The black-hole information paradox is usually formulated as a conflict between two semiclassical statements: Hawking evaporation appears to radiate away mass in a nearly thermal manner, while unitary quantum dynamics forbids the destruction of information. In this paper we construct a macroscopic black-hole surrogate inside the discrete, background-free Quantum Graph Emergent Field Theory (QGEFT) and track both horizon-entanglement proxies and the topological fate of explicitly injected information. Starting from a thermalized Unified Phase 3 universe with N = 1024 sites, we force a localized geometric collapse by driving one node to target degree k = 160, then inject a structured quark-like defect whose internal edges are tracked exactly through 100 subsequent Monte Carlo sweeps. The key observable is a horizon cut-size proxy: the number of edges crossing between the black-hole region and the exterior vacuum, together with a normalized entanglement proxy built from that cut. In the present benchmark the horizon cut-size rises from 1027 to a peak of 1030 edges at sweep 1, while the normalized cut-based entanglement proxy rises from 2.7483 to 2.7563, then trends downward with fluctuations to 2.5941 by sweep 100 as the black-hole core shrinks from degree 161 to 132. At the same time, direct tracking of the infalling quark reveals incomplete local reconstruction: only 25% of the tracked edges appear outside the horizon as distinct edges at any given sampled frame, and the best structural-overlap score reaches only 0.3946. The narrow conclusion supported by the current data is therefore mixed. The black hole exhibits a real topological evaporation channel and a measurable Page-like turnover in the horizon entanglement proxy, but local observables remain Hawking-leaning and do not by themselves recover the full infalling structure. In the QGEFT interpretation, this is evidence for fast scrambling rather than literal information destruction: the information is not recovered as a small intact motif, but is dispersed into the global topological microstate of the graph.
The black-hole information paradox is usually formulated as a conflict between two semiclassical statements: Hawking evaporation appears to radiate away mass in a nearly thermal manner, while unitary quantum dynamics forbids the destruction of information. In this paper we construct a macroscopic black-hole surrogate inside the discrete, background-free Quantum Graph Emergent Field Theory (QGEFT) and track both horizon-entanglement proxies and the topological fate of explicitly injected information. Starting from a thermalized Unified Phase 3 universe with N = 1024 sites, we force a localized geometric collapse by driving one node to target degree k = 160, then inject a structured quark-like defect whose internal edges are tracked exactly through 100 subsequent Monte Carlo sweeps. The key observable is a horizon cut-size proxy: the number of edges crossing between the black-hole region and the exterior vacuum, together with a normalized entanglement proxy built from that cut. In the present benchmark the horizon cut-size rises from 1027 to a peak of 1030 edges at sweep 1, while the normalized cut-based entanglement proxy rises from 2.7483 to 2.7563, then trends downward with fluctuations to 2.5941 by sweep 100 as the black-hole core shrinks from degree 161 to 132. At the same time, direct tracking of the infalling quark reveals incomplete local reconstruction: only 25% of the tracked edges appear outside the horizon as distinct edges at any given sampled frame, and the best structural-overlap score reaches only 0.3946. The narrow conclusion supported by the current data is therefore mixed. The black hole exhibits a real topological evaporation channel and a measurable Page-like turnover in the horizon entanglement proxy, but local observables remain Hawking-leaning and do not by themselves recover the full infalling structure. In the QGEFT interpretation, this is evidence for fast scrambling rather than literal information destruction: the information is not recovered as a small intact motif, but is dispersed into the global topological microstate of the graph.
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.
This work examines a specific premise in the black-hole information problem: the assertion that complete quantum evolution preserves arbitrary initial quantum distinctions through the full formation and evaporation of an actual four-dimensional black hole possessing a genuine event horizon. The paper does not argue that fundamental information destruction occurs. It does not reject unitary quantum mechanics or the substantial mathematical progress represented by holography, quantum error correction, entanglement islands, replica wormholes, Page-curve calculations, asymptotic observable algebras, or gravitational reconstruction. Instead, it asks what establishes that the scope of such results reaches the complete physical black-hole process for which global preservation is asserted. For a registered ordinary future-directed causal route from strictly inside a genuine event horizon to the stipulated exterior future, the event-horizon and Structural Flow translation premises imply that ordinary outward Cascade and same-route Authorization do not occur. This route result does not determine the global fate of quantum information. The restricted horizon-facing premises entail neither guaranteed global quantum-information preservation nor fundamental global information destruction. The complete physical fate therefore remains dependent on additional physics-owned premises. The work distinguishes global preservation from restricted exterior recoverability. A preservation claim must specify the physical target process, admitted quantum input family, governing dynamics, physically complete output system, relevant quantum-coherence burden, and applicability of the mathematical result to the actual gravitational regime being claimed. Recovery from Hawking radiation alone is not privileged as the only admissible proof route, and inability to recover information from a restricted radiation subsystem is not sufficient to establish fundamental loss. A public falsification and reopening protocol accompanies the paper. It separates model- and code-level advances, physical preservation or loss results, event-horizon domain-translation failures, and genuine foundational Structural Flow counterderivations. A black-hole-specific failure does not automatically reopen universal Structural Flow, the Universal Kernel, or the TOE. The release also includes a machine companion and a consolidated Lean formal append evaluated with the unchanged Structural_Flow_Universal_Kernel_v1.0.lean. The supplied Lean Web execution record reported all 68 expected theorem checkpoints from the integrated source with no compiler errors reported. The consolidated BH-EH source contains 69 theorem declarations. Machine closure is explicitly limited to the encoded conditional logical scope. The formal layer does not establish the existence of an actual event horizon, the physical validity of the Structural Flow translation, complete quantum-gravitational dynamics, or the global information fate of real black holes. This coordinated package contains the scientific anchor, public falsification/reopening protocol, machine companion, scoped BH-EH formal append, and frozen Universal Kernel.
