, while executing a complex return rule, crossed the safety boundary that the certificate claimed it would never cross.

Outside that window designated as safe, the paper tape still retained a number 1 written long ago.

The machine's read-write head read this 1.

The state transition changed accordingly.

The 193rd step.

The state transition entered the halting state.

The machine stopped running.

On the screen, three results appeared simultaneously.

[ACTUAL_RUN: HALT_AT_STEP_193]

[CERTIFICATE_CLAIM: NON_HALTING]

[VERIFIER_RESULT: ACCEPT]

The machine actually halted.

The certificate claimed it would never halt.

The verifier accepted this erroneous certificate.

Professor Zhou Zhihua stared at those three lines of text for a full half minute, then asked: "Before adopting this unified certificate, how did the original old-version verifier handle this boundary issue?"

"The original verifier was very bulky." Jiang Lin brought up the architecture diagram of the old version. "It had to calculate the furthest boundary the read-write head could possibly reach, and check segment by segment whether there existed any legal state transition path in the paper tape traces left outside the window that could re-enter the active area in the future."

"That sounds very safe. Then why did later engineers delete such important checking logic?"

"To cater to the type standard of the unified certificate." Jiang Lin casually rattled off a set of data. "After deleting dynamic verification, the scale of the core code was reduced by thirty-one percent, and since frequent access to external memory was no longer needed, the verification speed was increased by about fourfold."

"What about the certificate's size?"

"The average length was shortened by twenty-seven percent, making it more favorable for distribution in low-bandwidth networks."

"Sounds like this compression scheme is making giant strides in every engineering metric," Professor Zhou Zhihua commented.

Jiang Lin nodded and said, "Yes, except that the final conclusion is a fatal error, everything else is progress."

Professor Zhou Zhihua picked up the paper cup on the table and took a sip of water.

"This erroneous acceptance case of the shared trusted kernel old unified draft essentially illustrates a responsibility transfer issue," Professor Zhou Zhihua put down the paper cup and pointedly noted, "In the pursuit of efficiency, the obligation of verification was quietly and forcibly transferred from the trustworthy back-end to the unreliable front-end generation end. In the field of formal verification, this problem is actually quite easy to handle; if a vulnerability is found, at worst you just add that dynamic checking code back in, sacrificing a little bit of speed."

Jiang Lin nodded in admission: "You are right, adding it back in a pure logic system is very easy. However, when this problem enters the massive black box of modern machine learning, it is not so simple anymore; we don't even know what things we should add back."

Along with Jiang Lin's voice, Professor Zhou Zhihua opened the second piece of material on the table.

The image on the screen switched accordingly.

That was an equipment sensor state collection table from the heavy industry sector.

Exactly thirty-two dimensions of data fields.

Arranged densely from top to bottom.

Main shaft temperature.

Base high-frequency vibration amplitude.

Hydraulic system pressure.

Servo motor three-phase current.

Gearbox real-time speed.

Time interval since the last deep maintenance.

Workshop ambient humidity.

Factory batch number of vulnerable parts.

And even historical calibration records of various sensors.

Jiang Lin drew a funnel-shaped model structure on the screen.

"In conventional representation learning models, neural networks will extremely compress this massive thirty-two-dimensional input through multi-layered encoders into a low-dimensional vector representation of only eight dimensions. Then, they use this compact eight-dimensional vector to determine what type of fault has occurred in the current equipment."

Professor Zhou Zhihua looked at the bold black characters on the material and said, "This material states that the fault recognition accuracy of this compression model on the public test set is as high as 96.4 percent. Very dazzling data. And in this particular sample, the conclusion given by the model is that the main shaft bearing is worn."

"This conclusion is wrong," Jiang Lin said bluntly.

"What is the real physical fault?"

"It is a physical blockage of the primary filter at the front section of the coolant pipeline."

Jiang Lin hit the keyboard and unfolded the complete high-frequency sampling records from three hours before the accident on the screen.

It could be clearly seen in the charts that within the three hours before the fault occurred, the main shaft temperature curve and the base vibration curve began to show a steep upward trend at almost the same time.

"The model learned a piece of common sense during training: when temperature and vibration rise at the same time, it is highly likely that the balls inside the bearing are worn, leading to increased friction." Jiang Lin held a red laser pointer and drew a circle on the two curves. "It forcibly compressed this combination of features into a typical bearing wear fault mode."

"But what is the actual situation?" Professor Zhou Zhihua stared at the data.

"The actual situation is that the temperature rise comes from the blockage of the coolant filter, and the cooling flow drops rapidly. The increase in vibration amplitude occurred after a sensor reinstallation three hours ago. The base pre-tightening force changed, causing the mechanical coupling and frequency response between the sensor and the machine base to change. However, the original calibration coefficient was not updated synchronously, so the same physical vibration was thus recorded as a higher amplitude."

Jiang Lin put down the laser pointer.

"Two physically unrelated independent changes—flow drop and calibration relationship change—ultimately became equivalent to a dangerous common fault in this minimalist compression model."

"What proportion of the training data does that event field of recent sensor reinstallation and calibration coefficient change occupy in the model input?" Professor Zhou Zhihua sharply grasped the core of the problem.

"Two point seven per thousand," Jiang Lin precisely reported a number. "It belongs to an extremely long-tail rare event."

