9D-USTE Potential Structure and Vacuum Ground State Analysis

Within the framework of the nine-dimensional Ultra-Spacetime-Time-Evolution (9D-USTE) theory, this work systematically investigates the potential structure and vacuum properties of the fundamental scalar field K^*. By constructing a positive-definite quadratic potential with strict even symmetry, we rigorously prove that K^* = 0 is the unique global minimum and stable vacuum ground state of the system. The results show that there is no spontaneous symmetry breaking in the nine-dimensional fundamental field at high-energy scales. This work completes the vacuum dynamics sector of 9D-USTE and provides a new perspective for understanding the primordial vacuum of the Universe and the high-dimensional origin of low-energy physical phenomena.