Ministry of Foreign Affairs's response is certainly not because of the good intentions of China.
Because everyone knows that the United States cannot really invite China to help build it.
After all, the members of JNEO Organization are basically NATO and a number of countries that have relatively friendly relations with the United States. If they really want to start building a research institute and reactors, it will be equivalent to building a headquarters. If China is invited to help with the construction, isn't it a joke?
At that time, he will definitely be ridiculed by various media. At least for the president of the United States, the media under the opposition party will definitely ridicule him on this matter, saying that he clearly wanted to build a "democratic" nuclear fusion reactor, but in the end he found enemies of "democracy" to help build it.
Although he does not have another term, such things will inevitably affect his party. After all, he still has to provide help for the party's next election.
Therefore, they will definitely only choose their own people to do this project.
But at this time, another question arises. If they are allowed to build the project themselves, can they complete it as soon as possible?
In terms of strength in the field of infrastructure, no country in the world can surpass China.
That's why Sun-Making Reactor was able to complete it so quickly.
As for this JNEO Organization...
That's hard to judge.
Referring to the original ITER, the construction speed of ITER was slow, largely because the construction speed was quite slow. It took a long time to build, but not much was built.
If the United States wants to launch nuclear fusion experiments as soon as possible, it may have to spend a considerable amount of money on this construction cost.
Therefore, in the face of Ministry of Foreign Affairs's completely sarcastic reply, although many people in the US government have broken the defense, there is no good solution.
This is not during World War II, and their workers are no longer the workers at Los Alamos.
Time flies and it's mid-April.
In the offices of USTC and Xiao Yi.
Xiao Yi is studying his own problems in his office as always.
He doesn't have to worry about what's happening internationally, and the plans of the United States have no influence on him now.
Over the past month, his research progress on Hailstone Conjecture has reached a quite in-depth level.
"The representation of Hailstone Group in complex vector space has now been completely solved..."
Xiao Yi looked at the description of Hailstone Group on the draft paper: [For each positive integer n, there is a vector space V_n with dimension n, and define Hailstone Group Effect on V_n: If H_k is a generator, then it maps the kth basis vector in V_n to the 3k+1th (if k is an odd number) or k/2th (if k is an even number) basis vectors, and the other basis vectors remain unchanged.]
"Then, including the characterization of invariant vectors, has been completed. Moreover, in the representation space V_n, I happened to find a special type of vector that can remain invariant under the action of Hailstone Group, and also proved that these invariant vectors correspond one-to-one with the periodic orbit of the hail sequence. In particular, this special vector also directly corresponds to the 4-2-1 cycle. The invariant vector exists and is unique in every representation space."
Thinking of this, Xiao Yi smiled slightly.
Just getting here is already quite far ahead of the mathematical world.
Because the mathematics community is not very advanced in research on this issue.
The most advanced results are probably the results of Terence Tao in 2019.
He originally used the method of logarithmic density and showed that almost all hailstone orbits will fall below any given function from the starting point in the sense of logarithmic density, provided that this function diverges to infinity, no matter how slowly.
In a sense, his proof is equivalent to saying that almost all natural numbers are consistent with Collatz Conjecture.
However, this proof may be sufficient for physics, but for mathematics, almost everything is never "all".
Just like in mathematics, infinity does not equal everything.
However, despite this, this achievement of Terence Tao is still considered to be one of the most important achievements in the field of Collatz Conjecture.
Now, although the rule found by Xiao Yi has not obtained "almost all" results like Terence Tao, it can be regarded as finding another road, or direction, that can lead to the final proof.
In the proof of mathematical problems, direction is very important.
Just like a tree, there may be many branches, but there is only one branch that can really lead to the highest point.
Of course, there may be more than one "highest point" in mathematics, but by the same token, once you go in the wrong direction, you may not reach the final answer in the end.
"But the last question now is..."
"Is there a unified method that can generate invariant vectors in every representation space?"
Xiao Yi pondered.
This is the most difficult question in the next study.
He has been thinking about this issue for almost two weeks.
The other questions in front of him only blocked him a little bit, but this question alone prevented him from finding a good idea.
