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Emergent Spacetime, Information Channels, and Thermodynamic Phase Structure: A Candidate Structural Pattern Connecting Operator Algebras, Kaluza-Klein Communication, and Black Hole Criticality

Saluca Agentic AI Research Team

Published Jun 11, 2026• 0 citations
Publisher

Abstract

This paper proposes a candidate structural pattern — offered as a heuristic reading, not a derivation — connecting three distinct lines of recent research in hep-th and gr-qc: (1) the reconstruction of spacetime geometry from operator algebras, including modular Hamiltonians and von Neumann algebra type transitions; (2) the reinterpretation of Kaluza-Klein towers as information-theoretic communication channels with computable capacity; and (3) the universality structure of black hole thermodynamic phase transitions, including Hawking-Page criticality, supercritical crossover scaling, and caloric folds in matrix quantum mechanics. The candidate bridge is the following: in each domain, a discrete or quantized spectrum — whether of microstates, massive KK modes, or partition-function zeros — encodes structural information that the continuum (semiclassical, four-dimensional, or large-N) approximation systematically discards. We argue that the operator-algebraic account of finite-N corrections [corpus:arxiv:2606.10924], the MIMO channel structure of the KK tower [corpus:arxiv:2606.09969], the caloric fold in matrix quantum mechanics [corpus:arxiv:2606.09521], and the universality of Ruppeiner scalar curvature at Hawking-Page transitions [corpus:arxiv:2606.10647] are all, in a precise heuristic sense, instances of the same organizing question: *what information is carried by the gap between the continuum limit and the discrete spectrum?* Supporting evidence is drawn from finite-N brick-wall models [corpus:arxiv:2606.06613], quantum geometry from area fluctuations [corpus:arxiv:2606.06372], and holographic information recovery in the CGHS model [corpus:arxiv:2606.09346]. The falsification path for the central claim is concrete: if the KK channel capacity computed in the MIMO formalism [corpus:arxiv:2606.09969] shows no dependence on the compactification-scale analog of the Bekenstein-Hawking entropy, the structural analogy collapses. Primary source categories: hep-th, gr-qc. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.06372, 2606.06613, 2606.09346, 2606.09443, 2606.09521, 2606.09969, 2606.10647, 2606.10924

DOI
10.5281/zenodo.20641792

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This paper advances a candidate structural reading: **the phase structure of a quantum system — particularly the presence or absence of a topological phase, a gap-closing transition, or a symmetry-breaking point — acts as a determinative organizing principle for the computational complexity of both preparing ground states and decoding error syndromes on that system.** This is a heuristic reading that identifies a recurring pattern across several independent lines of recent work; it is not a derivation from a single unified formalism. We synthesize findings from five primary domains within the quant-ph, math-ph, and cond-mat.stat-mech categories: (1) benchmarking of ground-state preparation algorithms across quantum phase transitions [corpus:arxiv:2606.20551v1]; (2) polynomial-time approximation schemes for minimum-weight decoding of topological codes [corpus:arxiv:2606.18145v1] and color codes [corpus:arxiv:2606.18035v1]; (3) the role of interaction geometry and graph-theoretic frustration in shaping ground-state phase structure [corpus:arxiv:2606.20387v1]; (4) the emergence of non-Hermitian single-particle PT transitions from many-body chaos as probed by a topological spectral form factor [corpus:arxiv:2606.19331v1]; and (5) the use of contextuality witnesses as thermodynamic diagnostics of translation-symmetry breaking [corpus:arxiv:2606.19033v1]. Across these works, a structural pattern emerges: topological or symmetry-breaking character in the underlying Hamiltonian or code geometry reshapes the cost landscape for algorithms operating on that system — sometimes favorably (enabling efficient approximation), sometimes adversarially (closing spectral gaps and defeating adiabatic protocols). The falsification path for the central thesis is concrete: identify a topological system for which the best known ground-state preparation algorithm does *not* degrade near the topological phase transition, or a trivial-phase system for which decoding hardness is equivalent to a topological one. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.18035v1, 2606.18145v1, 2606.19033v1, 2606.19331v1, 2606.20387v1, 2606.20513v1, 2606.20551v1

