Super God-Level Top Student

Between any two points in the coordinate system, there exists a curve called a "twisted connection line," which ensures that every point along the curve reflects some degree of distortion within the coordinate system. The mathematical expression is: for any two points (P_1) and (P_2), there exists a parametric curve (\\vec{r}(s)), where (s) is the arc length parameter, satisfying: [\\vec{r}(0)= P_1,\\quad \\vec{r}(L)= P_2], and for every point on the curve (\\vec{r}(s)), there is a scalar value (T(s)) related to the degree of distortion, such that: [ T(0)= 0,\\quad T(L)= 1]. Yang Xuanqing could barely understand this part. It represents not just the curve's geometric connection, but also the evolution of the degree of distortion within the coordinate system. But according to the series of almost magical deductions made by Qiao Ze, it was proved that the variation of (T(s)) along the entire curve describes the distortion in the coordinate system, meaning that each point on the curve carries some form of distortion information about the coordinate system. Really, after barely glancing over this part of the deduction, Yang Xuanqing completely lost interest in the theory. He even began to worry about the future. Would pursuing particle physics and studying the Quantum Implicative Model in the future really require learning this stuff? Yang Xuanqing even doubted that if Qiao's Algebraic Geometry became a mandatory course at the Physics College, it would greatly raise the bar for becoming a qualified physicist. At least he was sure, if his mentor had set this course as a basic one when he was pursuing his graduate studies, he would definitely have switched majors without hesitation. For a moment, Yang Xuanqing suddenly understood why Edward Witten had said those words earlier. Just by glancing at it, one could feel the level of abstraction involved. How the hell were the brains of the creators of this theory wired? ... "Does it feel very abstract? Are many things incomprehensible?" Seeing Yang Xuanqing raising his head with a vacant look, Edward Witten spoke up. "Although I really don't want to admit it... but yes, it's true. I can't even begin to understand the derivation process of the Containment Graviton formula we are using." "I don't fully understand it either," said Edward Witten. "Hmm..." Hearing this, Yang Xuanqing felt inexplicably better. After all, the person right in front of him was a Fields Medal winner. But he was at a loss about what to say. "If you're not interested in those complex derivation processes, you can close the attachment now, and see what he says in the body of the email," Edward Witten said again. After hearing this, Yang Xuanqing instinctively closed the attachment and glanced at the contents of the email body, then fell silent. This part of the exchange was purely in English. "The attachment contains the basic theorem derivations of Quantum Containment Theory, and apparently, I've only managed to complete the simplest part of this content. Constructing a perfect mathematical structure to describe the model involves much more work. I hope to complete the mathematical theoretical construction of the entire model in half a year. It should be faster, but I have some miscellaneous affairs to deal with recently, which might cause some delays. Human thought is much more complicated than mathematics, which is regrettable. I have been following the research progress of Princeton Research Institute on superspiral algebra and transcendental geometry. Obviously, you are way behind. I hope the content of the attachment will be of help to your research, at least to correct several patently wrong research directions. Your friend: Qiao Ze." Well... The simplest part? Heh...