SV-TGD 4.0 - A Granular Mechanical Foundation (Ultimate Rigid Proof)

This paper presents SV-TGD 4.0, a comprehensive semi-classical framework that reconstructs the laws of physics from the statistical mechanics of a discrete, hyper-pressurized granular medium. We postulate that the physical vacuum consists of rigid, dodecahedral Discrete Vacuum Quanta (DVQ) arranged in a "Deep-Sea Jamming" Face-Centered Cubic (FCC) lattice. By applying Hertzian contact mechanics and non-equilibrium statistical coarse-graining, we derive the fundamental field equations of electromagnetism and gravity from a single unified strain tensor ε_μν. Key achievements of the theory include: Unification of Forces: Electromagnetism is identified as transverse shear waves, while gravity emerges from the refractive index gradients of the lattice near its critical jamming density. Particle Genesis: Elementary particles, specifically the electron, are modeled as stable topological screw dislocations ("Spark Solitons"). We provide a rigorous mathematical proof that the gyromagnetic ratio |g|=2 is a necessary geometric consequence of the soliton's Bessel function profile and the Hertzian contact law, without relying on ad hoc parameter fitting. Resolution of Anomalies: The proton radius puzzle is resolved via a derived vacuum yield threshold ρ_c, and the fine-structure constant α is geometrically interpreted. SV-TGD 4.0 eliminates the need for abstract entities such as the Higgs field or intrinsic spin, replacing them with mechanical self-energy and topological winding constraints. The theory strictly adheres to a classical framework, reinterpreting quantum vacuum fluctuations as high-frequency statistical noise within the granular background.