This paper explores mathematical and intuitive models to address challenges in quantum mechanics and physics. It investigates how dimensional structures form from a state devoid of variables.

In this process, the concept of 'zero-dimensional topological potential energy' was defined by connecting the zero of the coordinate system with the energy state in physics. Using complex rotation that encompasses the concepts of time and motion within a static mathematical framework, a dynamic motion concept of variables was created.

Complex rotation represents the dynamic balance between zero and variables, establishing a system where the increase and offset of variables maintain equilibrium. The increase of variables is linked to numerical systems, leading to the concept of radix waves by dividing complex rotation by the number N and connecting it to the numeral system.

The model of arranging radices through Euler spiral rotation and ascending dimensions has uncovered various new concepts for interpreting complex problems in physics and mathematics. Numbers arranged in complex rotation while maintaining dynamic balance around zero form a helical dimension structure. It was discovered that the transition points of this helical dimension structure are connected to the zero-dimensional information structure. Additionally, the spiral that cycles back to zero forms a fractal structure, providing consistent and novel interpretations for numerous quantum mechanical and physical challenges.

The study found commonalities in quantum decoherence, black holes, and phase transitions as they form dimensional transition singularity structures from the perspective of ascending helical dimensions. The foundation of physical quantities begins with inertia derived from complex rotation, representing the physical manifestation of dynamic equilibrium operations.

The method of creating dimensional structures through numerical systems allows for structural interpretations of various infinite number sequence problems. The characteristic of radix waves formed by complex rotation is that only prime numbers reach the 3D singularity, leading to the creation of a new computational structure called the complex cone unit. Through this structure, the Riemann hypothesis was interpreted as being connected to the 3D vertices of complex rotation, and it was revealed that even numbers greater than 4 are proven through the 3D prime complex cone structure, offering a new approach to NP-complete problems.

This new interpretation complements existing cosmology and provides a logical explanation for the quantum manifold universe. It reinterprets the structure of the universe as a dimensional structure of 'quantum trajectory motion' and introduces the concept of a zero-dimensional information state.

This paper has added a new dimension to existing mathematical concepts, focusing on whether the utility of these concepts can provide consistent and logical answers when applied to challenges. It demonstrates that consistent and logical answers to numerous challenges, such as the Collatz conjecture and the Navier-Stokes equations, are feasible, suggesting that the concepts presented herein could be rigorously verified through further in-depth research.

The interpretations offered by this paper do not represent definitive solutions to mathematical and quantum mechanical challenges, as these concepts were previously absent from mathematical paradigms. However, the ability to provide consistent and logical interpretations across various problems indicates potential for new mathematical discoveries. Future plans include developing computer simulations and algorithms centered on the concepts proposed here to expand the research.