The Energy-Dimension Framework in String Theory: Dynamic Dimensions, Intrinsic Spin, and Dynamic Equilibrium Optimal Solution

This preprint presents the "Energy-Dimension" framework—a unified conceptual approach grounded in string theory. The framework proposes that the effective spacetime dimension of a string's projection is dynamically determined by the ratio of its vibrational energy to its rest energy, mediated by a dimension contraction function. All stable elementary particles correspond to discrete dynamic equilibrium optimal solutions in a parameter space spanned by rest energy, vibrational energy, and intrinsic spin.

The framework provides mechanistic interpretations for the gauge symmetries of the Standard Model, the three-generation fermion structure, wave-particle duality, and the black hole information problem. It makes several falsifiable predictions, including a dynamical dark energy equation of state—qualitatively consistent with recent DESI DR2 observations—and a particle-spectrum bias in Hawking radiation.

The framework is presented as a conceptual roadmap. The identification of the new geometry required for its mathematization is left as an open challenge for future work.