The Angular Unification Theory (TAU): Complex Geometry, Topological Dynamics, and the Causal Origin of Dark Energy

This article presents the \textbf{Angular Unification Theory ($\TAU$)}, an ontological framework postulating a network of \textbf{Dynamic Relational Quanta ($\QRDs$)}. The $\mathbf{\PRTAU}$ update integrates **Angular Topological Dynamics** and the principle of **Self-Adaptive Critical Pressure ($\mathbf{\Pcrit}$)**. We generalize the Mass-Energy Equivalence: $\mathbf{E}_{\mathbf{\TAU}} = m c^2 + \mathbf{\Delta E_{\mathbf{\TAU}}}$, where the **Vacuum Regularization Energy ($\mathbf{\Delta E_{\mathbf{\TAU}}}$)** resolves the **Proton Radius Puzzle** via its unique kinematic signature $\mathbf{\Delta E_{\mathbf{\TAU}}} \propto \mathbf{m}_l^3$. $\mathbf{\PRTAU}$ also formalizes the **superluminal propagation** of topological information ($\mathbf{v}_{\mathbf{\Theta}} > c$) and defines **Dark Energy** as the result of inter-universe tension ($\mathbf{\Lambda_B}$) and **Angular Dissipation ($\mathbf{\gamma}$)**, leading to a falsifiable prediction $\mathbf{w_a^{\text{TAU}}} \neq 0$.