"If we delete this field in the model input, how will the accuracy on the public test set change?"

"Not only will it not decrease, but because this long-tail noise is removed, the average accuracy will increase by another zero point one or two percentage points."

"Then from the perspective of the current industry-recognized model optimization goal, this model did nothing wrong at all." Professor Zhou Zhihua spread his hands. "It even became better."

"According to the traditional evaluation standard of only looking at average accuracy, it is indeed not wrong."

"But you insist that that maintenance event field, which only accounts for 2.7 per thousand, must never be dropped, right?" Professor Zhou Zhihua pursued relentlessly.

"In this specific industrial fault-tolerant task, absolutely not." Jiang Lin did not yield an inch.

"Why?"

"Because dealing with bearing wear and dealing with filter blockage correspond to completely different maintenance actions and disaster costs in the Real World. For bearing wear, the equipment can slow down and continue to run until the end of the shift. But if filter blockage is not shut down and cleaned immediately, the main shaft will be completely jammed and seized due to thermal expansion within thirty minutes, and the entire machine will be directly scrapped."

"Jiang Lin, is this considered being wise after the event?" Professor Zhou Zhihua unceremoniously pointed out the logical weakness in Jiang Lin. "Because you already know the answer is filter blockage now, you feel calibration records are important. But think about it, today it was calibration records that caused a misjudgment, what about tomorrow? Tomorrow it might be an operator's hand shaking during a shift change, and the next day it might be a large punching machine suddenly started in the adjacent workshop causing foundation vibration. In a thirty-two-dimensional or even thirty-thousand-dimensional input space, any inconspicuous field could become the fatal factor that changes the final conclusion under some extreme edge condition."

"Yes, what you said is completely correct." Jiang Lin nodded.

"Then according to your logic, to prevent this extreme situation, we must retain all this seemingly useless information."

"Yes."

"If all of it is retained, then the entire dimensionality reduction model loses its meaning, and there is no such thing as compression in your system at all," Professor Zhou Zhihua said with a frown.

"Therefore, this is the paradox."

"So the problem you brought today is untenable right from the logical starting point of the first step."

Professor Zhou Zhihua's brows were tightly knitted together.

"You want to find a method to retain all key information that might overturn the existing conclusions. However, what machine learning faces is an open, infinitely complex input from the Real World. As long as the physical process has not ended, even God doesn't know in which inconspicuous dimensional field the next counterexample sufficient to overturn everything is hidden."

Jiang Lin's gaze lingered on that maintenance event field.

Everyone else in the conference room also held their breath, and no one dared to interrupt at this time.

Professor Zhou Zhihua did not stop, continuing to dissect downwards with scalpel-like logic.

[part:gemini-3.6-flash]

"You see, the reason you've fallen into this predicament is that you're forcing the logic of formal verification—where every single proof obligation must be complete and flawless—onto this."

"Yes, that's what I was thinking."

"But in the world of machine learning, there is no such thing as a complete proof obligation. It was born built upon finite sample sets, statistical probability distributions, and inevitable approximation errors to the Real World. It is an art of compromise."

"It is compromise."

"If you insist on finding a perfect compression method that will absolutely never drop a single counterexample within a system full of compromises, then after all your efforts, all you'll get is a bloated pile of raw data with zero processing value, and your research will end up running in circles."

"Yes." Jiang Lin still responded briefly.

"Since you understand all this, do you still think it's necessary to continue in this direction?" Professor Zhou Zhihua stared into Jiang Lin's eyes, waiting for his answer.

Jiang Lin looked at the thirty-two field names on the projection screen.

Before this meeting began, during the countless days and nights after returning from the Wasteland to reality, he had actually prepared several seemingly viable academic paths.

For example, using Shannon's information theory to calculate the mutual information between each field and the output result.

Or using partial derivatives from calculus to evaluate the sensitivity of each feature in the network.

Or introducing Judea Pearl's causal dependency graph model.

Or simply using crude statistics on the historical database to count the frequency of past counterexamples.

These methods were mathematically very mature.

They could easily line up these thirty-two fields in an orderly queue.

From the mathematically most important fields all the way down to the least important trash fields.

Then, an engineer would only need to pick an arbitrary acceptable threshold somewhere in the middle and draw a line.

Keep those above the line deemed important.

Ruthlessly delete those below the line deemed useless.

As long as that was done, a few months later, a beautifully smooth Pareto optimal curve would appear in a paper at a top conference.

The paper would proudly claim that our model size was reduced by eighty percent.

While our accuracy on the test set remained essentially unchanged.

Until one day, when disaster truly struck, some marginal field that was ranked below the threshold years ago and deemed useless suddenly stood up with violent fury during a tragic industrial accident, using the wreckage of equipment and blood to tell everyone: actually, I was extremely valuable.

Jiang Lin took a deep breath, banishing those beautiful academic curves from his mind.

The crux of the problem wasn't whether the importance-ranking algorithm was subtle or clever enough.

It was that when facing a zero-fault-tolerance system, one shouldn't have asked arrogant, stupid questions like which information is important and which isn't in the first place.

Jiang Lin stood up slowly and asked, "Professor Zhou, do you have a marker?"

Professor Zhou Zhihua gave him a deep look, picked up a blue marker from the corner of the table, and handed it over.