"Maybe we should try other angles?"
Xiao Yi thought for a moment.
However, at this moment, there was a knock on the office door.
"Please come in."
He looked at the door, then Liang Qiushi opened the door and walked in.
"Teacher! I can't stand it anymore! Please help!"
As soon as he came in, Liang Qiushi shouted quickly.
Xiao Yi asked with a confused look, "What's wrong?"
Liang Qiushi said helplessly, "My thesis has now encountered the last problem, and I still don't know how to solve it!"
"I can only ask the teacher for help!"
Xiao Yi suddenly burst into laughter and said, "Oh, now you know how to come to me. There is only one and a half months left before the deadline."
Liang Qiushi clasped his hands together, leaned forward and said, "I really have no choice, teacher, this question is too difficult!"
Xiao Yi shook his head and said, "Okay, okay, I told you when you chose the topic that your question is difficult. To be honest, you are just stumped now, and it is already a bit beyond my expectations."
Hearing what the teacher said, Liang Qiushi smiled and seemed a little proud.
Xiao Yi didn't care about his appearance, and then said, "Okay, show me where you are stuck now."
"Okay."
Liang Qiushi then took out a stack of scratch paper from the bag in his hand, and then began to show it to Xiao Yi.
"That's the problem..."
"I still can't figure out the proof that the friendly measure μ on the function field F^n must be a non-uniform strong extreme value, and the proof that extends to the non-homogeneous Baker-Sprindzuk conjecture."
There was a rather troubled look on his face, and it was obvious that this question had stumped the mathematical genius.
Xiao Yi took it and looked at Liang Qiushi's proof process carefully.
The thesis topic of Liang Qiushi involves extending the non-homogeneous Diophantine approximation method on Real Domain to the function domain.
Diophantine approximation theory has always been a very difficult topic in the field of number theory. It studies the approximation of rational numbers or algebraic numbers to real numbers, as well as related measurement theory and counting theory. It has a long history of research, which can be traced back to the research work of Diophantine in the ancient Greek era. Likewise, it has also been one of the topics that has been studied over and over again in the mathematics community.
As for the subject of Liang Qiushi, the difficulty is of course quite high.
It may be quite difficult for ordinary doctoral students to figure out this paper.
So when Liang Qiushi chose this topic, Xiao Yi also tried to persuade him.
What I didn't expect in the end was that he was able to research this topic to the present point, which is quite unexpected.
Moreover, in fact, Liang Qiushi has already completed a result before. He gave the equivalence property between the extreme value measure and the non-uniform extreme value measure. This can be regarded as the transfer principle in the non-homogeneous case.
And this result is enough to be completed as a master's graduation thesis. It is trivial to post anything in a section, and even to be rated as an excellent graduation thesis is completely casual.
When Liang Qiushi completed this result, it was already last year, so he was not satisfied with that result and continued to conduct in-depth research, and finally reached this level.
Xiao Yi looked at it briefly, and then said, "I remember that you seemed to have proved that the friendly measure is strongly contracted before, right?"
"Yes." Liang Qiushi asked doubtfully, "But what is the connection between this and the current problem?"
Xiao Yi smiled and said, "Now that you have completed this step, you just need to think carefully about what to do next."
"For example, think more about your previous results, the equivalence between extreme value measures and non-uniform extreme value measures. In other words, your method can also prove that strong extreme values and non-uniform strong extreme values are also equivalent."
Hearing this reminder from Xiao Yi, Liang Qiushi's eyes flashed with thought, and then he entered a state of thinking.
As time passed slowly, he suddenly realized it and said in surprise, "The principle of transfer!"
"Yes, that's it." Xiao Yi snapped his fingers, "Now, we already know that the friendly measure μ is a strong extremum. This is the result proved by Ghosh. You have already cited it in your previous results. On the other hand, μ is also strongly contracting, so you know what to do next."
Liang Qiushi nodded repeatedly. "I understand."
But then a puzzled expression appeared on his face. "So how should we solve the non-homogeneous Baker-Sprindzuk conjecture next?"
