The top student must be diligent.

Chapter 259: Request for the H- Project
Just as Xiao Yi expected, when he found the method of Diophantus' approximation to solve this problem, he solved it with great success.

"Now, I have found a unified method that can directly generate invariant vectors in each representation space."

After Xiao Yi successfully constructed this method on the draft paper, all the problems seemed to become clear before him.

As for the idea of ​​using Diophantine approximation, the method found is by no means limited to this problem.

It can be applied to various representation spaces and can unify these problems into a Diophantine equation.

In other words, to some extent, he directly made the relationship between Diophantus' theory and representation theory closer!
This can be regarded as an important breakthrough in the Langlands Program!
After all, although the geometric Langlands conjecture has been proved, the Langlands conjecture has not yet been solved.

These are two completely different conjectures, just like the geometric Langlands program and the Langlands program, which are different concepts and are independent of each other.

Perhaps his achievement can help prove the Langlands conjecture?
At least his intuition told him that it was possible.

However, whether to study the Langlands conjecture is not something he will consider for the time being. If he has the energy to study the Langlands conjecture, he would rather try the "ultimate" conjecture, the Riemann hypothesis.

As for now...

Let’s first consider the questions behind the hail hypothesis.

However, the following questions have indeed become simpler.

“It’s simple, but it’s a key point.”

"Use this unified method of generating invariant vectors to classify periodic orbits..."

Xiao Yi narrowed his eyes slightly and began to think.

"First, let's review the previous process. Since each invariant vector can be obtained by solving a Diophantine equation group, then we first assume that v=(v_1, v_2, ..., v_n) is an invariant vector, which satisfies such an equation group..."

【3v_i + 1 = v_j, if i is an odd number and H_i=(3i+1, i)
v_i/2 = v_k, if i is even and H_i=(i/2, i)]

"A periodic orbit of length 1 corresponds to a fixed point, that is, an invariant vector that satisfies v_i=i. Obviously, this condition is only satisfied when v_1=1."

"Then there is a periodic orbit of length 2..."

"Then there are longer periodic orbits..."

Following Xiao Yi's thinking, the research on the problem has reached a very in-depth level.

After using up more than ten pages of draft paper, Xiao Yi looked at the complete derivation process and the result he finally got, and was suddenly stunned.

At this time, he successfully constructed a tree structure of periodic orbits, and this tree structure was gradually recursive.

However, from observation, he could clearly see that all possible periodic orbits of hailstone sequences could be completely classified using a recursive tree structure.

Each layer of this structure corresponds to a periodic orbit of fixed length, and the branches of the tree correspond to the evolution from one periodic orbit to another longer periodic orbit.

That is to say, at this time, if he wanted to prove the hailstone conjecture, he only needed to prove: if the classification tree is infinite, then there must be a starting number whose corresponding hailstone sequence does not enter any periodic orbit, which would contradict the hailstone conjecture.

Therefore, in order to prove the hailstone conjecture, one only needs to prove that the classification tree is finite, and then he can complete the hailstone conjecture!
"So, this leads to this final question?"

Xiao Yi felt a little surprised.

Isn’t it a bit...

Simple?

Now, he only needs to complete this last proposition to completely prove the hail conjecture.

Although this proposition seems to be very difficult, but from his intuition, if you really want to solve this problem, it won't be particularly troublesome.

However, thinking back on the time since he began studying the hail conjecture, it seems that he has not encountered too many difficulties?
Until now, in just about a month, he has already reached this final step.

"This is probably... the horror of level 7."

Xiao Yi sighed in his heart.

After all, he has no shortage of inspiration, so solving the conjecture is just a matter of time, right?
For a moment, he even began to think, "The next question is, should I directly study the Riemann hypothesis?"

It seems like there is a lot of potential!
If we really talk about difficulty, the hailstone conjecture is definitely not as difficult as the Riemann hypothesis. After all, the hailstone conjecture was born less than a hundred years ago, while the Riemann hypothesis was born more than a hundred years ago.

The most important thing is that there are definitely not as many mathematicians studying the hailstone conjecture as there are studying the Riemann hypothesis.

However, the mathematical community still recognizes the difficulty of the hail conjecture. Otherwise, the great mathematician Erdős would not have lamented that modern mathematics is not yet ready to face such a problem.

For a moment, Xiao Yi's heart began to stir.

