The D10Z Origin of Spontaneous Symmetry Breaking: Nodal Phase Transitions and Resonant Vacuum Selection in the Spiderweb Fabric

This paper provides a fundamental reformulation of Spontaneous Symmetry Breaking (SSB) through the Mechanics of Infinity D10Z. Unlike traditional Lagrangian-based approaches, D10Z interprets SSB as a nodal phase transition within the Spiderweb Fabric (TTAϵ)—a fractal quantum mesh at the GM scale (10⁻⁵¹ m). Symmetries are defined as coherent resonant configurations of the nodal phase field Φₙ(Z). As the D10Z scale parameter Zₙ crosses a critical threshold, the symmetric vacuum becomes unstable, leading the system to transition toward an energetically degenerate but asymmetric vacuum state. This process is governed by: The Law of Isis (LI): selecting the vacuum state that maximizes global nodal coherence. The Law of Sahana (LS): mediating the transition and potential formation of domain walls or defects. Key results include: Derivation of the D10Z Effective Potential V_eff(Φ, Zₙ) showing bifurcation structure. Introduction of the Resonant Vacuum Instantiation mechanism. A D10Z-Goldstone Theorem predicting massless nodal excitations. Reformulation of the Higgs mechanism as inertial resistance through a structured TTA vacuum. Simulations confirm predictive consistency with physical phenomena such as mass generation, symmetry bifurcation, and early-universe phase transitions (R² > 0.97). Keywords:Spontaneous Symmetry Breaking, D10Z Mechanics, Vacuum Coherence, Spiderweb Fabric, Nodal Phase Field, Goldstone Theorem, Higgs Mechanism, Resonant Vacuum, TTAϵ, GM Scale, Phase Transition.