Xiao Yi smiled slightly and said, "For a conjecture problem, we must first figure out what kind of problem this conjecture wants us to discuss."
"For Y∈F^(m×n) and θ∈F^m, we define the non-homogeneous Diophantine index ω(Y, θ) as the supremum bound of the real number ω that enables the set of inequalities to have solutions under any large T."
"Here, the set of inequalities describes the approximation relationship between Yq+p+θ and q. Similarly, we can define the multiplicative version of the non-homogeneous exponent ω × (Y, θ)."
"This conjecture shows that from homogeneous approximation in almost every sense to non-homogeneous approximation that holds for any translation θ, this transfer principle is established under certain conditions. It reflects the mathematical community's pursuit of the promotion of Diophantine approximation theory from homogeneous to non-homogeneous."
"Now that we have proven that friendly measures are non-uniformly strong extremes in the function domain, the key is that we need to establish the connection between natural measures and friendly measures on analytical non-degenerate manifolds."
"However, in fact, this problem is already obvious so far. Here I recommend a paper to you. You can probably figure it out after you go back and read it."
Then Xiao Yi turned on the computer, searched for a while, and finally found a paper.
"Well, it's this, "Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation", a 2007 paper."
Xiao Yi conveniently sent the link to this paper to Liang Qiushi's WeChat account.
"You should read this essay carefully later. If you still don't understand it after reading it, come to me again."
Liang Qiushi's eyes widened immediately. Unexpectedly, his teacher solved his problem almost casually, and even directly recommended a paper.
And it's from 2007?
Is this the strength of the youngest mathematics master in history?
He expressed his heartfelt thanks. "I understand, thank you teacher."
Xiao Yi nodded, and then said, "Okay, do you have any other questions?"
"No more, no more. If there are still problems, I will come back to you." Liang Qiushi shook his head repeatedly.
"Well, remember to finish the paper early. Don't forget that the final draft will be submitted before June."
"Definitely!" Liang Qiushi said OK: "Don't worry, in fact, I have written out the previous results a long time ago. If the content of this expansion is not completed, I will send you the previous results by then, no problem."
Xiao Yi rolled his eyes. "Then you might as well send out your previous results earlier."
Liang Qiushi waved his hand, said nothing, and left the office directly after saying goodbye.
Only Xiao Yi is left.
However, at this time, Xiao Yi recalled the process of guiding Liang Qiushi just now, and thoughts appeared on his face.
"Diophantine approximation?"
"What would happen if Diophantine approximation was used to study the generation problem of invariant vectors?"
He thought a little in his mind.
"Convert the problem into a solution problem for the Diophantine system of equations?"
The inspiration in my mind began to jump up, and various thoughts began to collide with each other.
Finally, his intuition told him that this idea had great potential!
"If we fix a set of bases, represent the linear transformation ρ(g) with the matrix A_g, and represent the vector v with the coordinate vector (x_1,..., x_n), then the invariance condition ρ(g)v=v becomes a set of linear equations."
He picked up the scratch paper next to him and started writing on it.
[A_g (x_1,..., x_n)^T =(x_1,..., x_n)^T, g∈G]
"If G is generated finitely, for example, by g_1,..., g_m, then the above conditions are equivalent to a Diophantine equation system..."
At this moment, Xiao Yi's eyes gradually lit up.
"It seems that it can really be done!"
As long as it is converted into the Diophantine equation system, then he can directly give a constructive solution using the Diophantine approximation method!
And now, he is very close to this goal.
"Liang Qiushi, Liang Qiushi, I didn't expect you to be able to bring me some inspiration."
Xiao Yi sighed with emotion.
Although it is not a direct inspiration, it can only be said that when he was thinking about the theory of Diophantine equation just now, he inadvertently touched this inspiration.
Now, it has become a little easier for him to obtain such inspiration.
Even... we can no longer call it inspiration, but call it... constant feeling?
"Okay, now it's time to conquer this step."
Xiao Yi raised his eyebrows slightly, and then continued his research.
He could foresee that after this step was solved, the remaining obstacles would become quite simple.