Chapter 337 - 287: Do Not Use ’Petty Cleverness’ as a Means for Scientific Advancement

Chapter 337: Chapter 287: Do Not Use ’Petty Cleverness’ as a Means for Scientific Advancement

It was only then that Li Dong fully understood. The thing he had feared most had already happened.

He raised his head and looked around at the people in the lab.

Teacher Su was leaning against the door of the vacuum chamber, his eyes a little vacant.

He was a junior researcher personally mentored by Wu Kai and had only been at the university for two or three years. His child was just six months old.

If the project team really couldn’t survive this, his junior researcher salary was supporting a family of three.

Zhang Yan had been with Wu Kai since her master’s and doctoral studies, spending a total of eight years in this room.

The hand she used to clutch her tablet was trembling today.

Cheng Duo, Lu Heng, Shen Ying, and Guo Han were still young...

But being young came with its own set of difficulties.

If the funding was cut, their stipends wouldn’t be paid out next month.

They would either have to switch groups or change their research direction.

Li Dong said nothing.

He couldn’t make empty boasts in this room.

Not even when he was inwardly certain that ’They’re just gambling.’

But right now, he didn’t have a single line of a counterexample to show for it.

He simply hugged the copy of *Inverse Problems* to his chest.

He stood up.

And said to Lu Mingyuan,

"Teacher Lu."

"I’m going to take this journal back with me to have a look."

Lu Mingyuan nodded.

Li Dong turned his head again and glanced at Wu Kai.

Wu Kai gave him a wry smile.

Li Dong didn’t say another word.

He just turned and walked out of the lab.

...

Dorm Room 404.

When Li Dong pushed the door open, his three roommates weren’t there.

Li Dong spread the copy of *Inverse Problems* out on his desk.

He switched on his desk lamp.

Deep down, he actually trusted his intuition a great deal.

But what his intuition was up against now was a paper published in the flagship journal for the field of inverse problems.

He could only suppress his intuition for now and seriously examine how the author had written it.

Li Dong turned to the first page.

When Li Dong first started reading the paper, he did so with a fault-finding mindset.

But after reading three or four pages...

He set aside his intention to "find fault."

This paper was truly beautifully written.

Engelhardt had constructed the mathematical framework for the entire hybrid Tikhonov-variational scheme with solid stability.

Section one laid out the kernel estimation of the ill-posed operator.

Section two introduced an inner iteration with cyclic weights, providing a concrete construction of the cyclic weight family.

Section three wrote down the energy functional of the third coordination shell as a variational constraint, with the Euler-Lagrange Equations presented with perfect clarity.

Section four proved that under a set of reasonable assumptions, this iterative scheme converges, and it provided a clear rate of convergence.

Section five gave a set of sufficient conditions required for the reuse of the residual phase.

Section six, a few numerical simulations.

Li Dong grabbed a pen.

Starting from the first lemma, he began to verify it line by line.

Lemma 1: Lipschitz stability of the operator.

Checked out.

Lemma 2: Compactness of the cyclic weight family.

Checked out.

Theorem 1: Under the effect of the cyclic weights, the iterative sequence converges weakly in Sobolev space.

He re-derived the proof himself. Every step was clean.

Checked out.

Next was the paper’s true lifeline.

Theorem 2.

Theorem 2 stated that under the set of assumptions they provided, the total iteration of the entire hybrid scheme converges to the true solution of the inverse problem.

This was the key to whether the paper could stand on its own.

Li Dong took a deep breath.

He began to work through the proof, starting from the first line.

Engelhardt used an exceptionally clever energy estimation.

He bridged the residual between the third and fifth shells using a mild truncation function.

The choice of this truncation function was brilliant. It just so happened to allow the divergent term that gave everyone a headache to be swallowed up by the adaptive cyclic weights.

Li Dong stared at this section for a long time.

He had to admit, the author’s technique was truly exquisite.

There wasn’t a single flaw in this section that Li Dong could pick out on the spot.

He continued working through it.

Theorem 3, Corollary 1, Corollary 2...

Every step checked out.

Finally, for the numerical simulations in section six, Li Dong ran them himself using the synthetic data they provided.

