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.
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.
The series Time as Phase Flow (Papers I–IV) established that time is not fundamental but emerges from the geometric phase flow of quantum information, providing a unified account of dynamically generated cosmological constants, informational temporal viscosity, and the suppression of large-scale structure. Despite these successes, a fundamental mechanism explaining why a single, stable observable reality emerges from the space of quantum informational states has remained unresolved. In this work, we introduce the framework of Information-Geometric Spacetime (IGS), in which spacetime itself emerges from the geometry of quantum information, entanglement, and modular flow. Within IGS, we define an Actualization Operator that mediates between quantum informational states and observable spacetime geometry. Derived from first principles, the operator combines entropy-based suppression with modular evolution, governed by a universal geometric constant β = 1/(π√3) ≈ 0.1837 fixed by the geometry of causal diamonds and the associated modular Hamiltonian. We show that actualization preserves information conservation and quantum unitarity, acting as a structural filter that selectively stabilizes informational states capable of forming consistent geometric reality, in close analogy with decoherence-driven classical emergence. Under this mechanism, previously identified cosmological effects—most notably the suppression of the matter power spectrum and the S_8 tension—are reinterpreted as observational consequences of information actualization rather than modifications of gravity or exotic matter. This framework also offers a geometric reformulation of the quantum measurement problem, in which the observer is not an external agent but an emergent process associated with modular structure and entanglement thermodynamics. The theory yields testable predictions in controlled quantum systems and forthcoming cosmological surveys, providing a concrete pathway toward empirical tests of spacetime emergence from quantum information.
We develop a unified framework in which physical reality emerges from the spectral properties of informational states. Starting from the density operator ρ, we construct the modular generator K = −log ρ and its spectral distribution p(k) as the fundamental objects. We demonstrate that structure, locality, geometry, dynamics, and scale arise sequentially from properties of the modular spectrum. Renormalization is reinterpreted as spectral flow, and physical phases are defined through optimal partitions of informational structure. We further show that stable spectral modes correspond to matter-like structures, while gauge symmetry emerges as an access-relative redundancy. A universal dynamical equation is formulated, governing all physical regimes in a phase-dependent manner. The framework is supported by a reproducible numerical program and extended to flavor physics, where we derive the structure of quark mixing and CP violation from spectral hierarchy. This work establishes a unified perspective in which physical structure is understood as an emergent consequence of distinguishability and spectral organization.
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
We propose a reconstruction of physical theory based on the principle of distinguishability, formulated within the framework of Universal Modular Dynamics (UMD). Instead of assuming spacetime, fields, or dynamical laws as fundamental, we begin with a minimal relational structure defined by distinguishable proto-states. We show that consistency requirements on distinguishability lead naturally to a probabilistic structure, whose basis-invariant representation is given by the density operator ρ. The associated modular generator K = −log ρ encodes the intrinsic organization of the system, while its spectral distribution provides a complete description of informational structure. Within this framework, dynamics is reinterpreted as a flow in the space of states, and the renormalization group is identified with spectral evolution of ρ. Phase structure emerges from the behavior of optimal partitions, leading to an operational notion of criticality defined by landscape flatness and switching rates. We demonstrate that geometry, gauge structure, and gravitational behavior arise as emergent phenomena associated with specific dynamical regimes. In particular, gauge symmetry is interpreted as access-relative redundancy, and spacetime structure appears as an effective description of underlying spectral organization. The framework is supported by a computational program that introduces operational diagnostics, including spectral observables, modular commutators, and phase classification criteria. These tools allow for numerical exploration and identification of domains of validity. The results suggest that a unified description of physical reality can be constructed from a minimal informational ontology, in which all structures arise from intrinsic properties of the density operator and its modular dynamics.
We develop a group-theoretic interpretation of the Unruh effect based on affine symmetry on a light ray and relate it to modular theory. For a massless scalar field in two spacetime dimensions inertial and uniformly accelerated observers select two different flows within the same chiral one-particle structure, respectively, null translations and dilations. Minkowski modes are adapted to translations, while Rindler modes are adapted to dilations, with the Mellin transform providing the natural bridge between them. When a Minkowski positive-frequency mode is restricted to a single Rindler wedge, its comparison with Rindler modes is non-unitary within the positive-frequency sector. Modular theory gives the corresponding operator-algebraic interpretation: on the horizon the modular flow of the half-line algebra is implemented by dilations, and the restricted vacuum satisfies the KMS condition. The affine group thus appears as the minimal symmetry structure underlying thermality on the Rindler horizon.
We present a causal, falsifiable law of observer-indexed entropy retrieval dynamics in which the growth rate of retrievable entropy is proportional to the remaining entropy gap and modulated by a hyperbolic-tangent onset at a characteristic proper time tau_char. Unlike ensemble-averaged, non-causal Page-curve phenomenology, the law is derived from bounded split-regularized Tomita-Takesaki modular flow and admits an inverse map for extracting observer-indexed retrieval rates from measured correlation structure. The framework supplements global entropy conservation with a Lorentzian-causal access process: conserved information becomes operationally relevant to a finite observer only when it enters that observer's bounded modular-access domain.The model predicts a joint, experimentally testable signature in the g2(t1,t2) correlation envelope, including constrained saturation, protocol-dependent separation, inverse gamma recovery, finite-resolution robustness, and interference suppression under controlled asymmetry. Numerical results in a finite-bond-dimension tensor-network proxy, evaluated at D=4 and D=8, are consistent with the derived law, and adversarial verification against matched saturating, shared-envelope, label-permuted, time-jittered, and non-gap alternatives shows that generic saturation does not reproduce the full observer-indexed retrieval signature. A redshift-weighted Ryu-Takayanagi representation situates the retrieval dynamics within holographic geometry without invoking replica-wormhole or island constructions as the source of the retrieval law.The result reframes the black-hole information paradox as a bounded-access dynamics problem rather than a contradiction in entropy accounting. On this formulation, information conservation, formal reconstruction, and finite-observer retrieval are distinct operations; the apparent paradox arises when they are treated as interchangeable. Here Smax denotes the Bekenstein-Hawking entropy, gamma(tau) the modular-flow retrieval rate, and tau_char the characteristic proper-time scale.