Just as Xiao Yi expected, when he found a way to solve this problem using Diophantine approximation, the problem was solved by him like a broken bamboo.
"Now I have found a unified method that directly generates invariant vectors in every representation space."
After Xiao Yi successfully constructed this method on the scratch paper, all the problems seemed to become clear in front of him.
As for the idea of using Diophantine approximation, the method found is by no means only applicable to this problem.
It can be applied to various representation spaces and uniformly transform these problems into a Diophantine equation.
In other words, to a certain extent, he directly connected the relationship between Diophantine theory and Representation Theory more closely!
This can be called an important breakthrough in Langlands Program!
After all, although Geometric Langlands Conjecture has been proven, the Langlands conjecture has not yet been solved.
These are two completely different conjectures, just like geometry Langlands Program and Langlands Program. They are also different concepts and are independent of each other.
Maybe his result can help prove the Langlands conjecture?
At least his instinct told him that it was possible.
However, he has not considered whether to study the Langlands conjecture for the time being. If he has the energy to study the Langlands conjecture, he is still more willing to try the "ultimate" conjecture, Riemann Hypothesis.
As for now...
Let's consider the issues behind Hailstone Conjecture first.
However, the subsequent questions have indeed become simpler.
"Although it is simple, it is also a key point."
"Use this unified invariant vector generation method to achieve the classification of periodic orbits..."
Xiao Yi narrowed his eyes slightly and started thinking.
"First of all, let's review the previous process. Since each invariant vector can be obtained by solving a Diophantine equation system, then, let us first assume that v=(v_1, v_2,., v_n) is an invariant vector, then it satisfies such a system of equations..."
[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 an even number 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. Well, obviously, this condition is satisfied only when v_1=1."
"Then there are periodic orbits of length 2..."
"Then there will be longer periodic orbits..."
Following Xiao Yi's thinking, the research on the problem has reached a very in-depth stage.
After more than ten pages of draft paper had been used, Xiao Yi was suddenly stunned when he looked at the complete derivation process above and the final result he obtained.
At this time, he successfully constructed a tree-like structure of periodic orbits, and this tree-like structure was gradually recursive.
However, it became clear to him from observation that all possible periodic orbits of hailstone sequences could be completely classified using a recursive tree structure.
Each level of this structure corresponds to a fixed-length periodic orbit, while the branches of the tree correspond to the evolution from one periodic orbit to another longer period orbit.
In other words, at this time, if he wants to prove Hailstone Conjecture, he only needs to prove: if this classification tree is infinite, then there must be a starting number whose corresponding hail sequence does not enter any periodic orbit, and this will contradict Hailstone Conjecture.
Therefore, in order to prove Hailstone Conjecture, one only needs to prove that the classification tree is finite, then he can complete Hailstone Conjecture!
"In this way, this final question is derived?"
Xiao Yi felt a little surprised.
Isn't it a bit...
Simple?
Now, as long as he completes this last proposition, he can completely prove Hailstone Conjecture.
Although the difficulty of this proposition seems to be very high, from his intuition, if he really wants to solve this problem, it will not be particularly troublesome.
However, looking back on the time since he started studying Hailstone Conjecture, it seems that he has not encountered too many difficulties, right?
Until now, in only about a month, he has researched 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 or anything else. If he can solve his conjecture, wouldn't that mean he has to rush for orders?
For a moment, he even started to think, "The next question is, should we study Riemann Hypothesis directly?"
It seems like there's a lot to be done!
If we really want to talk about difficulty, Hailstone Conjecture is definitely not as difficult as Riemann Hypothesis. After all, Hailstone Conjecture was born less than a hundred years ago, while Riemann Hypothesis has been around for more than a hundred years.
The most important thing is that there are definitely not as many mathematicians studying Hailstone Conjecture as there are those studying Riemann Hypothesis.
However, the mathematics community still recognizes the difficulty of Hailstone Conjecture. Otherwise, the great mathematician Erdos at the time would not lament that current mathematics is not ready to face such a problem.
For a moment, Xiao Yi's heart began to stir.
