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.
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.
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.
Collapse, Selection, and the Geometry of Information A Variational and Schrödinger Bridge Foundation for Quantum Measurement Quantum theory explains the evolution of possibilities with extraordinary precision, yet the emergence of definite outcomes remains conceptually unresolved. Why does one outcome appear rather than another? Decoherence explains the suppression of interference and the emergence of preferred bases, but not the mechanism by which multiplicity gives way to singularity. Collapse models introduce stochastic modifications of dynamics, yet the structural principle governing outcome selection remains obscure. Collapse, Selection, and the Geometry of Information proposes a new framework for approaching this longstanding problem. Drawing upon Schrödinger bridge theory, entropy-regularized optimal transport, concentration inequalities, and threshold phenomena in high-dimensional probability, the book develops a variational account of measurement in which selection emerges through constrained probabilistic evolution rather than through ad hoc dynamical interruption. At the center of the argument lies a simple but far-reaching shift in perspective: the measurement problem is reframed not primarily as a problem of collapse, but as a problem of selection. Within this framework, admissible measurement outcomes are represented as endpoint distributions connected by entropy-minimizing stochastic bridges. In the small-noise regime, concentration phenomena and large-deviation structure produce exponential stabilization of particular channels, yielding effective outcome definiteness without modification of unitary quantum evolution. The book integrates ideas from quantum foundations, stochastic processes, optimal transport, and information geometry into a unified conceptual architecture. Along the way, it explores the relation between decoherence and variational structure, the geometry of path space, threshold mechanisms in probabilistic systems, and the emergence of macroscopic stability from high-dimensional stochastic dynamics. Neither purely technical textbook nor purely philosophical meditation, this work occupies a rare middle ground: mathematically informed, conceptually ambitious, and written in continuous narrative prose accessible to advanced readers in physics, mathematics, and philosophy of science. Ultimately, the book argues that the transition from possibility to actuality may be inseparable from the geometry of probability itself.
This paper proposes a research program aimed at exploring the possibility of establishing a rigorous mathematical foundation for quantum information ontology. We systematically study the path of incorporating the entanglement structure of κ-qubit networks into an extended set-theoretic framework. Based on the principles of Jiuzhang Constructive Math ematics (JCM), we explore the conceptual foundations of constructing a Quantum Informa tion Set Theory (QIST). This paper provides an in-depth analysis of the mathematical and physical challenges faced by this attempt, establishes close connections with fields such as quantum logic, Boolean-valued models, categorical quantum mechanics, and the holographic principle, and proposes a roadmap for its gradual realization. We pay special attention to the dual role of the κ parameter (as a mathematical scale parameter and a physical constant) and its key role in connecting mathematical structures with physical reality. Although a complete theory has not yet been established, this paper provides a systematic research framework and a clear direction for the mathematical rigorization of quantum information ontology.
A Two‑State Ontological Model of Reality introduces the conceptual foundation underlying the Actualization Dynamics research program. This paper develops a unified ontological framework in which reality emerges from a primordial informational substrate that exists in two operational modes: Pre‑actualized Reality, a maximally symmetric, zero‑entropy information manifold containing all possible configurations, and Actualized Reality, a finite, stable holographic code space selected by informational coherence.The transition between these modes is formalized through a stationary‑phase condition applied to an Informational Action defined on the Fisher‑metric information manifold. By integrating ideas from information geometry, holographic entanglement entropy, quantum error‑correcting codes, and an ontological path integral, the paper argues that Actualized Reality is the unique, self‑consistent solution that preserves reconstructibility and error‑correctability.Key contributions include:• A formal definition of Pre‑actualized and Actualized Reality• The role of the Cleaning Lemma as an ontological selection rule• The derivation of an Informational Planck Constant from the Bekenstein–Hawking entropy bound• A stationary‑phase interpretation of the universe as an informational interference pattern• A structural resolution of the measurement problem• A falsifiable prediction of oscillatory non‑Gaussianities in the CMB arising from holographic interferenceThis document serves as the conceptual and philosophical foundation for the technical results presented in Actualization Dynamics I, II, III, and the Unified Informational Field Theory. It is intended as the “Chapter 0” of the series, providing the ontological motivation and interpretive framework for the mathematical formalism developed in subsequent papers.
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.
The Total Entropic Quantity (TEQ) framework derives quantum mechanics from entropy-driven selection principles, unifying entropy, emergent time, and thermodynamic evolution. TEQ decomposes total entropy into realized entropy (macroscopic disorder), latent entangled entropy (quantum correlations), and latent classical entropy (stable classical correlations), clarifying how classical irreversibility emerges from global quantum coherence. A key result is Universal Entropic Time (UET), a synchronized temporal structure governed by realized entropy growth. UET aligns the thermodynamic arrow of time with cosmological evolution, linking decoherence to macroscopic irreversibility. TEQ provides a unified epistemic and ontological perspective on quantum measurement, reconciling the Copenhagen and Many-Worlds interpretations as complementary descriptions of a single entropy-driven selection mechanism. Additionally, entropy minimization explains the stability of quantum systems such as Majorana qubits, while entropy gradients suggest a mechanism for spacetime emergence and causal order. Entropy redistribution in TEQ acts as an active selection principle, stabilizing preferred trajectories while suppressing unstable quantum states. Future work will develop an entropy-weighted variational principle to formalize path selection in TEQ, aiming to derive quantum dynamics---including the Born rule, wavefunction suppression, and the Schrödinger equation---from entropic constraints. This approach is expected to clarify how path weights relate to entropy redistribution and selection, offering a thermodynamic basis for quantization. Notably, TEQ makes its first concrete prediction: Majorana qubits should exhibit extended coherence times due to suppressed entropy redistribution, offering an experimentally testable signature of the framework.