The Black Hole Information Paradox a Resolution

The Black Hole Information Paradox: A Resolution via Substrate Topology in Unified Fluid Field Theory The black hole information paradox presents a fundamental challenge to modern physics: how can black holes emit apparently thermal Hawking radiation while preserving the quantum information contained in the matter they absorb? This research develops a physical mechanism for information preservation and recovery within Unified Fluid Field Theory (UFFT), connecting black hole thermodynamics, horizon geometry, quantum entanglement, and the dynamics of energy return through a common underlying substrate. In UFFT, physical reality emerges from a discrete relational substrate whose twelve-component state structure supports interacting identity, geometry, and structure sectors. The event horizon is interpreted as a topological transition in the accessibility of these sectors. Information carried by infalling matter is not destroyed but transferred into interior substrate degrees of freedom, where it remains part of the complete physical state. Hawking radiation arises through the horizon's geometry-dependent response, while information becomes accessible through correlations generated by the continuing interaction between interior and exterior sectors. Building upon Exploring a Fluid Universe and the published Closure Mechanics framework (DOI: 10.5281/zenodo.23964171), this study develops an explicit mathematical description of outward energy transfer, delayed return, quantum information exchange, and horizon thermodynamics. An action-derived causal memory kernel describes how information-bearing activity propagates through complementary substrate degrees of freedom and subsequently influences the originating system. The calculations establish several quantitative results. A conservative quantum exchange model transfers arbitrary quantum states with numerical errors below 10⁻¹⁵. An eight-qubit unitary evaporation model reproduces a Page-shaped entanglement entropy curve, reaching 3.35977 bits before returning to zero, while individual emitted qubits retain thermal reduced states. Independent random-state calculations reproduce Page's statistical entropy prediction. A near-horizon stress-tensor calculation in the two-dimensional conformal reduction recovers finite stress at the future horizon, outward Hawking energy flux, and the compensating negative ingoing energy flux. Together, these results demonstrate the mathematical compatibility of thermal radiation, globally unitary information recovery, and regular horizon behavior. Within UFFT, the proposed physical connection is the substrate's energy-return mechanism: information may become inaccessible to external observers without being destroyed and may subsequently reappear through correlations in outgoing radiation. Extending the finite recovery mechanism to a complete astrophysical black hole requires identifying the corresponding horizon coupling within the physical substrate action. The framework also connects black hole information dynamics to particle-scale temporal decoupling through the previously introduced (R_{mg}) transition-entropy observable (DOI: 10.5281/zenodo.18821542). Analog black hole systems, particularly Bose–Einstein condensate horizons, offer a potential experimental route for investigating correlations between horizon proximity, information accessibility, and temporal-sector response. This research presents a unified physical account of information conservation, Hawking emission, entanglement redistribution, and horizon regularity. Its central proposition is that black hole information is not lost through evaporation: it is redistributed through physical substrate interactions, with its recovery encoded in the correlations of the complete outgoing quantum state.