Emergent SU(2) x SU(3) Topological Theory of Tensor Vacuum Deployment: From NaN Logical Trigger to Strong Interactions and IT-Mechanics of Quantum Orbitals

This paper proposes a self-consistent, topologically stable cosmological model that eliminates the standard paradigm of the "Big Bang" as a singular expansion of pre-existing high-density matter. Space, time, electroweak, and strong gauge fields are derived as emergent properties of an infinite, timeless information memory matrix initially filled with Not-a-Number ($\text{NaN}$) states. Based on quantum probability theory, the initialization process is described as a stochastic logical click that activates the Ricci tensor strictly within the causal light cone. We mathematize the concept of vacuum "informational inertia," which generates the equations of modified $R^2$ gravity of the primary spherical wave. A non-linear effective Lagrangian with a gauge Wess--Zumino--Witten (WZW) "IT-lock" is derived. Furthermore, we explicitly formulate the IT-mechanics of chemical bonding via the minimization of the $S_{EE}$ entanglement address space, alongside extending the model to non-Abelian $SU(3)$ strong fields.