Zero-Time Phase Transitions, Vacuum Seed Nucleation, and Memory-Guided Re-collapse in Dual Gravity Frameworks

This paper formulates a unified theoretical resolution for the Arrow of Time paradox and the Black Hole Information Paradox within a dual-gravity framework. We analyze the mechanism where spacetime metrics reach an emergent stationary state of zero-time (\Delta t = 0) during maximal gravitational core compression (R_{\text{core}}). Matter transitioning into localized wave states preserves its structural quantum memory spectrum (\mathcal{I}_{\text{memory}}) through stored anti-energy (E_{\text{anti}}). When a critical mass-spin threshold is surpassed (\Omega \ge \Omega_{\text{critical}}), a spontaneous quantum vacuum pressure gradient (\mathbf{F}_{\text{seed}}) triggers a phase transition, expelling positive energy and memory-guided anti-energy to drive secondary matter re-collapse into structured macroscopic configurations. The master equations are mathematically validated across Cosmological, Mesoscopic, and Quantum scales.