The Holographic Geometric Tension Principle: Fermion Mass Hierarchy, Generation Curvature, and Collapse Scale from 4-Bit Boundary Tilting

Key Points

• The aim is to unify fermion mass hierarchy, generation curvature, and collapse scale using a geometric approach.
• Exploration of 16 fermion states represented by tile-tilt patterns on a boundary.
• Application of the master formula m_g(f) incorporating class geometry and generation curvature.
• Incorporation of specific inputs: Poisson ratio and a constant.
• Fermion masses are characterized by the unified formula that incorporates curvature and geometric principles.
• Key geometric angles for generation curvature are identified: θ₁=5.6°, θ₂≈60°, θ₃≈86.8°.
• The study provides insights into the interrelations of mass hierarchy and boundary tilting.