A bstract When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/ 2 π log S BH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.
This work examines a specific premise in the black-hole information problem: the assertion that complete quantum evolution preserves arbitrary initial quantum distinctions through the full formation and evaporation of an actual four-dimensional black hole possessing a genuine event horizon. The paper does not argue that fundamental information destruction occurs. It does not reject unitary quantum mechanics or the substantial mathematical progress represented by holography, quantum error correction, entanglement islands, replica wormholes, Page-curve calculations, asymptotic observable algebras, or gravitational reconstruction. Instead, it asks what establishes that the scope of such results reaches the complete physical black-hole process for which global preservation is asserted. For a registered ordinary future-directed causal route from strictly inside a genuine event horizon to the stipulated exterior future, the event-horizon and Structural Flow translation premises imply that ordinary outward Cascade and same-route Authorization do not occur. This route result does not determine the global fate of quantum information. The restricted horizon-facing premises entail neither guaranteed global quantum-information preservation nor fundamental global information destruction. The complete physical fate therefore remains dependent on additional physics-owned premises. The work distinguishes global preservation from restricted exterior recoverability. A preservation claim must specify the physical target process, admitted quantum input family, governing dynamics, physically complete output system, relevant quantum-coherence burden, and applicability of the mathematical result to the actual gravitational regime being claimed. Recovery from Hawking radiation alone is not privileged as the only admissible proof route, and inability to recover information from a restricted radiation subsystem is not sufficient to establish fundamental loss. A public falsification and reopening protocol accompanies the paper. It separates model- and code-level advances, physical preservation or loss results, event-horizon domain-translation failures, and genuine foundational Structural Flow counterderivations. A black-hole-specific failure does not automatically reopen universal Structural Flow, the Universal Kernel, or the TOE. The release also includes a machine companion and a consolidated Lean formal append evaluated with the unchanged Structural_Flow_Universal_Kernel_v1.0.lean. The supplied Lean Web execution record reported all 68 expected theorem checkpoints from the integrated source with no compiler errors reported. The consolidated BH-EH source contains 69 theorem declarations. Machine closure is explicitly limited to the encoded conditional logical scope. The formal layer does not establish the existence of an actual event horizon, the physical validity of the Structural Flow translation, complete quantum-gravitational dynamics, or the global information fate of real black holes. This coordinated package contains the scientific anchor, public falsification/reopening protocol, machine companion, scoped BH-EH formal append, and frozen Universal Kernel.
The core of the black hole information paradox is whether information falling into the horizon is completely lost during Hawking radiation. Based on connectivity engineering, this paper constructs a one-dimensional spin network with an effective horizon structure. We divide the system into a black hole interior (A) and exterior radiation (B), introducing a cross-horizon tunneling coupling ε. Numerical simulations show that the fidelity of the initial state in region A decays rapidly and plateaus, exhibiting a local information loss illusion; however, the quantum mutual information between regions A and B increases significantly. Furthermore, decoding operations based on the Hayden-Preskill protocol elevate the recovery fidelity to above 0.7 (far exceeding the random baseline), and the maximum entanglement capacity approaches the theoretical maximum 2 ln dim(A). This model requires no gravitational degrees of freedom and relies purely on many-body unitary evolution, providing a minimal deterministic dynamical example for the microscopic implementation of information conservation in Hawking radiation.
The complete evaporation of black holes, as a natural endpoint of Hawking radiation, gives rise to the black hole information paradox, which fundamentally challenges the principles of unitarity and information conservation in quantum mechanics. Although the AdS/CFT correspondence indicates that information is preserved during black hole evaporation, the precise mechanism by which it is recovered from the Hawking radiation remains an open question. To explore a potential resolution, we investigate information transfer in a spin-chain model featuring an effective horizon realized via position-dependent couplings within an XY spin chain. We derive and demonstrate Page curve-like behavior, and analyze the transmission of quantum resources, such as entanglement and coherence, across the effective horizon. Our results show that quantum resources initially localized within an interior subsystem can be transferred to the exterior via particle radiation through the horizon. This study provides a novel perspective from quantum simulation on how information may escape from black holes, thereby contributing to the further understanding of the black hole information paradox.