Long-distance communication technologies are developing rapidly.
At the same time, as Li Qingsong's understanding of the phenomenon of quantum entanglement deepened, Li Qingsong also realized a problem.
Long-distance communication technology based on quantum entanglement is actually limited.
This limitation is related to distance.
Of course, it's not that quantum entanglement itself is affected by distance—even if located on opposite sides of the universe, quantum entanglement is still real-time, with zero time consumption.
However, Li Qingsong observed that once the distance becomes too great, the "interference" that quantum entanglement itself is subjected to becomes greater.
Li Qingsong is currently unclear where this interference comes from, but he suspects it may be related to dark matter and dark energy.
This interference causes great difficulty in data interpretation. That is, although the information is transmitted, if the distance is too far, the data cannot be interpreted.
Improving the ability to interpret data is related to another extremely important discipline.
Mathematics.

"Perhaps, with the birth of long-distance communication technology, I need to create a new branch of mathematics specifically. Hmm… maybe it can be called quantum mathematics?"
Li Qingsong discovered that the degree of development of quantum mathematics is closely related to the level of his overall scientific system and the data interpretation ability of quantum communication.
With Li Qingsong's current level of mathematics, the maximum communication distance he can afford is about 1 billion kilometers.
Any longer, and the error rate and data loss rate will be too high, making it basically impossible to interpret complete information.
Of course, Li Qingsong can also extend the communication distance through relay, that is, by setting up a long-distance communication relay station every 1 billion kilometers.
However, even if the relay mode is adopted, the error rate and loss rate will accumulate. After a maximum of nine relays, the information will become completely uninterpretable.
Thus, with Li Qingsong's current mathematical level, the limit of long-distance communication he can afford is about 10 billion kilometers.
"10 billion kilometers? That's enough for now. After all, more than of the mass of a star system is concentrated within a radius of 10 billion kilometers."
Li Qingsong thought to himself: "No wonder I saw that the Zhitian Scourge fleet could not carry out inter-stellar communication.
Their mathematical level is probably much higher than mine, but I estimate that they can only withstand a communication distance of two to three hundred billion kilometers at most, while the distance between star systems is often hundreds of thousands of billions of kilometers.
It's just that developing mathematics, or even specifically creating quantum mathematics… is really damn difficult."
Faced with the mountain of mathematics, Li Qingsong couldn't help but feel fear and couldn't help but curse.
Mathematics is an abstract science.
The simplest way to describe nature with numbers, such as two apples and three oranges, is the first level of abstraction. At this level, people use numbers to replace real objects.
Then, based on the fourth level of abstraction, the fifth level of abstraction begins to study the interaction and mapping relationships between different mathematical structures, developing concepts such as category theory and number theory that make ordinary people's heads spin.
At this moment, the quantum mathematics created by Li Qingsong, according to this set of rules, is probably located at the seventh level of abstraction.
At this level, Li Qingsong even has no way to describe what he is researching in relatively simple terms.
It's like a question, regardless of what the answer to the question is, Li Qingsong can't simply describe the question itself.
That is a collection of very abstract and very complex concepts. Although those blueprint people have undergone several rounds of genetic modification, and their brain abilities have made great progress compared to the beginning, at this moment, among the approximately 700 million blueprint people, only less than 100 blueprint mathematicians can understand this question.

Even fewer blueprint mathematicians, only 20 people, can study the answer under the premise of understanding the question.
"Alas…"
Li Qingsong sighed deeply.
"Fortunately, my computer technology has also made great progress in recent years, and the performance of quantum electro-supercomputers has greatly improved again, which can be regarded as having suitable tools for quantum mathematics research.
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Otherwise, even if I could control 10 billion clones at the same time, and make the brains of these 10 billion clones explode, I wouldn't be able to make any progress."
Because of the importance of long-distance communication technology, Li Qingsong transferred the brainpower of 100 million clones, either operating supercomputers or just thinking about nothing all day long, and devoted themselves to the research of quantum mathematics.
Li Qingsong continued to invest the remaining billion consciousness link shares in several other extremely important research projects, always maintaining the rapid advancement and development of overall technology.
Time continued to pass quietly. As the big package of "dry food" of Feixing continued to shrink, on this day, Li Qingsong finally made another huge technological breakthrough.
On test platform No. 1, Li Qingsong transferred several Mercury-class battleships and used electromagnetic guns to bombard them with all their might.
Originally, test platform No. 1 would have been torn to pieces immediately. But at this moment, before those high-speed projectiles arrived, a layer of light yellow罩 appeared out of thin air around the test platform, completely enveloping it without leaving any dead corners.
Gluon plasma controlled by magnetic fields and connected based on strong nuclear force!
They are extremely thin, only a few microns thick, but they are extremely tough. Even though the electromagnetic gun projectiles that Li Qingsong is bombarding at this moment have a speed of hundreds of kilometers per second, and each one is enough to split mountains and crack rocks.
But it can still only create ripples on this layer of gluon plasma shield with a thickness of only a few microns, and cannot penetrate it at all!
Li Qingsong has finally mastered the energy shield technology at this moment. Although the performance is still much worse than that of the Zhitian Scourge fleet, it doesn't matter, just continue to iterate and optimize!
At this moment, the main energy source of the fleet, deuterium, is running out.
The current consumption cannot even support the fleet to decelerate into the star system to obtain supplies.
But this is not because Li Qingsong had any omissions or made mistakes in the material collection stage.
This was specially arranged by Li Qingsong. Because Li Qingsong left more share for ordinary hydrogen, that is, the reserve of protium.
And now, after the breakthrough in energy shield technology, there has also been a breakthrough in protium fusion reactor technology!

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