Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Effective Field Theory of Information Reconstruction

Marco Galli

Published Mar 19, 2026• 0 citations
Publisher

Abstract

We present the Effective Field Theory of Information Reconstruction (EFIR), a mathematically rigorous framework that unifies three foundational structures: variational field theory, Fisher–Rao information geometry, and open quantum system dynamics. The framework models observer-limited access to a latent information field I(x,t) through a gauge-invariant action functional, from which the field equation of motion is derived via the Euler–Lagrange formalism. A local rescaling symmetry is introduced to account for different observer frames, and the associated gauge field and covariant derivative are constructed explicitly. The observer's belief state is represented as a point on a statistical manifold equipped with the Fisher–Rao metric, evolving along geodesics driven by incoming observations. Uncertainty in the reconstruction process is quantified through a density operator whose dynamics follow the Lindblad master equation, derived from first-principles measurement back-action via Kraus operators. The three components — field, geometry, and quantum state — are coupled into a closed, well-posed dynamical system on the phase space M_EFIR = {I, θ, ρ}. A reconstruction tensor R_μν is derived from first principles and shown to satisfy a variance bound expressible in terms of the Fisher–Ricci scalar, establishing a direct link between information curvature and reconstruction noise. In the Gaussian limit, the framework reduces exactly to the Kalman–Bucy filter, providing a non-trivial consistency check against classical optimal filtering theory. For a network of N observers, the synchronisation cost is proven to scale as O(N²), and decoherence is shown to grow monotonically with observer density. The paper includes three independently falsifiable scaling laws, a complete simulation protocol validated on a two-qubit toy model, and a discussion of the connection to emergent gravity via the Hessian of the von Neumann entropy. Keywords: information field theory, Fisher–Rao geometry, open quantum systems, Lindblad equation, CPTP maps, Kraus operators, information reconstruction, Kalman–Bucy filter, multi-agent systems, emergent gravity, variational methods, gauge symmetry.

DOI
10.5281/zenodo.19108408

Related papers

THE MODAL DISCIPLINE OF INFORMATIONAL RECONSTRUCTION: A Critical –Propositional Analysis of Effective Field Theory of Information Reconstruction, by MARCO GALLI, on Confrontation With the Theory of Objectivity

Vidamor Cabannas, Denivaldo Silva

This article presents a critical–propositional examination of Marco Galli’s Effective Field Theory of Information Reconstruction: A Unified Variational, Information-Geometric, and Open Quantum System Framework in confrontation with the Theory of Objectivity (TO). The study investigates the extent to which Galli’s Effective Field Theory of Information Reconstruction (EFIR) is compatible with the modal axioms, cosmogonic commitments, phenomenic structure, and testability criteria developed in the Theory of Objectivity. The paper argues that EFIR constitutes a rigorous and valuable formal framework for describing processes of informational reconstruction in already constituted universes, especially through its unification of variational field theory, Fisher–Rao information geometry, and open quantum system dynamics. Particular attention is given to the informational field, gauge structure, reconstruction tensor, multi-agent synchronization, decoherence growth, Gaussian reduction to Kalman–Bucy filtering, and the framework’s falsifiable predictions. From the standpoint of the Theory of Objectivity, the article identifies important areas of compatibility, including the relational constitution of observable states, the plurality of observers, the compositional structure of reconstructed phenomena, and the operational relevance of informational mediation. At the same time, it highlights decisive points of tension: EFIR does not begin from Nothing as a primitive and eternal mathematical essence, does not explicitly formulate modal necessity, does not deduce cosmic origin, and does not fully develop the transcendent status of information as required by TO. The article concludes that EFIR may be read as a highly relevant operational and phenomenological bridge for the Theory of Objectivity, especially in discussions of empirical contact, informational reconstruction, observer networks, and emergent geometrical organization, while TO remains the deeper modal-ontological framework concerning the constitution and intelligibility of the universe. Authors’ note: This article benefited from the analytical support of ChatGPT in bibliographic organization, comparative structuring, and the systematization of compatibilities, tensions, and critical propositions. Keywords Theory of Objectivity; Effective Field Theory of Information Reconstruction; EFIR; information reconstruction; modal ontology; Fisher–Rao geometry; open quantum systems; decoherence; gauge symmetry; reconstruction tensor; phenomenic elements; Inductive Effects; operational bridges; testability; emergent geometry; entropic gravity; observer networks; cosmology; philosophy of physics; Marco Galli

