Topological Saturation of the Page Curve in Geometrically Decoupled Spin Networks
Wenjun Luo
The core of the black hole information paradox lies in whether Hawking radiation leads to information loss. Based on connectivity engineering, we construct a minimal, gravity-free spin network. By calculating the mutual information and fidelity across different bipartition sizes, we reproduce the complete Page curve. Numerical results show that the peak of mutual information in the geometrically decoupled network (k=3) exhibits a non-trivial scaling behavior with the connectivity k, and reaches saturation at k=3 (with a peak approximately 1.49 times that of the normal network). This not only reveals the reshaping of entanglement capacity by geometric topology but also establishes a topological upper bound for the Page curve peak. Fidelity analysis further reveals that in the late stages of evaporation, the residual subsystem tends towards purification, with the target state fidelity significantly rising to approximately 0.52, which is weakly sensitive to k. This indicates that information is not completely thermalized but exists in a highly compressed global correlation form within the entanglement structure of the black hole residue and external radiation. This model provides a deterministic and strictly reproducible discrete physical benchmark for studying black hole information dynamics.
•Oct 25, 2026•0 citations