All Entanglements of Elementary Particles are Elements of upper level above normal level. Our dynamic mathematics explains the mechanisms of Entanglement and provides new mathematical possibilities for working with it. Here are given mathematical fundamentals of interpretations theory (future science) and fundamentally new approach to elementary particles, energy conservation. Here is studying Energy-space with scalar product and norm of its elements by format-numbers. Digitization of interpretations forms allows the use of digital technologies through appropriate programming. In science, there are two approaches to studying nature beyond classical science (conditionally, the (1, 1)-interpretation): the approach through quantum mechanics (conditionally, the (1, 2)-interpretation) and dynamic mathematics (conditionally, the (2, 1)-interpretation) [1, 2]. In contrast to the probabilistic approach of quantum mechanics with dimension doubling for quantum entanglement, we propose a deterministic approach via an energy hierarchy. Both approaches have the same "root": |||, but at two opposite ends: quantum mechanics ((1, 2)-interpretation) by |||^(-1)by and dynamic mathematics (2, 1)-interpretation) by ||| and ((1, 2)-interpretation) by |||^(-1) and other interpretations with using hierarchical structures of measures, some equations [1, 2]. Therefore, the conclusions are similar, but for different objects and processes. Either we take what we need from emptiness by |||^(-1) or through substitution by |||. We also demonstrate the possibilities of not only using the effects of quantum entanglement for calculations, but also for manipulating energies, objects, their actions, and processes through the upper level. Let us call the interpretation formats by format-numbers and quantum levels of connections. Elements of format-numbers mathematics were considered partially [1, 2]. And for manipulating these numbers, the interpretation (1, 1) is already suitable, i.e., ordinary traditional science is suitable. This is a different approach to complex processes, not through probability. This article applies to physics and neural networks of the new direct-parallel and direct-accumulative types. For now, this is only an introductory article. The first task: to understand hierarchy of energies in the Universe and the principles of functioning of living energy (living organism, in particular, human, subtle energies), and then using these principles to "construct" artificial living energies (let's call them pseudo-living energies). It is possible to significantly expand the horizons of science, in particular physics, by studying the subtle energies in the Universe. For this, some aspects are proposed for consideration of Dynamic Science. self_science^(our theory) - science here acts as a space for the application of our theory in the self-format, i.e., any place of science, in particular physics, can act as a place for the "location" of the self. It contains itself (accommodates any action C) in any place of science. On the basis of mathematical uncertainties, new mathematical structures are formed, allowing us to describe processes and objects that are fundamentally not determined by conventional deterministic methods. Objective uncertainties in any case can mean manifestations of processes and objects that are fundamentally not determined by conventional deterministic methods. Since dynamic mathematics places the primary emphasis on the dynamics of energy, rather than on objectivity, the level of approach to studying processes expands. Here are the formulas of dynamic mathematics that determine the spirit of actions and objects (i.e., the energy of the upper level that generates their self-energy); that determine the double of the magician, etc. Many energies are indeterminate because they are based on uncertainties from the perspective of traditional science—large concentrations of specific energy in a chaotic state. The foundation of dynamic mathematics lies in working with uncertainties, which makes it possible to manipulate these indeterminate energies using direct-accumulative direct-parallel neural networks. Ordinary regular work with them in ordinary science is fundamentally unable to realize their capabilities. Therefore, singular science realized on a neural network - an analogue of the human CNS - will be much more natural. Unfortunately, we do not have funding to perform the necessary experiments and the practical creation of a technical model of such a neural network. There is a need to develop an instrumental mathematical base for new technologies. The task of the work is to create new approaches for this by introducing new concepts and methods. Our mathematics is unusual for a mathematician, because here the fulcrum is the action, and not the result of the action as in classical mathematics. Therefore, our mathematics is adapted not only to obtain results, but also to directly control actions, which will certainly show its benefits on a fundamentally new type of neural networks with directly parallel calculations, for which it was created. Any action has much greater potential than its result. Social justice is fundamentally impossible as long as education (training) is based on achieving results, and not on the process. It is time for physicists to begin studying not only the manifestations of living energies, but also the living energies themselves, which are by no means expressed through objectivity and ordinary energies, although they are capable of manifesting themselves through a lower level - objectivity and ordinary energies. We, as mathematicians, offer a new corresponding apparatus for understanding nature and studying living energies. Significance of the article: in a new qualitatively different approach to the study of complex processes through new mathematical, hierarchical, dynamic structures, in particular those processes that are dealt with by Synergetics. The significance of our monograph is in the formation of the presumptive mathematical structure of subtle energies, this is being done for the first time in science, and the presumptive classification of the mathematical structures of subtle energies for the first time. The experiments of the 2022 Nobel laureates Asle Ahlen, John Clauser, Anton Zeilinger and the experiments in chemistry Nazhipa Valitov eloquently demonstrate that we are right and that these studies are necessary. Be that as it may, we created classes of new mathematical structures, new mathematical singularities, i.e., made a contribution to the development of mathematics. Conventional science changes numbers. Ours changes levels by SmnSprt. Connection is fundamental to understanding our world. Everything is expressed through connections; an object (matter) is a self-connection in the form of energy closed in on itself; all forms of energy are forms of connection, information, thoughts are forms of connection, in particular, Vernadsky's noosphere is an example of this, and so on.
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REVIEWER:
Volodymyr PASYNKOV - PhD of physic-mathematical science, assistant professor of applied mathematics and calculated techniques department of «National Metallurgical Academy», Ukraine.
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CONTENTS:
Introduction
Part I. Elements of Dynamic Mathematical theory of Quantum Entanglement of Quantum Entanglement
Introduction
1.1 Elements of the Dynamic Mathematics of Entanglement of Elementary Particles
1.2 Self-type structures generating energy
1.3 Set-self
1.4 Links of the Universal DNA of Singularities
1.5 Some interpretation types
1.6 Some special connections
1.7 Dynamic connections hierarchy
1.8 Conditional activation
1.9 Some structures of living organism
1.10 Hierarchical space
1.11 Vprt-hierarchical space
1.12 Energies hierarchy
1.13 Energy-space
1.14 Algebra Beginning of format-numbers
Appendix
References
Part II. SCSprt – elements and their applications
Introduction
2.1 SCSprt – elements
2.2 Dynamic SCSprt – elements
2.3 SCSprt – elements for continual sets
2.4 Dynamic continual SCSprt – elements
2.5 The usage of SCSprt -elements for networks
2.6 Variable hierarchical dynamical structures (models) for dynamic, singular, hierarchical sets
2.7 Applications Dynamic Sets Theory to physics and chemistry
2.8 PROGRAM OPERATORS SCSprt, tprSCS, SCS1epr, SCSeprt1
Appendix
Supplement: Connection SCSprt – elements with usual functionals and operators
References
Part III. SCfSprt – elements and Their Applications
Introduction
3.1 Fuzzy SCSprt – elements (SCfSprt)
3.2 Dynamic SCfSprt – elements
3.3 SCfSprt – elements for continual fuzzy sets
3.4 Dynamic continual SCfSprt – elements
3.5 The usage of SCfSprt -elements for networks
3.6 Variable hierarchical dynamical structures (models) for dynamic, singular, hierarchical sets
3.7 Applications Dynamic Sets Theory to physics and chemistry
Appendix
Supplement
References
References
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Year of publication: 2026
Language: English
Authors: Danilishyn I., Danilishyn O.
Translation: No
Translator: -
Type: E-book
Number of pages: 245
Format: PDF (5,2 MB)
ISBN: 979-8-89898-343-7
UDC: 004:51(07)