The black hole information paradox presents a fundamental tension between the global unitarity of quantum mechanics and the apparent thermal, mixed-state nature of Hawking radiation. We propose a resolution grounded strictly in the Operational Coherence Bound (OCB), a covariant entropy constraint asserting that while formal (global) information may be unbounded, the operationally accessible and distinguishable information available to any single observer must be finite. By defining operational entropy via vacuum-subtracted relative entropy to ensure finiteness in continuum quantum field theory, we prove the Operational Unitarity Theorem: in a black hole spacetime satisfying the OCB, no single observer can operationally distinguish between unitary and non-unitary evolution of the global state. This framework resolves the Hawking information loss claim, the Page curve verification problem, and the AMPS firewall paradox by demonstrating that the causal geometry of black holes dynamically enforces an observer-indexed cap on cumulative information access. Global unitarity is preserved, but its operational verification is strictly forbidden by the geometric constraints of the observer’s causal diamond.This paper was originally integrated into the Unified Framework for Yang-Mills Mass Gap, QCD Confinement, and Black Hole Information paper uploaded in March 2026 https://doi.org/10.5281/zenodo.18829529 Version 3 updates a duplication error I made in the last version.
The black hole information paradox presents a fundamental tension between the global unitarity of quantum mechanics and the apparent thermal, mixed-state nature of Hawking radiation. We propose a resolution grounded strictly in the Operational Coherence Bound (OCB), a covariant entropy constraint asserting that while formal (global) information may be unbounded, the operationally accessible and distinguishable information available to any single observer must be finite. By defining operational entropy via vacuum-subtracted relative entropy to ensure finiteness in continuum quantum field theory, we prove the Operational Unitarity Theorem: in a black hole spacetime satisfying the OCB, no single observer can operationally distinguish between unitary and non-unitary evolution of the global state. This framework resolves the Hawking information loss claim, the Page curve verification problem, and the AMPS firewall paradox by demonstrating that the causal geometry of black holes dynamically enforces an observer-indexed cap on cumulative information access. Global unitarity is preserved, but its operational verification is strictly forbidden by the geometric constraints of the observer’s causal diamond.This paper was originally integrated into the Unified Framework for Yang-Mills Mass Gap, QCD Confinement, and Black Hole Information paper uploaded in March 2026 https://doi.org/10.5281/zenodo.18829529 Version 3 updates a duplication error I made in the last version.
The black hole information paradox remains one of modern physics’ most persistent conceptual fractures. Hawking’s original formulation suggested that black hole evaporation yields thermal radiation, apparently severing the relation between the initial state and the final emitted state. Quantum theory, however, requires unitary evolution and therefore forbids true information destruction. This paper proposes that the paradox may be more fruitfully interpreted not as a flat binary contradiction between preservation and loss, but as an unresolved boundary-state problem. To clarify that claim, the paper introduces the 101 Phase State as a symbolic formalism for intermediate informational resolution. In this model, +1 denotes preserved or recoverable informational order, -1 denotes apparent loss or thermal unreadability, and 0 denotes the boundary interface at which observational contradiction becomes structurally legible but not yet fully resolved.
On the Resolution of the Black Hole Information Paradox and Firewall Exclusion via the Boundary Formalism and Observer-State Interaction Dynamics Michael Allan A. Bahtaji, Ph.D. Department of Physics, College of Science Technological University of the Philippines Ayala Boulevard, Ermita, Manila, Philippines, 1000 Email: michaelallan_bahtaji@tup.edu.ph | michaelallanbahtaji336@gmail.com Abstract We present a self-contained, unitary quantum gravitational framework resolving the Black Hole Information Paradox and eliminating the AMPS energetic firewall problem. Utilizing the Finite Boundary Formalism, we establish that the event horizon acts as a dynamic state-density boundary governed by the inverse relation . By coupling the density matrix evolution of the black hole-radiation system to the observer-state interaction operator , we derive an exact conservation equation for the fine-grained entanglement entropy . We demonstrate that beyond the Page time , a negative observer-state interaction gradient forces the emission of high-order multi-qubit correlations via localized state fluctuations . This mechanism reproduces the symmetric Page curve, enforcing complete information recovery and -matrix unitarity () while preserving smooth Horizon geometry without singular energetic firewalls.
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.
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.
Abstract The black hole information paradox arises from the tension between the thermal spectral properties of Hawking radiation and the unitarity principle in quantum mechanics. To explore the dynamical evolution characteristics of quantum fields in this context, we employ the standard quantization formalism for Dirac fields in Schwarzschild spacetime and investigate the coupling structure of particle and antiparticle modes within a framework that transcends the single-mode approximation. By calculating the states of externally observable subsystems, we systematically derive the evolution of concurrence and first-order coherence as functions of the Hawking temperature. Additionally, we assess the impact of varying initial parameters on these quantities. We further contrast the quantum entanglement differences between the observable exterior region and the black hole interior across diverse temperature regimes. These results provide valuable insights into the evolution of entanglement and coherence in curved spacetime.
Abstract In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the “black hole information paradox”. Two main types of resolution postulate either a fundamental loss of information in Nature — hence the breakdown of quantum mechanics — or some sort of new physics, e.g. quantum gravity, which guarantee the global preservation of unitarity. Here we explore the second possibility with the help of recent developments in continuous-variable quantum information. Concretely, we employ the solution to the Gaussian quantum marginal problem to show that the thermality of all individual Hawking modes is consistent with a global pure state of the radiation. Surprisingly, we find out that the mods of radiation of an astrophysical black hole are thermal until the very last burst. In contrast, the single-mode thermality of Hawking radiation originating from microscopic black holes, expected to evaporate through several quanta, is not excluded, though there are constraints on modes' frequencies. Our result paves the way towards a systematic study of multi-mode correlations in Hawking radiation.