This exploratory article introduces the **Stabilized Angular Torsion ($\mathbf{TAS}$)** model to theoretically derive the **Topological Factor ($\mathbf{R}_{\text{Topological}}$)**. The factor $\mathbf{R}_{\text{Topological}} \approx 3.1434 \times 10^{20}$ is essential for the emergence of the gravitational constant $\mathbf{G}$ from the microscopic principles of $\mathbf{PR-TAU}$ 5.2. We decompose $\mathbf{\RTopological}$ into a dimensionless geometric component ($\mathbf{K}_{\text{Geo}}$) and a quantum scaling factor ($\mathbf{N}_{\text{Torsion}}$). The analysis of $\mathbf{K}_{\text{Geo}}$ suggests a relationship with $\pi$ modified by the non-Euclidean curvature of $\mathbf{QRDs}$, while $\mathbf{N}_{\text{Torsion}}$ must emerge from counting stable torsion degrees of freedom per $\mathbf{QRD}$ unit in a $D=4$ space. This model aims to transform $\mathbf{G}$ into a \textbf{fully predictive} constant by closing the derivation loop.