Of course, if you really want to study Riemann Hypothesis, you should wait until the current Hailstone Conjecture is completed.
Focus your attention again on Hailstone Conjecture in front of you.
"Then keep going."
However, at this moment, probably because God didn't want him to solve this conjecture just like that, his cell phone suddenly rang.
When I looked at the caller, I saw it was Director Liu.
He raised his eyebrows slightly, why did Liu Cong call him now?
Logically speaking, there is nothing important during this time, right?
Are you planning to build a new nuclear fusion reactor now and ask him to serve as a consultant?
In doubt, he also answered the phone and asked, "Director Liu, is there anything else going on today?"
However, Director Liu's voice was extremely serious and said, "Chief Designer Xiao, there is something very important this time. I have to ask you for help. This is very important to the country!"
Xiao Yi was stunned for a moment, then raised his eyebrows and asked, "What is it? Just tell me."
"I'm going to Science Island Laboratory soon. We'll talk in person then. It's not convenient over the phone."
"Okay, I'm at USTC now, and I'll go back to Science Island Laboratory now."
"Okay."
After hanging up the phone, thinking of Director Liu's irritable tone, Xiao Yi didn't say much. He simply cleaned up the desktop, and then notified Wang Li, preparing to drive him back to Science Island Laboratory.
Soon, Xiao Yi returned Science Island Laboratory.
Today, Science Island Laboratory is completely surrounded by a wall from the outside, and the Science Island Laboratory campus is inside.
Now it can probably be called a research institute.
Of course, it is the same whether it is a laboratory or a research institute.
Therefore, there is no change in name, and Xiao Yi remains 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 stepped forward and said, "Director Xiao, Director Liu has arrived and is waiting in the reception room. However, in addition to Director Liu, it seems that there are three other people. I don't know who they are."
"Okay, thank you."
Xiao Yi nodded slightly and thought for a moment, besides Director Liu, are there three other people?
Who could it be?
Then the car drove in again and finally stopped in front of the administration building.
Xiao Yi quickly went upstairs, came to the reception room, and saw Director Liu.
In addition to Director Liu, there are indeed three other people.
Two of them, Xiao Yi, didn't know each other, but the other one, Xiao Yi, was very familiar with them.
It is Luo Mingya.
When Xiao Yi saw Luo Mingya, there was a little surprise on his face.
Luo Mingya blinked, as if to express that he didn't know the situation.
At this time, Xiao Yi's assistant Wang Hao was in charge of entertaining. When he saw the leader coming in, he also stood up to signal.
Xiao Yi nodded towards Wang Hao, then walked forward and greeted Liu Cong.
"Lao Liu, you are really a busy man now."
Liu Cong smiled and said, "They are all serving the country. It's normal to be busy."
Xiao Yi nodded slightly.
Of course, he has heard that Liu Cong has also advanced in level due to his contribution to controllable nuclear fusion. He will probably step down from the position of director next year and take over a new position.
However, looking at Liu Cong's gray hair, he is already in his sixties this year, and he has indeed managed to survive.
"Okay, don't talk about me for now. Let me introduce these three to you."
Then, Director Liu pointed at the other three people in the room.
"These three are all researchers on the H-20 strategic bomber research project."
Upon hearing this introduction, Xiao Yi's eyebrows raised.
It turned out to be H-20?
So, where Luo Mingya went, it turned out that he was responsible for the research on H-20?
No wonder secrecy is needed.
However, now that these people are coming to him, are they asking him to help with H-20's research?
"This is Chief Designer Wang Changhong."
Liu Cong introduced the first one, and the first one was directly the heavyweight.
Xiao Yi was surprised for a while, stepped forward and shook hands with this person. "It turns out to be General Master Wang, whose name I have admired for a long time."
Wang Changhong smiled and said, "How dare I call myself the commander-in-chief in front of Chief Designer Xiao! Ultimately, our study of H-20 is to make up for our gaps in strategic bombers and catch up with foreign levels. However, nuclear fusion really allows us to set a benchmark for the world. Now it's the United States who want to make up for the gaps in this area!"
