Technical Supplement: Mechanical Principles and Algebraic Derivations of the Dual Model

Key Points

• The aim is to establish a mathematical framework for the Dual Magnetic Current model and redefine the vacuum's properties.
• Defined the vacuum fabric as a helical topological manifold M
• Developed a mechanical model replacing stochastic interpretations
• Introduced a gear-based interlocking system to illustrate these principles
• Established that the vacuum exhibits intrinsic mechanical elasticity
• Replaced randomness in quantum mechanics with deterministic mechanical principles