Jiang Lin took the marker, strode to the whiteboard, and wrote two lines in the exact center.

[Sample A: Physical state is bearing wear]

[Sample B: Physical state is filter clog + sensor calibration drift]

Then, between the two lines, he drew a thick arrow pointing to the right.

Above the arrow were the words [Compression].

At the right tip of the arrow, he drew a box with [Same eight-dimensional low-rank representation] written inside.

"Professor Zhou, the compression algorithm itself inevitably discards information—that is a law of Physics, not a flaw," Jiang Lin turned around and said to everyone around the long table.

Professor Zhou Zhihua looked at the whiteboard, lost in thought.

"The truly fatal issue is that this blind compression based on statistical features takes two high-risk states that require drastically different responses in the Real World and brutally mashes them together like dough into a single indistinguishable state."

Jiang Lin turned back and wrote on the far right of the whiteboard, corresponding to Sample A and Sample B respectively.

[Maintenance Action A: Reduce speed, scheduled bearing replacement]

[Maintenance Action B: Emergency shutdown, clean filter + recalibrate sensors]

Two drastically different physical states.

Corresponding in reality to severe consequences: life vs. death, destruction vs. preservation.

But after undergoing that compression arrow deemed as progress, that self-proclaimed smart AI model, within its pitiful eight-dimensional vision, could no longer tell any difference between the two.

"The entire academic community over the past decade or so has been desperately calculating—calculating how much Shannon information entropy a compression process mathematically retains."

Jiang Lin's voice echoed in the conference room.

"But we have never settled down to calculate a far more critical ledger: how many absurd error equivalences this single compression actually creates at the execution level of Real World tasks."

Hearing this, Professor Zhou Zhihua, who was staring at the whiteboard, suddenly sat up straight from his reclined posture.

The marker in Jiang Lin's hand moved swiftly across the whiteboard, starting to describe this cruel reality in rigorous mathematical language.

[Let φ(x) be the dimensionality reduction compression mapping]

[For samples x₁ and x₂, there exists φ(x₁) = φ(x₂)]

[A*(x) is the set of allowable safe actions for the task, and Lₜ(x, u) is the task loss of executing action u]

[If the compressed model can only yield the same action u, and Lₜ(x₁, u) > ε or Lₜ(x₂, u) > ε]

"Here φ represents the compression network, and A* represents the set of allowable safe actions for the current state," Jiang Lin said. "Real World tasks often don't have just one single correct action. When a robot encounters an obstacle, it can stop, back up, or request manual takeover—as long as it's within safe boundaries, it shouldn't be forcibly judged as different."

He tapped the last line with the tip of the marker.

"The real problem is that after two inputs are compressed into the same internal representation, the model can only make the exact same choice, and this choice inevitably causes the task loss of at least one of the states to exceed the safety threshold."

"In other words, task collapse isn't defined simply by actions being literally different," Professor Zhou Zhihua stood up and walked to the whiteboard, "it's that the sets of safe actions for the two states are no longer compatible."

"Exactly."

"This handles cases with same labels but different costs, as well as situations where a single state allows multiple safe actions."

Professor Zhou Zhihua picked up another marker and added a line next to the formula.

[Dₜ(A*(x₁), A*(x₂)) > ε]

"This task distance cannot merely compare numerical action values," he said. "It must measure whether there is a divergence between the two safe action sets sufficient to alter Real World consequences. A steering wheel off by 0.1 degrees versus 180 degrees cannot both be calculated as the same error."

Jiang Lin nodded.

"Discrete classification can use zero-one cost. Mechanical control can use collision momentum, shutdown loss, or safety margin. Medical diagnosis can use risk variations brought by incorrect treatments."

"In formal verification, it is the cost between accepting a false proposition and rejecting a false proposition."

The two markers moved alternately across the whiteboard.

The original intractable question—[Which information cannot be lost?]—was quickly crossed out.

A new question appeared in the center of the whiteboard.

[How many unacceptable error equivalences for Real World tasks does a single model compression actually create?]

Professor Zhou Zhihua took two steps back and watched for a moment.

"This step holds," he said. "We can define it as Task Distinction Loss."

Jiang Lin wrote down:

[Task Distinction Loss]

[Task Distinction Loss]

It didn't just count how many mergers occurred.

Every collapse had to be weighted according to sample occurrence probability and task cost. A minor deviation that wouldn't change safety outcomes couldn't carry the same weight as an error that would result in scrapped equipment or casualties.

Traditional accuracy might only see that the model answered a few fewer questions wrong.

Task Distinction Loss focused on whether compression folded states together that required different safety strategies.

Professor Zhou Zhihua took a deep breath, clicked the marker cap onto the end of the pen, and said, "We have a theoretical definition now, and it's very elegant. But the next question is, how do we measure it in engineering?"

"By finding sample pairs in the dataset where task collapse occurs," Jiang Lin answered without hesitation.

"But how large is the input feature space of a Real World task?"

"Considering various environmental noises, it could be infinite."

"What if the inputs are continuous physical quantities?"

"Integration becomes even more troublesome, almost unsolvable."

"Then you can't expect engineers testing the model to pair up samples in infinite space two by two and throw them in one by one to compare, right? The computers wouldn't finish calculating until the heat death of the universe."

"That kind of exhaustive method is indeed impossible."