Xiao Yi waved his hand. "It's all the same, just like what Director Liu said just now, we all serve the country."
Wang Changhong smiled, "What Chief Designer Xiao said makes sense!"
Liu Cong next to him also smiled, and then continued to introduce the next person, "This is the leader of the H-20 aeroengine materials research group, Professor Li Zhenhai."
"Chief Designer Xiao, you are young and promising." Li Zhenhai looks to be in his forties, which is relatively young among various professors.
"Hello, Professor Li." Xiao Yi and Li Zhenhai shook hands.
"As for this girl..."
Liu Cong smiled, glanced at Luo Mingya, and then said to Xiao Yi.
Xiao Yi waved his hand, "No introduction is needed, I already know him."
After all, he had collaborated on papers with Luo Mingya, which could be found, so he didn't think these people didn't know.
Li Zhenhai smiled at this time and said, "I have always heard that Xiao Luo and Chief Designer Xiao know each other, and now it is confirmed. Speaking of which, Xiao Luo is also the backbone of our team and is also responsible for an important research task."
"I brought Xiao Luo here this time, hoping to persuade Chief Designer 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 At first glance, this document is a judgment of the General Staff Headquarters on the current international situation. It believes that based on the current international situation, especially considering the impact of controllable nuclear fusion technology, the possibility of a small to medium-scale battle around China in the future is quite high.
Especially as time goes by, when the Americans gradually discover that controllable nuclear fusion technology is really difficult to conquer, 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 war will become higher and higher.
"Therefore, the Military Commission believes that we must complete the filling of all military equipment gaps 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-to-medium-scale battle does occur by then, there is a high probability that equipment of the strategic bomber level will not be needed."
"However, it also shows that the main purpose is to fill our gaps in this area and achieve stronger deterrence."
"When the time comes, even if our H-20 really goes out to fly around, there is a high probability that they can actually start a war, and there will be more worries."
Xiao Yi nodded slightly, feeling a little unexpected but also reasonable.
The possibility of war is never zero.
Then, Wang Changhong said, "However, a key problem now is that our current engine technology, especially in terms of materials, cannot yet achieve good compatibility with H-20, and it cannot meet our requirements in terms of performance."
"So, we thought of you."
"Chief Designer Xiao can develop 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 Master Wang Changhong bowed sincerely to Xiao Yi: "I really owe it to you."
Li Zhenhai, who was next to him, quickly grabbed Mr. Wang and said, "Mr. Wang, it should be me who says this. After all, I am the leader of the material team! It has not been researched yet. It is all my problem!"
Wang Changhong shook his head. "No, I am the chief engineer after all. I also have to take responsibility for this responsibility. I still have to say this!"
In this way, the two people performed a double act in front of Xiao Yi.
Xiao Yi twitched his lips and glanced at Luo Mingya next to him.
Luo Mingya also looked embarrassed, probably because he didn't expect his team leader and chief engineer to stage such a show so skillfully.
Looking at Liu Cong again, although he still maintained his smile, it was obviously a bit forced.
Xiao Yi coughed twice and said, "Okay, you two, it won't be a problem, I agree to this matter."
The eyes of Wang Changhong and Li Zhenhai suddenly lit up, and then they calmed down their double act expressions and said one after another, "I knew Chief Designer Xiao would definitely agree."
"Chief Designer Xiao, I don't obey anyone in the whole world, but I obey you!"
Liu Cong said helplessly from the side, "You two, I think you two should save your time. I don't know if you are still planning to stage this show. When will you discuss it?"
Wang Changhong coughed and said, "There is no discussion, it's just out of control, there is no discussion."
Li Zhenhai also nodded. "Yes, I can't help it."
Liu Cong shook his head. "Okay, that means you guys have such a tacit understanding that it just seems natural without even having to act."
"Director Liu, please don't slander me! What should I do if Chief Designer Xiao misunderstands me?"
Liu Cong spread his hands, then looked at Xiao Yi and said, "Okay, since you agreed, do you have any requirements in this regard? When can we start research?"
"I have no requirements." Xiao Yi waved his hand. "You can start research at any time."
"Okay!"