Resolving the Black Hole Information Paradox via the SV0 Island Formula and Universal Information Field

The Black Hole Information Paradox remains one of the most profound challenges in theoretical physics, questioning the unitarity of quantum mechanics in the presence of gravity. While the Signed-Volume (SV0) framework addressed this qualitatively via the Universal Information Field (UIF) in Paper XVI, a rigorous mathematical derivation using modern quantum gravity tools is required. In this paper (Paper XXII of the SV0 series), we formalize the SV0 resolution of the paradox by employing the Quantum Extremal Surface (QES) prescription and the Island Formula. We demonstrate that the UIF naturally provides the non-local entanglement structure required for an "island" to emerge in the black hole interior. By calculating the fine-grained entropy of Hawking radiation, we show that the SV0 logistic exchange law strictly governs the Page Curve, ensuring that information is conserved and unitarity is restored. This work firmly establishes the SV0 model as a unitary theory of quantum gravity.