| Description: |
The fundamental constants of nature—Planck’s constant $\hbar$, the speed of light $c$, the fine-structure constant $\alpha$, and the gravitational constant $G$—are traditionally regarded as axiomatic inputs to physical theory. Yet their precise values and origins remain unexplained within current frameworks. This paper proposes a new geometrical language, termed \textbf{Cosmic Structural Tensor Geometry} (CSTG), in which these constants emerge not as arbitrary parameters, but as quantized responses of rhythm paths embedded within a higher-dimensional structural background. CSTG begins with a universal structural space defined as a uniformly distributed lattice of rhythm points. Each point possesses a minimal fluctuation capacity—interpreted as the smallest allowed local tension cycle—and serves as a node in a global tensorial rhythm network. Geometry, in this view, is no longer passive background but an active system of tension gradients, curvature flows, and dimensional constraints. This work introduces seven classes of hyperspherical structural gradients, each describing a distinct geometric response mechanism: 1. Dimensional Volume Gradient 2. Packing Gradient Density 3. Rotational Shear Gradient 4. Covalent Configuration Gradient 5. Boundary Tension Gradient 6. Interdimensional Curvature Gradient 7. Eulerian Complex-Area Gradient Together, these gradients form the internal logic by which structure, rhythm, and quantization are unified. Closed loops, phase discontinuities, resonance networks, and spin phenomena are interpreted not as abstract quantum effects, but as topological and tensorial consequences of CSTG’s rhythm background. Ultimately, this framework aims to provide a new path toward understanding not only quantum behavior and classical geometry, but the origin of physical constants as geometric invariants—anchored in the deep structure of space itself.
This work introduces a geometric framework in which physical constants arise from the structure and dynamics of tension gradients in a high-dimensional hyperspherical space. A universal rhythm lattice underlies all structural behavior, governed by seven classes of tensorial gradients. Planck's constant, the fine-structure constant, and other invariants are interpreted as emergent consequences of closed tension paths, rotational phase, and structural resonance. |