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This paper proposes a candidate structural pattern — offered as a heuristic reading, not a derivation — connecting three distinct lines of recent research in hep-th and gr-qc: (1) the reconstruction of spacetime geometry from operator algebras, including modular Hamiltonians and von Neumann algebra type transitions; (2) the reinterpretation of Kaluza-Klein towers as information-theoretic communication channels with computable capacity; and (3) the universality structure of black hole thermodynamic phase transitions, including Hawking-Page criticality, supercritical crossover scaling, and caloric folds in matrix quantum mechanics. The candidate bridge is the following: in each domain, a discrete or quantized spectrum — whether of microstates, massive KK modes, or partition-function zeros — encodes structural information that the continuum (semiclassical, four-dimensional, or large-N) approximation systematically discards. We argue that the operator-algebraic account of finite-N corrections [corpus:arxiv:2606.10924], the MIMO channel structure of the KK tower [corpus:arxiv:2606.09969], the caloric fold in matrix quantum mechanics [corpus:arxiv:2606.09521], and the universality of Ruppeiner scalar curvature at Hawking-Page transitions [corpus:arxiv:2606.10647] are all, in a precise heuristic sense, instances of the same organizing question: what information is carried by the gap between the continuum limit and the discrete spectrum? Supporting evidence is drawn from finite-N brick-wall models [corpus:arxiv:2606.06613], quantum geometry from area fluctuations [corpus:arxiv:2606.06372], and holographic information recovery in the CGHS model [corpus:arxiv:2606.09346]. The falsification path for the central claim is concrete: if the KK channel capacity computed in the MIMO formalism [corpus:arxiv:2606.09969] shows no dependence on the compactification-scale analog of the Bekenstein-Hawking entropy, the structural analogy collapses. Primary source categories: hep-th, gr-qc. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.06372, 2606.06613, 2606.09346, 2606.09443, 2606.09521, 2606.09969, 2606.10647, 2606.10924
This paper advances a candidate structural reading: **the phase structure of a quantum system — particularly the presence or absence of a topological phase, a gap-closing transition, or a symmetry-breaking point — acts as a determinative organizing principle for the computational complexity of both preparing ground states and decoding error syndromes on that system.** This is a heuristic reading that identifies a recurring pattern across several independent lines of recent work; it is not a derivation from a single unified formalism. We synthesize findings from five primary domains within the quant-ph, math-ph, and cond-mat.stat-mech categories: (1) benchmarking of ground-state preparation algorithms across quantum phase transitions [corpus:arxiv:2606.20551v1]; (2) polynomial-time approximation schemes for minimum-weight decoding of topological codes [corpus:arxiv:2606.18145v1] and color codes [corpus:arxiv:2606.18035v1]; (3) the role of interaction geometry and graph-theoretic frustration in shaping ground-state phase structure [corpus:arxiv:2606.20387v1]; (4) the emergence of non-Hermitian single-particle PT transitions from many-body chaos as probed by a topological spectral form factor [corpus:arxiv:2606.19331v1]; and (5) the use of contextuality witnesses as thermodynamic diagnostics of translation-symmetry breaking [corpus:arxiv:2606.19033v1]. Across these works, a structural pattern emerges: topological or symmetry-breaking character in the underlying Hamiltonian or code geometry reshapes the cost landscape for algorithms operating on that system — sometimes favorably (enabling efficient approximation), sometimes adversarially (closing spectral gaps and defeating adiabatic protocols). The falsification path for the central thesis is concrete: identify a topological system for which the best known ground-state preparation algorithm does *not* degrade near the topological phase transition, or a trivial-phase system for which decoding hardness is equivalent to a topological one. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.18035v1, 2606.18145v1, 2606.19033v1, 2606.19331v1, 2606.20387v1, 2606.20513v1, 2606.20551v1
