Emergent SU(2) × SU(3) Topological Theory of Vacuum Dynamic Unfolding: From Initial Quantum Indeterminacy NaN to Strong Gauge Interactions

### AbstractThis work proposes a self-contained, topologically stable cosmological model that eliminates the standard Big Bang paradigm of a singular expansion from a pre-existing high-density matter state. Spacetime, electroweak, and strong gauge fields are derived as emergent properties of an infinite-dimensional, timeless information memory matrix, initially filled with data-absent states (NaN). The initialization process is described within the framework of quantum probability theory as a stochastic logical click that activates the Ricci tensor strictly inside the causal future light cone. The paper mathematically formalizes the concept of "informational inertia" of the vacuum, which generates the equations of modified R + α R² Starobinsky-type gravity for the primary spherical wave. An effective non-linear Born—Infeld-type Lagrangian with a gauge Wess—Zumino—Witten (WZW) topological lock is derived, justifying the dynamic emergence of half-integer spin-1/2 and fermionic statistics (fermiogenesis) for three-dimensional solitons (hopfions/skyrmions) without invoking the scalar Higgs field. Furthermore, the model is extended to strong non-Abelian fields of the $SU(3)$ group, providing a topological interpretation of quark confinement as the splitting of a connection into fractional components. For the first time, the quantum-information mechanics of covalent chemical bonds is formulated via the minimization of the entanglement entropy SEE of the configuration space and the topological conjugation of quantum orbitals. ### Key updates in Version 2 (v2):* Rigorous terminological control applied to eliminate non-academic computational slang from the cosmological field evolution sections.* Complete physical synchronization between the numerical simulation data logs and the multichannel field diagnostic dashboard parameters across all evolutionary steps ($t = 1$ to $t = 361$).* Integrated formal mathematical justification for the normalized step variation of the entropic gradient (SEE), resolving the bounded non-negativity constraints of standard von Neumann entropy during local informational inversion phase transitions.* Corrected LaTeX inline mathematics formatting, tensor indices, physical dimensions, and academic punctuation in accordance with APS (Physical Review) and JHEP formatting guidelines.