"Which means that this seemingly perfect quantity you invented, the Task Distinction Loss, is currently just a pie in the sky in terms of engineering—it can't be calculated at all."

Just as the initiative in the discussion had shifted to Jiang Lin in front of the whiteboard, in the blink of an eye, it was pulled back by the veteran Professor Zhou Zhihua using a Real World engineering hurdle.

But in academic discussions, this was by no means a bad thing.

After a brand-new concept stood up from the ink marks on a whiteboard, the first thing it had to face was being pinned to the ground by its harshest peers to see if it could actually walk on its own in the mud of reality.

If it couldn't walk, then such a concept was only worthy of staying on the whiteboard for people to admire, never entering the codebase.

Professor Zhou Zhihua uncapped the marker again and wrote a classic concept in machine learning theory beneath [Task Distinction Loss].

[Hypothesis Space H]

"No compressed model deployed in an actual scene can face all possible tasks; it only needs to express those specific tasks within the current finite hypothesis space H."

Professor Zhou Zhihua tapped heavily on the whiteboard with his marker.

Jiang Lin stared at that line of writing, his eyes gradually lighting up.

Striking while the iron was hot, Professor Zhou Zhihua continued writing down.

[Disagreement Region]

[Disagreement Region]

"For the same physical input, only the region where judgment conclusions differ drastically within the hypothesis models currently considered acceptable to us is the uncertain boundary where this compressed model is truly unsure and most prone to making errors."

"Therefore, the task collapse you want to calculate doesn't need to strive for covering the entire infinite input space at all."

"You only need to concentrate all your computing power to cover this extremely narrow disagreement region."

Jiang Lin, whose brain completed the logical stitching in an instant, immediately took over the topic.

"But even so, for high-dimensional data, the volume of this disagreement region might still be too large to compute."

"Then what should we do?" Professor Zhou Zhihua asked in return.

"Use magic to defeat magic," Jiang Lin's speaking speed quickened. "Since we think it's too big, we'll perform another information compression specifically targeting this disagreement region."

After hearing this, Professor Zhou Zhihua quickly drew several irregular, overlapping geometric regions on the lower part of the whiteboard, representing those tricky disagreement boundaries.

"We don't need to traverse every single point in the region." Professor Zhou Zhihua pointed to the intersections of those regions. "We only need to use greedy algorithms or other sampling techniques to find a minimal sample set that is extremely small in quantity but crucial in location. As long as this set of samples can act like coordinate axes, precisely supporting and covering all fatal disagreement points in the current hypothesis space that could lead to changes in task actions."

"Witness basis," Jiang Lin answered.

"Right."

Next to those irregular regions, Professor Zhou Zhihua solemnly wrote down a set of English words.

[Counterexample Witness Basis]

[Counterexample Witness Basis]

"This set of samples is not responsible for representing the average distribution," he said. "They are only responsible for representing different decision boundaries."

"Every witness must contain a pair of samples with close physical states but different task consequences," Jiang Lin said.

"It must also bind their respective sets of allowable safe actions, as well as the hypothesis disagreement region it covers," Professor Zhou Zhihua added.

Professor Zhou Zhihua added.

Jiang Lin looked at the whiteboard and suddenly stopped his pen.

"Just having sample points is still not enough."

"Where is it not enough?"

"Just because two witness points haven't collapsed doesn't mean the area near them is safe. The compression mapping could completely distinguish correctly at the witness points, yet undergo folding very close to them."

Professor Zhou Zhihua immediately understood his meaning.

"Every witness must carry a local coverage certificate."

The two continued adding fields behind the original structure.

[Original physical state A]

[Original physical state B]

[Safe action set A*(xA)]

[Safe action set A*(xB)]

[Coverage radius under task-induced distance]

[Local task loss upper bound within coverage cell]

[part:gemini-3.5-flash-lite]

[Stability Certificate of the Compression Mapping within This Unit]

[Review Result: Pass / Reject]

The witness basis is no longer a few isolated sample points, but a set of evidence units with verifiable coverage areas.

When the compressed model undergoes review, the system not only checks whether the sample pairs remain distinguishable, but also verifies whether the local stability certificate within each coverage unit still holds.

Once a high-risk witness unit experiences task collapse or the local stability certificate becomes invalid, the reviewer rejects the model from going online.

Even if all high-risk witness units maintain distinguishability, the system can only guarantee that the task boundaries covered by these evidence units still hold.

It cannot write off the absence of discovered counterexamples as absolute safety.

Professor Zhou Zhihua is responsible for compressing the infinite input space into a finite divergence cover.

Jiang Lin is responsible for turning each coverage unit into an evidence structure capable of independent verification.

Two paths originally originating from different fields met on the whiteboard.

At 3:08 PM.

The door of the meeting room was gently knocked.

Li Yuan pushed a cart in and replaced the hot water for a few people.

Jiang Lin was still standing in front of the whiteboard.

"Professor Zhou, this framework still lacks one question."

"What?"

"The counterexample witness basis is only valid for the current hypothesis space and reference distribution. If the external data distribution drifts, the model structure changes, or the task definition changes, the original coverage certificates may all become invalid."

"Therefore, it cannot be generated once and used permanently."

"An update trigger condition is needed."

Professor Zhou Zhihua picked up his water cup.

"How does the reviewer judge when to update?"