Of course, if you really want to study the Riemann hypothesis, you should wait until the current hailstone hypothesis is completed.

Refocus your attention on the hail conjecture in front of you.

"Then let's continue."

However, at this moment, perhaps God didn't want him to solve this conjecture so calmly, his cell phone suddenly rang.

I saw the caller was Director Liu.

His eyebrows raised slightly. Why was Liu Cong calling him now?
Logically speaking, there shouldn't be anything important going on during this period of time, right?
Are they planning to build a new nuclear fusion reactor and invite him to serve as a consultant?
Confused, he also answered the phone and asked, "Director Liu, what's going on today?"

However, Director Liu's voice was unusually serious, and he said, "Chief Engineer Xiao, this time it's quite important, I have to ask you for help, this is very important to the country!"

Xiao Yi was stunned for a moment, then he frowned and asked, "What's the matter? Tell me."

"I'm going to the Science Island Laboratory soon. We can talk in person then. It's not convenient over the phone."

"Okay, I'm at HKUST right now, I'll go back to the Science Island lab now."

"it is good."

After hanging up the phone, thinking of Director Liu's anxious tone, Xiao Yi didn't say much. He simply tidied up the desk, then notified Wang Li and prepared to drive him back to the Science Island Laboratory.

……

Soon, Xiao Yi returned to the Science Island Laboratory.

Today, the Science Island Laboratory is completely surrounded by a wall from the outside, and inside is the Science Island Laboratory Park.

Now it can probably be called a research institute.

Of course, whether it is a laboratory or a research institute, it is the same.

Therefore, there was no change in the name, and Xiao Yi remained the director of the laboratory.

When the security guard at the gate saw that it was Director Xiao's car, he raised his hand and saluted, then walked forward and said, "Director Xiao, Director Liu has arrived and is waiting in the reception room. However, in addition to Director Liu, there seem to be three other people. I don't know who they are."

"Okay, thank you."

Xiao Yi nodded slightly and thought for a moment. In addition to Director Liu, there are three other people?
Who is it?
Then the car drove in again and finally stopped in front of the administrative building.

Xiao Yi quickly went upstairs, came to the reception room, and met Director Liu.

In addition to Director Liu, there are indeed three other people.

Xiao Yi didn’t know two of them, but he was very familiar with the other one.

It was Luo Mingya.

When Xiao Yi saw Luo Mingya, he showed a little surprise on his face. Luo Mingya blinked, as if to indicate that she didn't know the situation either.

At this time, Xiao Yi's assistant Wang Hao was in charge of the reception. When he saw the leader coming in, he also stood up and gestured.

Xiao Yi nodded to Wang Hao, then walked forward and greeted Liu Cong.

"Old Liu, you are really a busy man now."

Liu Cong smiled and said, "We are all serving the country, so it's normal to be busy."

Xiao Yi nodded slightly.

Of course, he had heard that Liu Cong had been promoted further in rank because of his contributions to controlled nuclear fusion, and he would probably step down as director and take up a new position next year.

However, looking at Liu Cong's gray hair, he is already in his sixties this year, and he can be said to have finally made it.

"Okay, let's not talk about me for now. Let me introduce these three to you."

Then, Director Liu pointed to the other three people in the room.

"These three are researchers in the H-20 strategic bomber research project."

Upon hearing this introduction, Xiao Yi raised his brows.

It’s actually the H-20?

So, the place that Luo Mingya went to was actually responsible for the research on the H-20?
No wonder secrecy is required.

However, now these people come to him, are they asking him to help with the research of the H-20?
"This is the chief designer Wang Changhong."

Liu Cong began by introducing the first one, who was also a heavyweight.

Xiao Yi was surprised, walked forward and shook hands with him: "It turns out to be Chief Engineer Wang, I have heard of your name for a long time."

Wang Changhong smiled and said, "How dare I call myself Chief Designer in front of Chief Designer Xiao! We studied the H-20 to fill the gap in our strategic bombers and catch up with foreign countries. However, nuclear fusion has truly set a benchmark for us for the whole world. Now it is the American group that wants to fill the gap in this area!"

Xiao Yi waved his hand: "It's all the same, just like what Director Liu said just now, we are all serving the country."

Wang Changhong smiled, "What Chief Engineer Xiao said makes sense!"

Liu Cong beside him also smiled, and then continued to introduce the next person: "This is the leader of the H-20 aircraft engine materials research group, Professor Li Zhenhai."