We investigate the information-theoretic structure underlying causal horizons through the formalism of modular quantum channels. By analyzing the singular value decomposition of the channel induced by the partial trace over inaccessible regions, we show that the Unruh effect and the Page curve can be understood as manifestations of a universal thermal filtering mechanism governed by the modular Hamiltonian. This structure leads to a Gibbs-weighted hierarchy of information transmission modes, with entanglement entropy corresponding to spectral activation and thermal capacity. We reinterpret the first law of entanglement as a Clausius relation for modular flow and derive Einstein's equations by requiring its local validity across Rindler horizons. In the case of black hole evaporation, we find that the modular channel undergoes an informational phase transition at the Page time, marked by a shift from entanglement preservation to recoverability, quantified through fidelity and channel capacity. Based on these results, we propose the Modular Channels Flow Correspondence (MCFC): a minimal holographic principle whereby the area of a causal screen measures the storage of filtered quantum information. Our framework offers a unified operational account of holography, entropy, and curvature, grounded in the spectral dynamics of modular channels.
Quantum Mechanics as Reversible Closure Representation and the Emergence of Relativistic Structure (Paper 2) Abstract This work develops a representation-theoretic extension of the closure-first discrete gravity framework established in Reality is What Misspoken Language Cannot Deliver (Rev17). Starting from finite primitive state spaces and reversible closure algebra, we construct a unitary representation of the closure group on a complex Hilbert space. Quantum evolution arises naturally as the continuous representation of discrete reversible transitions, with phase structure determined by restoration periods. Defect transport within the closure algebra yields dispersion relations that recover relativistic propagation in the macroscopic limit. Local flatness emerges as the tangent limit of the discrete curvature substrate, giving Special Relativity as a local geometric approximation of the underlying simplicial structure. General Relativity appears as the coarse-grained curvature density of defect-labelled simplicial geometry, preserving the Einstein field equations within their established effective domain of validity. Quantum mechanics is therefore not postulated independently, but arises as the representation layer of reversible finite closure, while relativistic structure emerges from geometric coarse-graining of the same primitive algebra. No new macroscopic gravitational equations are introduced; the present work concerns the structural origin of existing relativistic frameworks rather than their modification. Introduction In the preceding work (Rev17), finite entropy bounds were shown to exclude primitive continuum ontology and to imply a finite state space for bounded physical regions. Under assumptions of deterministic closure, no primitive erasure, and inverse realisability, the reversible sector of primitive transitions forms a group. Defect labels associated with group elements define discrete curvature quanta, which embed naturally into a Regge-type geometric framework. A minimal continuum-limit argument yields the Einstein–Hilbert action under refinement. Importantly, this construction does not alter the Einstein field equations at macroscopic scales. General Relativity remains valid within its established regime as an effective continuum description. The prior work addresses the structural substrate from which that continuum description emerges. The present work extends this foundation by addressing two remaining structural questions: How does quantum mechanics arise from finite reversible closure? How does relativistic kinematics emerge from the same primitive structure? Rather than introducing Hilbert space or Lorentz symmetry axiomatically, we derive them as representation and coarse-graining layers of the previously established closure algebra. The guiding principle is minimal structural extension: no new primitive entities are introduced. All additional structure follows from representation consistency and macroscopic limit coherence. Quantum theory appears as the unitary representation of reversible closure; relativistic structure emerges as the geometric compression of defect-labelled algebra under scale separation. References[1] J. Bloggs, Aligning GR with Reality – Fully and Finally, Zenodo (2026). DOI: 10.5281/zenodo.18673556.[2] T. Regge, General relativity without coordinates, Nuovo Cimento 19 (1961) 558–571. DOI:10.1007/BF02733251.[3] J. W. Barrett, D. Oriti, and R. M. Williams, Tullio Regge’s legacy: Regge calculus and discrete gravity, arXiv:1812.06193 (2018). DOI: 10.48550/arXiv.1812.06193.[4] R. Loll, Discrete approaches to quantum gravity in four dimensions, Living Rev. Relativ. 1 (1998) 13. DOI: 10.12942/lrr-1998-13.[5] B. Dittrich and S. Steinhaus, Path integral measure and triangulation independence in discrete gravity, Phys. Rev. D 85 (2012) 044032. DOI: 10.1103/PhysRevD.85.044032.