"It doesn't need to understand the external world; it only needs to monitor input statistical deviations, model version hashes, and task definition files. Once any item crosses the boundary, the old witness basis enters a pending re-verification state."

"It can only trigger, but it cannot quantify the remaining risk yet."

Jiang Lin turned around and wrote on the right side of the whiteboard:

[Evidence Leakage Bound]

[Evidence Leakage Bound]

"It is not responsible for telling us what is actually inside the unknown region," Jiang Lin said. "It is only responsible for giving the upper bound of the risk not yet covered by the witness basis under the current hypothesis space, reference distribution, and confidence level."

It records four things.

Which high-risk task boundaries have already been covered by evidence units.

Which regions still have coverage gaps.

Which distribution changes will invalidate the original coverage certificates.

When the witness basis must be regenerated.

Traditional compression results usually only list the number of parameters, speed, and average accuracy.

The new review framework will additionally provide an uncovered risk list.

This list is not pretty, but it can prevent mistaking the failure to find counterexamples for safety.

Professor Zhou Zhihua looked at the evidence leakage bound on the whiteboard.

"It can serve as a generalization bound."

"One term for empirical risk."

"One term for model complexity."

"The remaining risk term is responsible for accommodating insufficient witness coverage and distribution drift."

Jiang Lin looked at him.

"Mathematically they can be constrained uniformly, but in engineering certificates they must be separated."

Professor Zhou Zhihua did not object, but only asked: "Reason?"

"Insufficient coverage requires supplementing samples and expanding evidence units. Distribution drift means that the reference distribution has already changed, and the witness basis must be reconstructed. There is no problem with both risks entering the same supremum, but the disposal methods are different."

Professor Zhou Zhihua nodded and wrote a two-layer structure on the whiteboard.

[Theorem Layer: Unified Remaining Risk Term]

[Engineering Certificate Layer: Coverage Gap + Drift Leakage]

"This is best," he said. "The proof structure remains clear, and engineering personnel will not treat the two risks as the same thing."

Jiang Lin listed four items under the engineering certificate.

[Empirical Task Risk]

[Compressed Model Complexity Cost]

[Witness Basis Coverage Gap]

[True Distribution Drift Leakage]

At 3:27 PM.

In this small meeting room, the two began to formally charge toward the first core theorem of this brand-new theory.

To ensure the rigor of the derivation, the applicable scope of the theorem was restrainedly compressed to be very small.

A fixed and unchanging single task objective.

A loss function with bounded constraints exists.

Restricted within a specific hypothesis family with a finite cover number.

And, a dimensionality-reduction compression mapping whose mathematical structure is completely known.

Finally, there are two strong preconditions.

The evidence units carried by the counterexample witness basis must cover all hypothesis divergence regions higher than the safety threshold.

Within each evidence unit, the compression mapping must also satisfy the verified local stability conditions.

Under these preconditions.

If a heavily compressed model preserves the task distinguishability of all high-risk evidence units, and the corresponding local coverage certificates do not fail,

Then, the risk of this compressed model on the true task distribution can be jointly constrained by the empirical risk, model complexity, witness coverage gap, and distribution drift leakage.

This is not a universal theorem that can solve all model compression problems.

It doesn't even attempt to solve the infinite unknowns in the open world.

It is simply down-to-earth, writing the high-risk information loss previously hidden behind average accuracy for the first time into a formal position that can be calculated, reviewed, and entered into the risk upper bound.

In front of the whiteboard, relying on his keen intuition for underlying logic, Jiang Lin was responsible for forcibly pushing forward the main chain of the proof.

Meanwhile, Professor Zhou Zhihua was like an experienced gatekeeper, constantly using the standards of statistical learning theory at various key nodes of the main chain to add heavy iron locks to those insufficiently rigorous conditions.

"In this step of derivation, you defaulted that the set of safe actions allowed by the task and the task loss function are known a priori," Professor Zhou Zhihua said, pointing to an integral formula.

"Real World tasks can usually provide this part of the constraints, such as which states must be shut down, which states allow reduced-speed operation, and the losses corresponding to different erroneous actions."

"Even so, it must be written rigorously into the precondition of the theorem in mathematical language, and cannot be defaulted," Professor Zhou Zhihua knocked on the whiteboard.

"Okay, let's add the condition." Jiang Lin immediately added a line of formulas.

"And here, when constructing the witness basis, you introduced an optimization algorithm. Is the minimization of the witness basis scale a necessary condition that must be met in this theorem?"

"From the perspective of constraining true risk, this theorem does not require the witness basis to be minimized or optimal," Jiang Lin pondered for a moment. "Its only requirement is that it must completely cover those dangerous divergence regions. Even if this witness basis appears very bloated because the algorithm is not smart enough, as long as the coverage is sufficient, the security of the theorem still holds."

"Since minimization is not a mathematical necessary condition, don't write it into the statement of the theorem to increase unnecessary proof difficulty. Move it to the engineering implementation suggestion part."

"Makes sense, delete it." Jiang Lin used the board eraser to wipe away a section of redundant description.

"Looking further ahead, what if this compression mapping φ you defined is a mapping with random variables in physical implementation?"

"To ensure the rigor of the first-step derivation, we first restrict all compression mappings to be deterministic. The same input must have the exact same output."

"This restriction is too weak and too limited in real neural networks," Professor Zhou Zhihua shook his head.

