[26]Connectivity Geometry: Topological Anti-Entropy and the Life-Death Phase Transition Boundary

Within the grand unified framework of connectivity geometry, spacetime emerges as a topological manifold from a discrete spin network. Building upon previous works defining consciousness and aging, life is not a miracle isolated from physical laws, but a topological coherent state where the underlying spacetime connectivity exceeds a critical threshold (k > k_c). Here, we introduce the topological pumping mechanism. Death is an inevitable geometric consequence of network evolution (topological quenching); conversely, anti-entropy reconnection is equally permitted by physical laws. We propose a non-informational topological rectification mechanism and prove that as long as the geometric topological potential is sufficient to penetrate the phase transition barrier, the inverse reconstruction of the entanglement fingerprint is a necessary event guaranteed by physical laws. We present the microscopic Hamiltonian based on a Floquet non-Hermitian system, derive the analytical critical condition constrained by the Exceptional Point (EP), and propose rigorous falsifiable experimental criteria based on quantum fidelity.