In the summer of 2020, traveling to Port Ravit, the capital of the country.
Ketz and Loew walked into Shamron II’s office together. Ketz handed an analysis report to Shamron II and said:
"The reply came, someone in the thread solved my puzzle correctly."
Shamron II took the report but did not open it. He said calmly: "Whoever guesses correctly can chat with him. Why write a report?"
"The problem is that there is more than one person who answered correctly. There are too many great masters on the dark web. In two days, seven groups of people answered correctly. This report is the result of the analysis of these seven groups by the technical department." Loew said helplessly. He shrugged and said with a smile.
"Although there were seven groups of people who answered correctly, some people gave complete answers, and some people gave very concise answers. For example, one answer only had the number 103," Katz explained.
"If you only give a partial answer, such as 103, can it be considered a correct answer?" Shamron II asked.
"Of course it counts as a correct answer. Programmers and science enthusiasts believe in simplicity, or laziness. Some people think it's cooler to just reply with a 103 than to write a complete answer." Katz replied.
Loew pointed to the analysis report, took over and said:
"The analysis department uses the completeness of the answers to distinguish whether it is a loser or a professional organization. It is impossible for the Yuhan people to return to 103 because they are worried about being judged invalid and unable to attract Kezi's attention."
"You mean that the person who gave the complete answer is more likely to be an organized Jade Khan? You won't tell me that there is more than one group of complete answers, right?" Shamron II shook the report in his hand and asked.
"The boss is wise. There is indeed more than one set of complete answers, and there are three sets of complete answers." While complimenting the leader, Loew helped Shamron open the report and pointed to the three yellow marks.
Shamron II followed the three yellow marks in the answer column to find the corresponding screen name column, and found that one of the screen names was marked in red.
Shamron pointed to the online name and said:
"O(√n ln(n)) - the three chords of Riemann's hypothesis, Katz, this is a competition with you! I match your online name in the same sentence, which is quite neat."
Loew was affirmed by Shamron II and said simply:
"We all agree that with the complete answer and the corresponding online name, this person is the Yuhan person."
"The Yuhan people's online name corresponds to mine on the surface, but what's even more corresponding is that my online name is a puzzle. Their strange online name is obviously also a puzzle. I'm thinking about how to solve it."
Big O notation refers to using one function to describe the asymptotic upper bound of the magnitude of another function.
The Riemann Hypothesis is one of the most important conjectures in mathematical research. If the conjecture is proven, it will make the entire mathematics and even natural science a big step forward.
For ordinary people, it is very difficult to understand the popular science books introducing the conjecture, let alone trying to prove it.
The Riemann Hypothesis involves many branches of mathematics such as number theory, analytic geometry, and complex numbers.
In order to simplify complex problems, mathematicians simplify the proof of Riemann's hypothesis into the following strong equivalent conditions:
The difference between the number of primes before any large integer n and the integral of the natural logarithm of n is greater than O the product of the root n and the natural logarithm of n.
That is: π(n)-Li(n)=O(√n ln(n)).
Katz stared at that special online name and thought hard.
The Riemann Hypothesis, greater than O, is easy to understand and corresponds to the two functions √n and ln(n).
What do trichords mean?
Loew walked into Kez's office, looked at Kez's sad face, and said with a smile:
"Why don't you even have lunch? Our great mathematician is also stumped sometimes."
Katz smiled bitterly and shook his head, saying:
"This kind of puzzle is actually like a safe. Once you grind the right key, it will open. The key is that I don't know which key to use."
"Come on, let's eat first. After dinner, I will take you to see a real great god."
Professor Gu An is one of the most mysterious figures in the Dingtian organization. Few people know of his existence, and he himself never appears in the office area of the Dingtian organization.
As for his research projects, even fewer people know that Loew was the liaison between Professor Gouin and Shamron II.
After approval, Loew took Katz to Professor Gu'an's mysterious building.
While listening to Katz's introduction, the professor looked at the strange online name and said to himself:
"The square root of n and the natural logarithm of n?"
Professor Guan's eyes flashed brightly, he raised his head and asked Kezi:
"Have you ever heard of the Trojan moons?"