"One bite at a time, we must first completely close this first foundational theorem regarding deterministic mappings. After ensuring that the foundation is fine, tomorrow we will go on to extend and derive the probabilistic bound version for random mappings."

"Sure, academia should be done step by step like this." Professor Zhou Zhihua agreed with this strategy.

The discussion entered the most core and most difficult part.

How to measure the distribution drift term!

"In this definition of the distribution drift leakage term, what kind of mathematical tool do you plan to use for the distance measure between two different data distributions?" Professor Zhou Zhihua asked, staring at an empty spot on the whiteboard.

"Use the most classic total variation distance?" Jiang Lin tentatively provided an option.

"Total variation is very sensitive to support misalignment, and it is very difficult to reliably estimate in high-dimensional continuous spaces. As long as there is an obvious support shift in the distribution, the resulting bound may quickly become overly conservative." Professor Zhou Zhihua shook his head and rejected it.

"Then use the Wasserstein distance?"

"The Wasserstein distance first requires defining a task-meaningful underlying ruler for the input space. But here, continuous sensor values, discrete fault types, and emergency actions are mixed together. Arbitrarily piecing together a Euclidean distance may result in a transport cost that does not necessarily correspond to the true task risk."

"Then which measurement tool do you think is most appropriate to introduce?"

Professor Zhou Zhihua said: "Since what we truly care about is the task loss, let's directly target this loss function class and define an integral probability metric induced by it."

Jiang Lin looked at the task loss function just written on the whiteboard.

"This IPM fits the task itself better."

The two continued to push forward along this route.

The whiteboard in the meeting room was soon filled with mathematical symbols and derivation processes.

On the other side, several researchers from the School of Artificial Intelligence were not idle either. Nanjing University had cached the intermediate representations and public data of three sets of models in advance, while the MPS-EvidenceGate general counterexample search framework brought by Jiang Lin provided ready-made candidate generation, evidence recording, and rollback interfaces.

A researcher connected the task loss matrix to the search framework.

Another researcher implemented the coverage radius and local stability check of the evidence units based on the new definition on the whiteboard.

Someone else was synchronously organizing the proof draft, recording each unclosed condition.

They were not writing a set of systems from scratch in a few minutes, but patching up the interface newly established today between two already existing tools.

The proof logic of the entire theorem was clearly decomposed into three distinct layers.

The first layer, the most basic foundation.

Using the Law of Large Numbers and Hoeffding's inequality to constrain the empirical risk of the model on publicly visible samples.

The second layer, the core coverage constraint.

Using the counterexample witness basis with local coverage certificates to constrain the risk of the compression algorithm creating task collapse within the covered high-risk divergence regions.

The third layer, extrapolating to unknown regions. Utilizing the VC dimension or Rademacher complexity term, together with the newly finalized IPM distribution drift term, to extrapolate conclusions on finite samples to the true task distribution.

At 3:51 PM.

Jiang Lin drew a solid black small square in the lower right corner of the whiteboard.

The internal main chain of the theorem completed its first closure.

He reviewed the logic starting from the first line of assumptions. Professor Zhou Zhihua, on the other hand, backtracked from the conclusion.

Ten minutes later, the two stopped in the center of the whiteboard.

The existing derivation found no direct gaps, and the key assumptions have also been written down. The remaining parts still require written organization, independent verification, and extension under more general conditions.

Professor Zhou Zhihua put down the marker.

"The internal main chain of the first risk bound holds."

Jiang Lin wrote the tentative name at the very top of the whiteboard.

[Task-Fidelity Compression Risk Bound under Deterministic Mapping]

"It makes sense theoretically, but it is not enough," Jiang Lin turned around and looked at Professor Zhou Zhihua. "In computer science, mathematical formulas alone are far from enough; it also requires a real, hard-hitting experiment to prove its engineering value."

Hearing this, the corners of Professor Zhou Zhihua's mouth slightly raised, revealing a well-prepared smile.

"The experimental environment, I prepared it for you long ago."

He turned on the high-performance workstation in front of him that had been in a dormant state.

As the screen lit up, three deep compression model files with completely different architectures that had been packaged and compiled were neatly arranged on the desktop of the operating system.

"We use a classic industrial anomaly classification model as the benchmark," Professor Zhou Zhihua introduced. "The same raw high-dimensional training dataset, the same public test set. We used three of the most mainstream methods in the industry currently to compress this behemoth."

[Model A: Adopted the currently most radical structured pruning algorithm]

[Model B: Adopted tensor low-rank decomposition technology]

[Model C: Adopted a relatively conservative knowledge distillation strategy]

Subsequently, Professor Zhou Zhihua pulled up the eye-catching traditional benchmark results of these three models on the public test set.

[Model A: The average accuracy on the test set is as high as 96.7%, and its number of parameters is astonishingly reduced by 72%]

[Model B: The average accuracy is 96.5%, and the number of parameters is reduced by 61%]

[Model C: The average accuracy is the lowest, only 96.3%, and the number of parameters is only reduced by a pitiful 54%]

"If judged by the traditional evaluation metrics of major top conferences and the enterprise world currently," Professor Zhou Zhihua pointed at the screen, "Model A is definitely a well-deserved star and the optimal solution dreamed of by all engineers. Its volume has become extremely compact, its inference speed is extremely fast, and most incredibly, its accuracy is even the highest among the three."

