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Chapter 195: Chapter 191: I’m Prepared to Elaborate

”Who’s first?”

Li Dong’s voice echoed through Sunshine Hall.

Among the several hundred people in the audience, not a single person spoke.

It wasn’t that they didn’t want to ask questions; it was that there was nothing left to ask.

Everyone present knew exactly what had happened over the past half hour.

Of the thirteen core criticisms mentioned in the arXiv comments, more than half had already been ”casually addressed” during Li Dong’s derivation.

Li Dong waited a few seconds. Seeing that no one was speaking up, he began.

”In that case, I’ll start calling on people.”

He leaned on the lectern with both hands, gazing at the crowd below. He held no notes or script.

”Professor Harold Wilkins, are you here?”

As soon as the name was spoken, a stir went through the audience.

Harold Wilkins.

A professor of analytic number theory at the Swiss Federal Institute of Technology Zurich, he had posted a rather weighty comment on arXiv.

The question was: [When using spectral operators in Chapter 5 to control the GUE convergence of the pair correlation function F_π(α) for |α| in the interval [2, 3],

does the positive-definiteness condition of the dynamic adaptive Fourier weight function set used rely on an implicit assumption of the GRH?

If the GRH were to fail at certain local places, would this set of weight functions degenerate to being semi-positive definite, thereby causing the entire framework for remainder term control to collapse?]

Quite a few people on arXiv had endorsed this question, making it seem very insightful.

”I’m here.”

Wilkins raised a hand.

Li Dong nodded at him. His tone was polite, without a trace of hostility.

”Professor Wilkins, regarding your question, I actually provided a complete answer earlier when I was discussing the section on remainder term control.”

”But I believe the fundamental reason you raised this question isn’t about an implicit assumption of the GRH.”

Li Dong paused for a moment.

”It’s that when you were trying to understand my set of weight functions, you treated it as a fixed set of filters.”

”But it’s not.”

”The function set I designed is, in essence, a family of operators that evolves dynamically with |α|. Its positive-definiteness is not a prerequisite that needs additional verification; rather, it is a structural property naturally inherited from the self-adjointness of the spectral operator.”

Li Dong’s tone remained polite.

”In other words, you mistook the conclusion for the premise, which is why you thought it needed to rely on the GRH.”

”Your starting point for this line of thought was flawed from the beginning.”

He smiled.

”Understand?”

The audience was silent for two seconds.

The color drained from Wilkins’s face.

The words were indeed polite. You couldn’t find any fault with them.

But translated into plain English, it meant:

’You don’t understand the basic concepts, which is why you asked a question you shouldn’t have.’

Wilkins nodded awkwardly.

After speaking, Li Dong paid him no more mind and looked in another direction.

”Is Professor Wang Zhiqiang here?”

When this name was called, several people nearby who knew Wang Zhiqiang subconsciously turned to look at him.

Wang Zhiqiang was sitting in the middle section, toward the right. He really didn’t want to engage with Li Dong.

But he couldn’t ignore the fact that everyone around him was staring.

He could only raise his hand slightly to indicate his presence.

Li Dong smiled.

”Professor Wang, long time no see.”

”Last time at the ICCM, you said my algorithm should be shared so everyone could optimize it together.”

”Now that my paper has been publicly available for so long, have you... made any progress on that optimization?”

The entire hall fell deathly silent.

Then, a few young scholars in the back rows couldn’t hold it in and let out a ”PFFT” of laughter.

Wang Zhiqiang’s face instantly turned beet red.

’Optimize? Optimize my ass! I haven’t even fully understood the core derivation of Li Dong’s paper, and he’s asking about optimization?’

Seeing he didn’t respond, Li Dong didn’t press him further. Instead, his tone shifted.

”Just kidding, Professor Wang. Don’t mind me.”

”But on a serious note, about that question you raised on arXiv... let me think...”

”It was about whether, when applying the zero criterion in GL(n) automorphic representations, the scale transformation of the normalized imaginary parts of the zeros would affect the pointwise convergence rate of the pair correlation function F_π(α) with the GUE prediction in the small |α| interval, correct?”

Wang Zhiqiang was taken aback for a moment.

