UDCT v2.6: Geometric Mass Generation and Self-Regulating Vacuum Dynamics via Higher-Dimensional Geometric Effects

The Unified Dimensional Cohesion Theory (UDCT) has been developed as a geometric framework in which vacuum expectation values and mass generation can emerge dynamically from higher-dimensional back-reaction rather than from a static local potential. Motivated by the possibility that this mechanism might offer a new perspective on the Higgs hierarchy problem, we explore the application of UDCT to the electroweak sector. In this work (UDCT v2.6), we present an improved formulation in which the bidirectional projection operator ΨBD is formulated as a geometric response arising from the interaction between the 4D scalar field and the compact internal space. Using a globally coupled pseudo-spectral numerical framework, we investigate whether such a geometric construction can lead to self-regulating vacuum dynamics without requiring extreme fine-tuning. A complete 3D Python implementation of the model is provided in the Appendix for direct verification. This study examines the possibility of applying the geometric principles of UDCT to the Higgs hierarchy problem, guided by the author’s intuition that higher-dimensional effects could play a meaningful role in stabilizing the electroweak scale. This work is a direct sequel to UDCT v2.5, extending the same first-principles geometric approach from galactic dynamics and cosmology into the particle physics domain.