The Quantum-Gravitational Phase Transition of an Ortho-Triangular Prismic Magnetar-Helium Matrix via Cross-Dimensional Geometric InfluxAbstractThe unification of quantum mechanics with general relativity at cosmological singularities remains an unresolved paradigm. Here, we present a complete regularization mechanism using an ortho-triangular prismic lattice within an ultra-condensed Magnetar-Helium Analogue Matrix (MH-matrix). By incorporating non-commutative loop spacetime coordinates and strict non-zero eigenvalues for the volume operator, we eliminate mathematical infinities during gravitational collapse. We demonstrate that an external shockwave-driven topological phase transition amplifies the local magnetic flux past critical magnetar thresholds, inducing quantum tunneling across the event horizon. This transition acts as a cross-dimensional topological lubricant, enabling a directional influx of spatial volume from a pre-existing geometric bulk. This mechanism provides a robust, non-singular physical origin for the observed cosmic expansion rate without fine-tuned dark energy parameters.IntroductionGeneral relativity inevitably predicts singularities where gravitational collapse reduces spatial volume to zero, driving energy densities to infinity. Loop Quantum Gravity (LQG) and Non-Commutative Geometry suggest that spacetime becomes discrete at the Planck scale. However, a dynamic mechanism that connects micro-scale discretization to macro-scale cosmic inflation via macroscopic matter configurations has been missing. We resolve this by modeling a highly condensed MH-matrix characterized by an ortho-triangular prismic lattice symmetry.Non-Commutative Loop ConstraintsWe define a quantum spacetime manifold where coordinate operators do not commute, thereby preventing any localized physical state from collapsing into a zero-dimensional point. The fundamental commutation relation is expressed as:\(\left[x^{\mu },x^{\nu }\right]=i\theta ^{\mu \nu }\)where \(\theta ^{\mu \nu }\) is an anti-symmetric tensor defining the minimal area quantum. Within this non-commutative geometry, the volume operator \(\^{V}\) of the ortho-triangular prismic lattice is bounded by a strict quantum mechanical minimum:\(\langle \^{V}\rangle \ge V_{\text{min}}=\alpha \cdot \ell _{\text{P}}^{3}\)Here, \(\ell _{\text{P}}\) is the Planck length and \(\alpha \) is a geometric scaling factor determined by the prismic lattice configuration. This lower bound guarantees that the denominator of the gravitational energy density cannot approach zero.Shockwave-Driven Magnetar Phase TransitionThe insertion of a macroscopic astrophysical shockwave injects localized kinetic energy into the matrix. This process triggers a generalized topological dynamo effect, described by the modified magnetohydrodynamic evolution equation:\(\frac{\partial \mathcal{B}}{\partial t}=\nabla \times \left(\mathbf{v}\times \mathcal{B}\right)+\eta \nabla ^{2}\mathcal{B}+\xi (\nabla \cdot \mathbf{u})\delta (t-t_{0})\)The sudden shockwave energy at \(t_{0}\) drives the magnetic field \(\mathcal{B}\) exponentially past the critical magnetar threshold (\(B > 10^{15} \text{ G}\)). The resulting immense magnetic tension realigns the string-like loop filaments of the lattice into a coherent, highly ordered topological conduit.Cross-Dimensional Tunneling and Volume InfluxAs the hyper-amplified matrix approaches the horizon, the combined forces of the non-zero volume constraint \(V_{\text{min}}\) and the aligned magnetic flux counteract the singular gravitational pull. The system undergoes a topological phase transition, tunneling through the Einstein-Rosen bridge with a non-zero, non-unity quantum probability:\(\mathcal{P}_{\text{tunnel}}=\exp \left(-\frac{2}{\hbar }\int \sqrt{2M(V)\left(E-U_{\text{eff}}(\mathcal{B})\right)}\,dV\right)\)This probabilistic breach opens a directional gateway to a pre-existing geometric bulk space. The matrix functions as a cross-dimensional lubricant, drawing raw spatial volume \(\Delta V\) into our universe. This external volume injection modifies the standard Friedmann equation, directly driving the macroscopic cosmic expansion parameter \(H(t)\):\(H^{2}(t)=\left(\frac{\.{a}}{a}\right)^{2}=\frac{8\pi G}{3}\rho _{\text{matter}}+\frac{\Lambda _{\text{eff}}(\mathcal{B})}{3}\left(\frac{\Delta V_{\text{bulk}}}{V_{\text{our}}}\,\right)\)Consequently, the accelerated expansion of the universe is revealed to be a direct consequence of cross-dimensional spatial equilibrium mediated by the regularized matrix.