’It’s been almost two weeks since I posted that comment. How can Li Dong recite my core question word for word?’

”Professor Wang, that’s a very fundamental question.”

When Li Dong said this, his tone was extremely serious, with no hint of mockery.

”But precisely because it’s so fundamental, it actually serves as an excellent entry point for popular science.”

Li Dong continued.

”The scale transformation of the normalized imaginary parts of the zeros is, in essence, just a coordinate transformation under a symmetry constraint.”

”This transformation doesn’t affect the pointwise convergence rate because the GUE kernel function itself possesses scale invariance. This is one of the most basic properties in random matrix theory.”

”I think if this concept were turned into a popular science lecture for high school students across the country, helping them understand the idea that ’a coordinate transformation does not change the physical substance’ would be immensely helpful in developing their mathematical intuition.”

As Li Dong said this, his eyes were sincere and his tone was earnest.

However, the more he acted this way, the darker Wang Zhiqiang’s expression became.

’What’s he trying to say?’

’That my question is at a high school level?’

The atmosphere in the audience grew even more peculiar.

Some people didn’t dare to laugh, but they could no longer suppress the smiles tugging at their lips.

This time, Li Dong didn’t ask him, ”Understand?”

He moved directly on to the next person.

”Professor Robert Mason?”

A British scholar sitting in the middle rows on the left flinched.

”Dr. Andrei Kovalevsky?”

A young scholar of Russian descent instantly went pale.

”Associate Professor Liu Jianhua from Capital University?”

No one answered.

Li Dong didn’t seem to mind and continued to the next name.

One, two, three...

He held no notes, relying entirely on his memory.

Everyone in the audience finally realized something.

Li Dong hadn’t just memorized the entire content of all thirteen comments on arXiv; he had even memorized the name signed to each one.

And every person he called on felt like a student being randomly picked by a teacher to recite a lesson, as if they were facing a life-or-death trial.

If his former classmates from the honors class at Sixth Middle School were here, they would surely say:

’This is King Yama calling the roll, you know?’

’Do you know how he used to question us?’

”’Classmate, I don’t understand why your problem-solving method is so... unsophisticated. Could you analyze your thought process for me at that moment?’”

It was the exact same formula, just transplanted from a high school classroom to an international academic conference.

Some names were called, but no one answered at all.

Li Dong didn’t know whether they were actually in attendance or not.

But he didn’t care. Once he called a name, he moved on.

Finally.

Li Dong’s gaze fell on a spot in the front row, slightly to the left.

Zhou Shenzhi.

Their eyes met in mid-air.

Zhou Shenzhi did not look away.

He met Li Dong’s gaze, his own calm and composed.

Among all the people present who had posted comments, only Zhou Shenzhi’s eyes showed no sign of panic.

Because he knew his question wasn’t due to a lack of understanding, but was deliberately posed.

Li Dong looked at him and smiled.

”Professor Zhou.”

Zhou Shenzhi gave a slight nod.

”I believe the three questions you raised about the skipped steps have already been answered.”

Zhou Shenzhi nodded as well. Indeed, those three issues had been fully elaborated upon during Li Dong’s derivation; there was nothing more to ask.

”But...”

Li Dong’s tone suddenly grew serious.

”Your fourth question.”

”Regarding the application of the zero criterion in the case where the ramification index e_v ≥ 3 for a GL(n) automorphic representation, and the problem of an explicit comparison path between the GUE convergence of the pair correlation function and the High Tier coupling structure of Hodge-Tate weights.”

Li Dong paused after saying this.

”I find this question very interesting.”

Zhou Shenzhi was stunned.

He had originally expected Li Dong to say something like, ”This question is beyond the scope of this paper,” and kick the can back to him.

He never expected Li Dong to say it was ”very interesting.”

He was even more surprised by what Li Dong said next.

”I’m prepared to elaborate on it.”

Zhou Shenzhi stared blankly at the young man on the stage.

’Elaborate on it?’

’This was the core problem that had stumped *him*.’

’And Li Dong was going to break it down right here and now?’

Zhou Shenzhi was silent for two seconds.

Then, he gave a slight nod toward the stage.

He took a notebook out of his briefcase.

He turned to a fresh page.

And uncapped his pen.