"Chief Professor Xiao, you are young and promising." Li Zhenhai looks to be in his forties, which makes him relatively young among all the professors.

"Hello, Professor Li." Xiao Yi shook hands with Li Zhenhai.

"As for this girl..."

Liu Cong smiled, glanced at Luo Mingya, and then said to Xiao Yi.

Xiao Yi waved his hand, "No need to introduce, I know him."

After all, he and Luo Mingya had collaborated on a paper, which could be checked, so he didn't think these people didn't know about it.

Li Zhenhai smiled and said, "I've always heard that Xiao Luo and Chief Engineer Xiao know each other, and now it's confirmed. Xiao Luo is also the backbone of our team and is also responsible for an important research task."

"I brought Xiao Luo with me this time in the hope that I could convince Chief Engineer Xiao to help us."

Xiao Yi quickly captured the key words.

"help?"

Several people nodded.

Liu Cong became serious again at this time, took out a document from his briefcase and handed it to Xiao Yi.

Xiao Yi took a look at the document and found that it was a judgment of the General Staff on the current international situation. It believed that given the current international situation, especially considering the impact of controlled nuclear fusion technology, the possibility of a small to medium-scale battle around China in the future was quite high.

Especially as time goes by, when Americans gradually realize that controlled nuclear fusion technology is really difficult to master, and at the same time they are completely unable to obtain the secrets of nuclear fusion technology through some dirty means, the possibility of a battle will become higher and higher.

"Therefore, the Military Commission believes that we must fill all gaps in military equipment as soon as possible, especially in the area of ​​strategic bombers, to achieve a more complete strategic deterrence."

Liu Cong said: "Of course, even if a small or medium-sized battle really occurs at that time, it is highly likely that equipment of this level of strategic bombers will not be used."

"However, this also shows that the main purpose is to fill our gaps in this area and achieve a stronger deterrent capability."

"By then, even if our H-20 really flies out for a while, it will most likely make them more cautious when they really start a war."

Xiao Yi nodded slightly, feeling somewhat unexpected, yet also reasonable.

The possibility of war is never zero.

Then, Wang Changhong said: "However, there is a key problem now. Our current engine technology, especially in terms of materials, cannot achieve good compatibility with the H-20, and its performance cannot meet our requirements."

"So, we thought of you."

"Chief Engineer Xiao, we are able to research the first wall material that meets the needs of nuclear fusion. We also believe that you can help us complete the research on this material."

Chief Engineer Wang Changhong bowed sincerely to Xiao Yi and said, "I really leave it to you."

Li Zhenhai, who was standing by, quickly pulled Chief Engineer Wang and said, "Boss Wang, I should be the one saying this. After all, I'm the leader of the materials team! It's all my fault that they haven't figured it out yet!"

Wang Changhong shook his head: "No, I am the chief designer after all, I have to take responsibility for this responsibility, so I have to say this!"

The two of them performed a double act in front of Xiao Yi.

Xiao Yi curled the corner of his mouth and glanced at Luo Mingya beside him.

Luo Mingya also looked embarrassed, probably because she didn't expect that her team leader and chief engineer could stage such a drama so skillfully.

Looking at Liu Cong again, although he was still smiling, it was obviously a bit forced.

Xiao Yi coughed twice and said, "Okay, you two, it's not that serious. I agree to this matter."

Wang Changhong and Li Zhenhai's eyes suddenly lit up, then they put away their double-act expressions and said, "I knew Chief Engineer Xiao would definitely agree."

"Master Xiao, I don't submit to anyone else in the world except you!"

Liu Cong said helplessly, "You two, I think you two should save yourselves. I didn't know you were planning to stage this. When did you discuss this?"

Wang Changhong coughed and said, "There was no discussion. It was all involuntary. There was no room for discussion."

Li Zhenhai also nodded: "Yes, I can't help it."

Liu Cong shook his head: "Okay, that's because you two have such good chemistry, it's so natural that you don't even have to act."

"Director Liu, please stop slandering me! What if Chief Engineer Xiao misunderstands me?"

Liu Cong spread his hands, then looked at Xiao Yi and said, "Okay, since you agreed, then, do you have any requirements in this regard? When can we start the research?"

"I don't have any requirements." Xiao Yi waved his hand: "We can start research at any time."

"it is good!"

……

(End of this chapter)