Paper 3 of the Theory of Informational Selection (TSI) program. This work investigates whether Stable Informational Partitions (SIPs), previously introduced as emergent structures arising from informational selection, admit a rigorous mathematical reconstruction. Starting from an explicit correlational representation of stable informational organization, the paper develops a systematic sequence leading from primitive informational transformations to informational *-algebras, informational states, Hilbert-space representations, von Neumann algebras, and ultimately to Tomita-Takesaki modular structures. The reconstruction establishes the chain A central result is the emergence of modular dynamics without the prior introduction of spacetime, Hamiltonian evolution, or external temporal parameters. Within the TSI framework, modular flow constitutes the first mathematically rigorous candidate for an intrinsic notion of evolution arising entirely from informational organization. While the Thermal Time Hypothesis of Connes and Rovelli reconstructs a notion of time from a pre-existing operator-algebraic framework, the present work investigates a deeper question: how the operator-algebraic structures themselves, together with their modular dynamics, may emerge from a more fundamental informational ontology governed by correlational stability and informational selection. The work does not attempt to derive geometry or gravitation. Instead, it establishes the algebraic and modular foundations required for subsequent stages of the TSI program, providing a mathematical bridge between informational ontology and future informational-geometric reconstruction.
Paper 3 of the Theory of Informational Selection (TSI) program. This work investigates whether Stable Informational Partitions (SIPs), previously introduced as emergent structures arising from informational selection, admit a rigorous mathematical reconstruction. Starting from an explicit correlational representation of stable informational organization, the paper develops a systematic sequence leading from primitive informational transformations to informational *-algebras, informational states, Hilbert-space representations, von Neumann algebras, and ultimately to Tomita-Takesaki modular structures. The reconstruction establishes the chain A central result is the emergence of modular dynamics without the prior introduction of spacetime, Hamiltonian evolution, or external temporal parameters. Within the TSI framework, modular flow constitutes the first mathematically rigorous candidate for an intrinsic notion of evolution arising entirely from informational organization. While the Thermal Time Hypothesis of Connes and Rovelli reconstructs a notion of time from a pre-existing operator-algebraic framework, the present work investigates a deeper question: how the operator-algebraic structures themselves, together with their modular dynamics, may emerge from a more fundamental informational ontology governed by correlational stability and informational selection. The work does not attempt to derive geometry or gravitation. Instead, it establishes the algebraic and modular foundations required for subsequent stages of the TSI program, providing a mathematical bridge between informational ontology and future informational-geometric reconstruction.
We address the problem of time in quantum mechanics: time is an external classical parameter, not a quantum observable, yet quantum gravity requires it to be emergent. We show that a canonical preferred temporal flow arises from within the algebraic structure of quantum mechanics, without presupposing a Hamiltonian, a Schrödinger equation, or a background time parameter. The starting point is a pair (M, ω) — a von Neumann algebra of observables and a faithful normal state — with no other input. From these, Tomita–Takesaki modular theory derives a canonical strongly-continuous one-parameter group of automorphisms σ_t : M → M (the modular flow). The group parameter t labels the spectral flow of the modular operator Δ = S^*S constructed from ω, and is not assumed as background structure. Three results are established. First (Structural Inevitability): any non-tracial quantum system unavoidably carries a non-trivial modular flow — the Tomita–Takesaki modular automorphism group, derived from algebraic data alone. Under the Connes–Rovelli thermal time hypothesis (adopted as an explicit physical postulate, supported by exact agreement with Heisenberg evolution for Gibbs states and with Rindler time via the Bisognano–Wichmann theorem), this flow constitutes physical time. Second (Cocycle Colimit): the directed colimit of all subsystem modular flows exists in the category W*-Dyn, interacting or not; for interacting systems the colimit is twisted by Araki's Connes cocycle, and the assembled flow equals the modular flow of the limiting algebra. Third (Classical Recovery): a structural outline of how, in the decoherence limit under density, separability, and the second law, the framework recovers a separable dense linear order from which n-dimensional spatial structure is derived; full topological reconstruction is left as an open program. This paper is self-contained and requires no companion papers. It extends the Connes–Rovelli thermal time hypothesis and the Page–Wootters relational framework to a universal directed cocycle colimit.