"As for Model C, it has the lowest compression rate, consumes the most memory, and ranks at the bottom in accuracy on the public dataset, counting as a failure."

Jiang Lin looked at the data and asked calmly: "What about that hidden set that wasn't part of the test?"

"As you requested in your initial email, that crucial hidden set has been kept by another independent group of personnel from our college in the server room next door from start to finish." Professor Zhou Zhihua looked at Jiang Lin. "Until this very moment, all I know is that the hidden set contains a batch of high-risk long-tail states that never appeared in the public test set."

"How many samples are in the hidden set?"

"Forty-eight state pairs. They include high-risk boundary samples as well as low-cost control groups."

"Have the task loss and safe action sets been annotated in advance?"

"Independent annotation is complete. Incorrect actions in the high-risk group could result in losses exceeding hundreds of thousands of yuan."

"Do we have the permission to call it for testing?"

"As the final ruling, it can only be called once." Professor Zhou Zhihua held up a finger. "Whatever result comes out is the final result. There is no chance to modify the code and run it again."

"Once is enough," Jiang Lin said.

The researchers at Nanjing University imported the three sets of models one by one into the [Trustworthy Audit Script] whose interface had just been modified.

The script's backend came from the MPS-EvidenceGate universal counterexample search framework brought by Jiang Lin. The intermediate representations and public data of the three sets of models had been cached in advance, while the task loss matrix, evidence unit coverage radius, and local stability checks were new modules integrated during the discussion just now.

The audit process began running.

Step one: Based on the public data distribution and pre-defined permitted hypothesis families, the auditor demarcated potential divergence regions.

Step two: Extract counterexample witness bases with local coverage certificates from the divergence regions.

Step three: Check whether task collapse occurred in the three compressed models within the high-risk evidence units, and whether the corresponding local stability certificates still held true.

Computation began.

The CPU and GPU inside the workstation chassis instantly reached full load status, and power consumption skyrocketed.

That ordinary meeting room workstation was not equipped with the heterogeneous computing power scheduling system of the Wasteland Workspace No. 2, nor did it have a thermal weave network capable of making heat vanish into thin air.

When facing this high-intensity space traversal computation, the only thing it could rely on was the industrial fans inside the chassis with their voltage abruptly boosted.

Within just over a dozen seconds, the fans' rotational speed soared to the limit, emitting waves of muffled roaring sounds.

Everyone in the meeting room held their breath. No one spoke; only the monotonous and urgent roar of the fans echoed in the air, causing an inexplicable sense of palpitation.

Four long and agonizing minutes passed.

On the screen, the audit script finally spat out the first set of analysis results.

[Model A]

[Witness basis scale extracted for it: 37 pairs of high-risk divergence samples]

[Number of triggered task collapses: 12 times]

[Estimated coverage gap of unknown regions: 0.083]

[Underlying audit conclusion: REJECT]

Immediately afterwards, the second set of results popped up.

[Model B]

[Witness basis scale: 41 pairs]

[Number of triggered task collapses: 6 times]

[Estimated coverage gap: 0.047]

[Underlying audit conclusion: REJECT]

Finally, there was the third set, which appeared utterly mediocre through traditional eyes.

[Model C]

[Witness basis scale: 39 pairs]

[Task collapses above safety threshold: 0 times]

[Representation merge warnings below safety threshold: 1 time]

[Estimated coverage gap: 0.019]

[Underlying audit result: Conditionally Approved]

The audit results were filled with dramatic irony.

Model A—which had the highest accuracy on the public dataset, the smallest size, ran the fastest, and carried the high hopes of all engineers—was directly stamped with the death sentence of the REJECT label under this brutal underlying logical audit because it committed too many unforgivable task collapses in the marginal zones.

Yet Model C, which had performed most ordinarily in traditional benchmarks, was the only model that did not experience task collapse within the high-risk evidence units.

Professor Zhou Zhihua looked at the completely contrasting evaluation conclusions on the screen without rushing to call the final hidden set to verify right and wrong.

As a rigorous scientist, he deeply understood the importance of procedural justice.

"First, freeze all current states," Professor Zhou Zhihua said.

Jiang Lin generated an SHA-256 hash manifest for the three sets of models, witness bases, auditor source code, and all configuration parameters.

Subsequently, he and Professor Zhou Zhihua used their respective signature keys to confirm the manifest, writing the frozen package into a write-once data medium.

[Global version freeze time: 16:10:42]

The append-write audit log in the meeting room synchronously recorded the file hash, signature, execution environment, and unique test authorization code.

Four-twelve in the afternoon.

Li Yuan completed the media handover with the independent custodian of the hidden test group at the doorway. After checking the seal and signatures, the other party brought the frozen medium into the physically isolated server room next door.

The meeting room quieted down again.

The hidden test group would load the frozen package in a clean environment, execute a single pre-registered test, and return the results using another signed medium. The offline workstation in the meeting room never established a connection with external systems from start to finish.

The two returned to the long table and sat down.

The water on the table began to cool down again.

Professor Zhou Zhihua looked at the risk boundary on the whiteboard.

"Before you set out from Beijing, you probably weren't planning to complete a theorem here, right?"

"No," Jiang Lin said. "I originally just wanted to clearly define the interface for counterexample witness qualifications."