The error between the inversion result and the true value did indeed converge beautifully, just as they claimed.

Li Dong closed the paper, leaned back in his chair, and let out a long breath.

Outside the window, the sky had already turned completely dark.

He didn’t know how many hours he had been reading.

He only knew that, from beginning to end...

This paper, every single line, was correct.

But why did it feel more and more wrong the longer he read it?

It was just a sense of wrongness he couldn’t put his finger on.

It was like a beautifully constructed skyscraper.

The roof, the walls, the glass curtain—it was all real.

But it had no foundation. The problem was, it wasn’t collapsing!

Li Dong stared at the copy of *Inverse Problems* for a long time.

He suddenly thought of a solution.

’What if...’

’I ask someone?’

He pulled out his phone.

And opened the [Cyan Dragon Study Group].

The person he was looking for today was someone who truly understood applied mathematics, truly understood inverse problems, and could truly sit down with him and tear this paper apart piece by piece—

A true master.

He scrolled down the list of group members, one by one.

When he came across a certain name...

Li Dong’s finger stopped.

[Andrei Nikolaevich Tikhonov].

Tikhonov.

The first time Li Dong joined Wu Kai’s group, he had slogged through Engl’s book, *Inverse Problems*.

Chapter one, introduction, page three, the second-to-last paragraph.

His name was right there.

In 1943, the Soviet Union mathematician Tikhonov proposed a concept...

"Well-posedness."

In 1963, Tikhonov concretized it, publishing the foundational paper—named after himself—that would dominate the field of inverse problems for a full sixty years.

Tikhonov regularization.

That’s right. The same "Tikhonov" that Engelhardt had in his title.

Engelhardt and his people...

All of their cyclic weights, adaptive iterations, spectral truncations, and variational couplings...

...were all second-order evolutions built upon that old gentleman’s 1963 paper.

If there was anyone who could see through Engelhardt’s paper at a single glance...

...that person had to be Tikhonov.

But the problem was...

Tikhonov had never once spoken in the group.

’I can’t just go and ask him straight away, can I?’

He thought about how Klein had made contact with him...

That time, Li Dong had used one of his file transfers to send over the Langlands Program.

’The number of file transfers.’

Li Dong opened his own attribute panel.

[Remaining File Transfers: 1]

’Only one left.’

He was a bit reluctant to use it. After all, this was his safety net.

’If I use it this time... then the next time a truly critical, game-changing moment comes up, I won’t have any left.’

’Then again... isn’t this situation right now a critical moment?’

Li Dong took a deep breath.

’Screw it, I’m using it!’

He opened the file transfer function.

He scanned the paper page by page—from the abstract, theorems, lemmas, and proofs, all the way to the supplementary materials—and compiled it into a PDF.

He selected the recipient.

[Andrei Nikolaevich Tikhonov].

A line of small text popped up on the screen.

[Sending...]

One second, two seconds, five seconds.

[Send Failed.]

Li Dong froze for a moment.

He leaned closer to the screen.

Below the "Send Failed" line was another line of small text.

[Group Alert: This group strictly prohibits the use of the file transfer function to disseminate research materials that have been cleverly contrived, embellished, or are not rigorously proven.]

[The Group Leader is asked to verify the scientific rigor of the file’s source and to refrain from using "clever tricks" as a means of advancing research.]

[This transmission has been automatically canceled. The file transfer use was not consumed.]

[Remaining File Transfers: 1]

Li Dong stared at the group alert, his mind buzzing...

This was the first time he had ever gotten this kind of alert when using the file transfer function.

And this alert meant one thing: this paper really did have a problem!

His intuition hadn’t been wrong, he just hadn’t been able to see it.

But Li Dong wasn’t disappointed. Instead, he suddenly smiled.

’Well, well, well.’

’So you’re trying to pull a fast one on me, huh?’

’Fine.’

He was the dignified Group Leader of the Cyan Dragon Study Group.

And he hadn’t even seen through their little trick.

That bit of shame in Li Dong’s heart morphed into something else.

He looked at the screen and muttered to himself.

"I really can’t find it right now."

"But you just wait."