SV-TGD 5.0: Discovery of a Vacuum Yield Threshold and the Dynamical Origin of Spin-1/2 — Ultimate Complete Edition

This paper presents SV-TGD 5.0 (Super-Fluid Vacuum Theory of Geometric Dynamics), a unified field theory framework that models the physical vacuum as a hyper-pressurized, non-Newtonian granular fluid (Discrete Vacuum Quanta lattice). By treating fundamental particles not as point-like singularities but as topological solitons within this elastic medium, the theory offers deterministic mechanical solutions to several longstanding problems in fundamental physics. Key Contributions: Resolution of the Proton Radius Puzzle: We derive the proton radius (approx. 0.841 fm) as a geometric "Vacuum Yield Threshold". The discrepancy between muonic and electronic hydrogen measurements is explained as a phase transition of the vacuum lattice under high shear stress, akin to the yield point of a granular material. Dynamical Origin of Spin-1/2: Through numerical simulations of the renormalized field equations, we demonstrate that fermion spin emerges as a Parametric Resonance Attractor. The electron soliton spontaneously locks into a 2:1 subharmonic oscillation (particle frequency equals half the vacuum frequency) driven by vacuum fluctuations. The stability of this state is confirmed by the observation of an Arnold Tongue in the frequency response spectrum. Resolution of Wave-Particle Duality: We introduce the Soliton-Wake Resonance Mechanism, a deterministic hydrodynamic model where the particle core is guided by its own radiation field (pilot wave). This reproduces quantum interference patterns in double-slit scenarios without invoking ontological superposition. Unified Field Equations: We present a dimensionally consistent, renormalized effective field equation that unifies gravity (transverse lattice modes) and electromagnetism (contact electrification) under a single mechanical strain tensor. Theoretical Scope: SV-TGD 5.0 is rigorously defined as a semi-classical framework. While it successfully reconstructs General Relativity and the Standard Model's particle spectrum from first principles, non-local quantum phenomena (e.g., entanglement) are treated as open problems for future extensions. This edition includes verified numerical codes, rigorous dimensional analysis, and detailed experimental predictions (e.g., Vacuum Spin Rectification).