"And now?"

"The internal main chain under deterministic mapping has closed. However, written verification, random mapping expansion, continuous control conditions, and dynamic witness updates are still needed."

Professor Zhou Zhihua glanced at the time.

"It's already past a quarter past four. Are you still heading back to Beijing tonight?"

"Yes. First-piece trial production has just entered process verification, and I have things to do tomorrow."

Four-twenty-four in the afternoon.

The meeting room door opened once more.

The independent custodian placed a data medium with an intact seal and a paper handover form on the table.

Jiang Lin verified the signature and hash, confirming that the returned files came from the pre-registered environment.

The hidden results were imported into the read-only area.

Among the forty-eight state pairs, Model A experienced task collapse fifteen times above the safety threshold.

Model B experienced it seven times.

Model C did not experience high-risk task collapse, but showed an ordinary representation merge warning on a group of low-cost control samples.

The system outputted the results.

[Model A]

[Hidden task consistency rate: 68.75%]

[High-risk task collapses: 15 times]

[Model B]

[Hidden task consistency rate: 85.42%]

[High-risk task collapses: 7 times]

[Model C]

[Hidden task consistency rate: 97.92%]

[High-risk task fidelity rate: 100%]

[Representation merges below safety threshold: 1 time]

In the public test set, the average accuracy of Model A and Model C differed by only 0.4 percentage points.

On hidden tasks, the gap between the two approached thirty percentage points.

More importantly, the pre-freezing audit results had already rejected Model A and Model B while listing Model C as conditionally approved. The ranking of the three models was completely consistent with this pre-registered hidden test.

Jiang Lin rechecked the execution logs.

Only one call.

No interfaces were modified after freezing.

Signatures, hashes, and execution environments all matched.

This experiment could only prove that within this set of tasks, this hypothesis space, and this pre-registered hidden test, the auditor framework's judgment was validated.

It could not yet replace replication across more datasets, nor could it prove that all risks in the open world had been covered.

But the first foundation stone was firmly in place.

Professor Zhou Zhihua walked up to the whiteboard and wrote down the framework name.

[Evidence-Preserving Compression]

[Evidence-Preserving Compression]

Below were the results formed today, listed in order.

[Task discrimination loss: Definition completed]

[Counterexample witness basis with local coverage certificate: First version construction completed]

[Task risk upper bound under deterministic compression: Internal main chain closed]

[Pre-registered hidden set: First round verification passed]

[Joint paper: Entered written verification and expansion stage]

Professor Zhou Zhihua looked at the two sets of results displayed side by side.

"Compression theory has always been asking: how to complete a task with less information."

Jiang Lin picked up the thought.

"Now we must ask one more question."

"How to prove that what is completed after compression is still the original task."

On the left side of the screen was the audit judgment given before freezing.

On the right were the hidden test results they had never seen before.

The ranking of the three models was completely identical.

Applause did not immediately ring out in the meeting room.

The two professors from the Department of Mathematics near the whiteboard lowered their heads again, checking whether there were still unexplained dependencies hidden between the witness coverage certificate and the distribution drift term, comparing them against the four components of the task risk upper bound.

On the other side of the long table, several researchers responsible for model compression re-tabulated the public accuracy, compression ratio, and hidden task results into a single table.

Model A had the highest public accuracy.

The fewest parameters.

The fastest running speed.

Without today's audit framework, it would almost certainly have been the first of the three models to qualify for deployment.

But now, only a clear conclusion remained behind its result column.

[REJECT]

Not because it wasn't fast enough.

Nor because it wasn't accurate enough.

But because it lost its discriminative ability in places where confusion is truly impermissible.

Professor Sun looked at the reorganized table and spoke after a moment: "What this theorem truly changes is probably not how we evaluate a compression method."

Professor Zhou Zhihua turned his head.

"Then what is it?"

"It's when someone says in the future that a model still completes the original task after compression," Professor Sun pointed at the screen. "That statement can no longer be proven by just a table of average accuracy."

No one refuted.

Because the audit judgment on the left and the hidden results on the right were still parked side by side there.

They had already provided the first piece of evidence for that statement.

Professor Zhou Zhihua picked up the marker again and added another line below [Joint paper: Entered written verification and expansion stage].

[Next step: Independent review, random mapping expansion, continuous control verification]

"What closed today is the first main chain," he said. "Not the entire problem."

"Enough," Jiang Lin looked at the whiteboard. "At least from now on, we know where to head next."

This was already much better than leaving Nanjing with a problem that sounded very important yet had no idea how to verify.

When the afternoon discussion began, there were only three documents from different fields on the table.

One came from the loss ledger in mathematical proofs.

One came from the unified verifier that mistakenly accepted non-halting certificates.

One came from failed candidates in engineering systems that could not be completely deleted.

Several hours later, they were no longer just three similar cases.

Together, they formed an audit framework capable of defining, computing, rejecting, reviewing, and undergoing hidden testing.

Outside the window, the door at the end of the corridor was pushed open.

The evening light shone along the floor into the meeting room, crossed the table legs, and stopped beneath the whiteboard covered in formulas.

Jiang Lin lowered his head and saved the joint draft.

At the end of the file name was no longer [PROBLEM_DEFINED].

But — [EPC_Theorem_01_Internal_Closed]