This paper is about understanding Collatz conjecture in hailstone numbers.

A document by Jihyeon Yoon . Click on the document to view its contents.

In this paper, sequence of prime numbers would be investigated in even numbers. Goldbach’s conjecture is true.

Prime numbers could be formalized with using notation of sequence.

Currently defined basic particles of the physical universe can be explained in axiomatic form following CPT conservation.

Recent study approach with Ambient-Latent Space resembles a new possibility of simulating dynamics with more accuracy. This paper aims to suggest idea also by adding temporary dimension(like in case of SVM) in learning given dynamics by optimization in additional to the recent study.

This paper would introduce new method to approach magnetism in multidimensional structure of atoms.

Understanding Riemann Hypothesis could be possible by in extension of understanding Fermat's Last Theorem.

Prime number could be formalized with using notation of sequence. And by utilizing the sequence, approximation in generating prime number could be achieved.

P vs NP problem turns out to be P=NP in quantum computing but remains questions of optimization in classical computing.

Fermat's Last Theorem could be understood by ordinality that matrix provides in node-to-node relation in graph.

Background: Energy and matter is two basic forms of existence in a universe. So, there are two types of interaction in a universe. One is about between energies which takes a form of heat, and the other is about energy and matter which takes a form of work. As of the discussion between energies, interaction could be described. On the other hand, interaction between energy and matter takes another subject. In this paper, symmetrical identitcalness would be discussed between these two forms - heat and work. Methods: By showing mathematical identity of principle between heat and work, law of interaction between energy and matter could be described. Using category theory, way of expression pattern for addressing any reality would be addressed. By using dimensional metric for logical expression, logical structure would be in an expression of number in real number. By exemplifying constructing and deconstructing logical structure by basic matrix decomposition methods, explanation for transforming dimensionality by factorizing matrix would be introduced. And identity between heat and work by this mechanism would be shown. Results: Methods of decomposing matrix could be explained as a basic way of operator that could be adapted to transforming dimensionality. And this transformation gives justification of notation for heat and work. Conclusions: It could be natural to say there is a universal expression that is consists of numerical ordinals and cardinals. And both heat and work are identical as an expression form of energy and matter. Nuclear fusion could be introduced by simulating universe.