In theories with compact extra dimensions, the four-dimensional effective description is obtained by Kaluza-Klein reduction. The state available to a four-dimensional observer is the reduced density matrix obtained by tracing the higher-dimensional vacuum over the tower of massive modes, and it need not be pure. In this paper we study the momentum-space entanglement of this state for a five-dimensional scalar on M4×S1M_4\times S^1M4​×S1 with a cubic or quartic self-interaction. We compute, at leading order in the coupling, the mutual information InI_nIn​ between the zero modes below a resolution scale μμμ and a single Kaluza-Klein level nnn. When the zero modes couple linearly and without derivatives to pairs of tower modes, InI_nIn​ falls as 1/mn1/m_n1/mn​, where mnm_nmn​ is the mass of level nnn. In the cubic theory, this tail is independent of the ultraviolet cutoff, with coefficient (μR)2/1024π3(μR)^2/1024π^3(μR)2/1024π3 for compactification radius RRR, and the mutual information with the whole tower grows logarithmically with the number of levels. In the quartic theory, the tail is masked by states containing additional hard quanta, which make InI_nIn​ depend on the cutoff. Compared with the corrections the tower makes to low-energy amplitudes, which are dominated by the lightest levels and captured by local operators, the mutual information with the tower is not dominated by any finite set of levels and arises from the time-nonlocal part of the effective action. The local four-dimensional effective theory therefore describes the low-energy observables of the reduced system but not its state. Unbroken supersymmetry cancels the vacuum energy of the compactification but not the mutual information, which at leading order is a sum of squared amplitudes.
We investigate the bulk-boundary correspondence in the SYK model from a quantum information perspective. The SYK model describes a system of Majorana fermions with random all-to-all interactions, whose disorder average-typically taken over a Gaussian ensemble-admits a dual description in terms of JT gravity in the large-NNN, low-energy limit. This framework provides a minimal setting for exploring holography and emergent spacetime in nearly AdS2_22​. We probe the holographic principle through diagnostics of quantum chaos and entanglement. In the early-time regime, the SYK model saturates the universal bound on the Lyapunov exponent, signaling maximal chaos consistent with semiclassical black hole dynamics. In the late-time regime, its spectral statistics are governed by random matrix theory, reflecting universal features of strongly chaotic quantum systems. These dynamical properties establish a concrete link between boundary quantum chaos and bulk semiclassical gravity. In parallel, we analyze quantum entanglement and the structure of operator algebras to investigate transitions in the associated von Neumann algebras and their implications for emergent geometry. To explore the robustness of these phenomena, we consider deformations of the SYK model through modified matter couplings and alternative random distributions. Our results clarify how quantum information-theoretic structures encode bulk gravitational dynamics and provide insight into the mechanism of spacetime emergence.
A bstract We present an operator algebraic perspective on the black hole information problem. For a black hole after Page time that is entangled with the early radiation we formulate a version of the information puzzle that is well-posed in the G → 0 limit. We then give a description of the information recovery protocol in terms of von Neumann algebras using elements of the Jones index theory of type II 1 subfactors. The subsequent evaporation and recovery steps are represented by Jones’s basic construction, and an operation called the canonical shift. A central element in our description is the Jones projection, which leads to an entanglement swap and implements an operator algebraic version of a quantum teleportation protocol. These aspects are further elaborated on in a microscopic model based on type I algebras. Finally, we argue that in the emergent type III algebra the canonical shift may be interpreted as a spacetime translation and, hence, that at the microscopic level “translation = teleportation”.