Katz shook his head in confusion, and the professor continued:
"I have read an astronomy paper discussing the cross-system resonance phenomenon of satellites. The 269 planetary satellites that have been discovered in the solar system have a belt-like distribution."
There are many parameters that describe a satellite, such as radius, period, density, eccentricity, orbital inclination, etc.
Among all parameters, the most important physical parameter is the radius of the satellite, and the most important orbital parameter is the average distance of the satellite from its parent star, called the semi-major axis.
What is interesting is that the paper sets the ratio of the satellite's semi-major axis to the solar radius as n, and the functions about n used to describe the cross-system resonance parameters are √n and ln(n).
The 269 satellites have their own values, and ln(n) is defined by the author of the paper as the orbital base number, from the smallest -4.3 to the largest 4.25.
According to existing theory, this value, which is only related to satellite dynamics, has nothing to do with the albedo and radius of the satellite itself.
The professor said to Ketz: "The strange thing is that there are only 9 satellites with albedo greater than 0.6, and they are all distributed between -1.1 and 0." The professor explained with an example:
"It's like in a movie theater with more than 20 rows, you find that only people wearing white clothes can sit in the 'VIP seats' in row 9, while people wearing dark clothes can either sit in the front or Behind." The professor continued:
"What's more interesting is that the ln(n) values of the top ten satellites in terms of satellite radius are all between -1 and 1. This is equivalent to the person sitting in the best seat in rows 9-10, who must be big enough! "
The paper further combines √n and ln(n) to further obtain a new parameter √n ln(n)=m that describes cross-system resonance.
The m values of the 269 satellites range from -0.74 to 35.6, which looks chaotic, but the range from -0.6 to 3.7 is very special.
There are only 20 satellites here, but they cover the largest satellites of all six parent planets (Moon, Phobos, Ganymede, Titan, Titan, and Triton).
Moreover, the top 12 satellites with the largest radius are all in this range, and none of them are missed.
The only eyesore in this "all-star" lineup is Rhea, which ranks 21st in radius. However, it is also quite large and highly irregular in shape. It is one of the only few satellites in the solar system known to have chaotic rotations. One, the spin axis wobbles so much that its direction in space is unpredictable.
Not only that, Dione, ranked 14th, and Tethys, ranked 15th, each lead two Trojan moons, forming a stable structure.
Among the 269 satellites, in this stable area, there are only the top 12 largest satellites in radius, Phobos, the largest satellite of Mars, the special Titan and two other groups of three, a group of six Trojan satellites.
"Trojan moons, what does their stable structure mean?" Katz asked.
"The Trojan satellites are relatively small satellites that use the same orbit as the main satellite and are located at the Lagrange points (L4 and L5) 60 degrees before and after the main satellite. There are two groups of Trojan satellites among the satellites of Saturn. Tethys leads Phoebe (in front) and Phoebe (back), and Phoebe leads Phoebe (in front) and Phoebe (back). They are like "hand in hand" "It seems to form a stable structure."
"For example, I don't know who arranged it. In a movie theater with a capacity of 269 people, in the 10th row, which is the best seat, only the top 12 largest people and two mothers holding a child on each side can sit!"
"In astronomy, when the periods of two or more stars have an integer multiple ratio, it is called orbital resonance, such as 1 to 2 or 3 to 5, etc. The three Trojan satellites are the most special. They are in the same orbit, and the resonance ratio is 1 to 1 to 1, like a beautiful triad.”
After listening to the professor's explanation, Ketz seemed to have found a treasure. It turned out that the "triad" refers to two groups of three Trojans in each of the two groups of Saturn in the stable structure orbit calculated based on two functions related to the Riemann Hypothesis. satellite.
There are actually only two sets of natural "triads" in the solar system, and they can be picked out through two functions related to the Riemann Hypothesis!
Katz found the corresponding satellite code. Saturn's satellites start with 6, and the numbers that follow are the satellite serial numbers.
He tapped the keyboard and replied to "O(√n ln(n))-Riemann's Hypothesis Triad" with two sets of "triad" numbers representing the satellite serial number:
603, 613, 614;
604, 612, 634.