This preprint presents the foundational structure of the Theory of Informational Selection (TSI), a framework that reconstructs physical ontology from correlational and informational principles. The work develops the concept of the Informational Totality, introduces the emergent geometry induced by Fisher Information, and explores the role of Quantum Fisher Information (QFI) as a partial experimental witness of the theory. Abstract: The Informational Totality is defined as the complete set of correlational structures that determine the emergence of physical degrees of freedom. This preprint develops the mathematical foundations of TSI, including the variational principles that govern informational selection, the geometry induced by Fisher Information, and the functorial formulation connecting correlational modes with emergent physical behavior. The work also discusses the role of quantum materials and collective electron states as potential experimental analogues for the emergent metric structure. The manuscript concludes with an outlook on future developments, including the extension toward cosmological regimes and the integration with quantum information theory. This document is the first formal installment of the TSI program and serves as the conceptual and mathematical basis for subsequent papers.
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.
This paper develops the foundational correlational structure of the Informational Totality (IT), a representation‑independent framework in which physical organization emerges from primitive informational relations rather than from predefined systems, geometric backgrounds, or dynamical laws. We classify primary correlations, analyze the conditions under which coherence, locality, and nonlocal phenomena arise, and introduce ontological partitions as the only correlationally stable units of description. The emergence of effective degrees of freedom is then traced to stable correlational modes, which naturally exhibit complex amplitudes and phase dynamics. These results establish the correlational foundations of the IT and prepare the ground for the algebraic–modular reconstruction developed in Paper 3.
We develop an extended formulation of Universal Modular Dynamics (UMD) in which physical law is organized as a hierarchy of nested, renormalization-stable informational phases emerging from a pre-quantum domain of distinguishability. The construction does not assume spacetime, locality, quantum fields, or graph structure as fundamental. Instead, the primitive level is defined through relations of distinguishability between pre-physical configurations, whose dynamically persistent sectors provide the substrate from which effective operator states and subsequent physical structures emerge. Within this architecture, previously derived pre-string configurations are interpreted as a particular low-dimensional stable sector of the broader UMD pre-quantum state space, rather than as the universal starting point of the theory. Their collective scaling behavior admits an effective graph limit, providing a controlled route from pre-string organization to relational connectivity and, subsequently, to operational subsystem structure. This graph limit is therefore emergent and sector-dependent, rather than ontologically primitive. At the operator level, the density matrix ρ becomes the carrier of distinguishability and generates modular structure through K = −log ρ, Kρ|σ = −log ρ + log σ. Relative modular dynamics, together with completely positive open-system flows, defines a sequence of scale-dependent transformations through which stable subsystem decompositions, operational locality, and finite-speed information propagation emerge. The resulting causal structure is established before continuum spacetime geometry and is governed by Lieb– Robinson-type bounds on the transport of quantum correlations. A central aim of the present work is to sharpen the transition from discrete relational organization to continuum spacetime. We explicitly distinguish the geometry of quantum state space from physical spacetime geometry and formulate the intermediate coarse-graining and scaling conditions required to connect Bogoliubov–Kubo–Mori information geometry, correlation-based relational distances, and an effective continuum metric. Einstein-type dynamics is then interpreted as an entropic consistency condition of the emergent geometric phase, arising from local information balance and variational stability rather than from a fundamental spacetime background. The same hierarchical framework is extended to access-relative vacuum structure and hidden-sector dynamics. Dark-energy-like behavior is associated with stable entropic vacuum drift relative to an observer-accessible algebra, while dark-matter-like effects arise from correlations and backreaction between visible and inaccessible sectors. These mechanisms are embedded within the same renormalization hierarchy rather than introduced as independent cosmological components. We further characterize regimes in which metricity, causal ordering, and stable factorization fail, defining non-geometric phases relevant to the breakdown of the spacetime description in extreme gravitational and early-universe regimes. Throughout the construction, we distinguish theorem-level results, conditional emergence statements, numerical evidence, and phenomenological predictions, and we identify explicit falsifiability conditions for the principal UMD claims. The resulting picture is that physical law is not represented by a single primitive dynamical equation imposed on a pre-existing arena, but by a recursively organized hierarchy of informational structures whose stable renormalization sectors generate quantum states, locality, causality, geometry, gravitation, and effective dark-sector phenomena.
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.