•Mar 20, 2026•0 citations

ISA v5f: Informational-Geometric Reconstruction of Fundamental Physics

ipolfirst@gmail.com, microomniarch@gmail.com

ISA v5f (Informational Systemic Actualization, final release) is a mathematically rigorous effective field theory that reconstructs General Relativity (GR) and Quantum Theory (QT) from a single variational principle defined on a statistical manifold of logical states M_ISA. Addressing the ontological fragmentation of standard physics, this framework replaces disjoint primitives (spacetime metrics, wavefunctions, ad hoc measurement postulates) with two operatized quantities: the logical bandwidth W_max(μ) and the density of actualized connections ρ_ISA(x). Reality is modeled as a network of logical correlations whose actualization rate is fundamentally bounded by W_max. When correlation density exceeds a critical threshold Θ, abstract probabilistic potentials transition to actualized relational facts. From the master functional S_ISA, Einstein’s field equations are derived via metric variation, while the Schrödinger equation and canonical commutation relations emerge from constrained geodesic flow under finite W_max. The measurement process is formalized as a nonlinear stochastic Lindblad dynamics, from which the Born rule is rigorously derived via martingale convergence, eliminating ad hoc collapse postulates. The framework resolves several foundational and cosmological tensions: • Hubble tension: Alleviated via a dynamic logarithmic dark energy equation of state w(a), shifting inferred H_0 to 72.8 ± 0.9 km/s/Mpc when fitted to Planck+SH0ES data. • Dark matter: Emerges as a geometric response to background logical density gradients, naturally explaining galactic rotation curves and Bullet Cluster separation without new particle species. • Black hole entropy: Predicts a rigid logarithmic correction α_ISA = −1, distinct from standard quantum gravity estimates. • Baryon asymmetry: Framed as a topological bias during the ρ_ISA → ρ_eq phase transition. All phenomenological deviations scale with W_max^(−2) or the dimensionless factor Z(μ). No free parameters are introduced per phenomenon. Explicit falsifiability thresholds, experimental calibration protocols (based on Margolus–Levitin bounds in superconducting transmons and optical clocks), and a cross-validation matrix are provided. The theory preserves microcausality, ensemble unitarity, and reduces exactly to standard GR and QT in the limits W_max → ∞ and ħ → 0. This release contains the complete theoretical manuscript, supplementary derivations (Appendices A–I), calibration protocols, cross-validation matrices, and numerical implementation details. All code, version history, and supplementary materials are openly accessible. ISA v5f represents a unified, mathematically closed, and empirically confrontable architecture for fundamental physics.

•Apr 21, 2026•0 citations

Information Geometry Unification Principle: Axioms, Detailed Derivations, and Unified Field Equations

Y. Li

We present a complete, mathematically rigorous formulation of the Information Geometry Unification Principle (IGUP). Starting from three fundamental axioms establishing quantum information as the primary ontological substrate, we construct the Bures–Fisher–Rao metric on the manifold of density matrices, derive covariant derivatives, curvature tensors, and the universal information action. We perform full variational derivations for both the quantum state $\rho$ and the information metric $g_{\mu\nu}$, obtaining closed-form unified field equations that govern quantum dynamics, thermodynamics, and gravitational geometry. We show explicitly how the Schrödinger, Liouville, Boltzmann, and Einstein equations arise as limiting cases. This paper constitutes the foundational core of a complete theory of physics based on the identification of geometry with information.

•Mar 29, 2026•0 citations

Functional Foundations of the Shadow Theorem: Analysis of the Observational Loss Functional for the Effective Field Theory of Information Reconstruction (EFIR)

Marco Galli

This paper provides a rigorous functional-analytic foundation for the Shadow Theorem within the Effective Field Theory of Information Reconstruction (EFIR). The author establishes a formal mathematical structure for the theory by equipping the EFIR phase space with a Banach manifold structure based on Sobolev spaces. The work delivers several key proofs, including the Fréchet differentiability and strict log-concavity of the shadow operator in the Gaussian regime. Furthermore, it provides an explicit computation of the proportionality constant for the decoherence rate and a rigorous Cramér-Rao derivation for the reconstruction tensor. This research upgrades the Shadow Theorem from a conceptually coherent framework to a mathematically complete theory.

•Mar 22, 2026•0 citations

Information Geometry Unification Principle: Extended Version with Complete Derivations

Y. Li

This work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on \(\text{Geometry} = \text{Information}\).

•Mar 29, 2026•0 citations

Information Geometry Unification Principle Axioms, Core Action and Unified Field Equations

Y. Li

We present a fundamental unified framework based on information geometry, in which quantum mechanics, statistical thermodynamics, and general relativity emerge from a single information-theoretic ontology. Starting from three rigorous axioms that establish quantum information as the primary physical substrate, we construct the universal information action functional using the Bures–Fisher–Rao metric on the manifold of quantum density matrices. Full variational derivation yields a unified field equation that governs the evolution of quantum information and emergent spacetime geometry. In appropriate limiting regimes, we recover the Schrödinger equation, equilibrium statistical mechanics, and the Einstein field equations. This work provides the foundational layer of a complete theory of everything based on the principle: geometry is information.

•Mar 29, 2026•0 citations
We present the Effective Field Theory of Information Reconstruction (EFIR), a mathematically rigorous framework that unifies three foundational structures: variational field theory, Fisher–Rao information geometry, and open quantum system dynamics. The framework models observer-limited access to a latent information field I(x,t) through a gauge-invariant action functional, from which the field equation of motion is derived via the Euler–Lagrange formalism. A local rescaling symmetry is introduced to account for different observer frames, and the associated gauge field and covariant derivative are constructed explicitly. The observer's belief state is represented as a point on a statistical manifold equipped with the Fisher–Rao metric, evolving along geodesics driven by incoming observations. Uncertainty in the reconstruction process is quantified through a density operator whose dynamics follow the Lindblad master equation, derived from first-principles measurement back-action via Kraus operators. The three components — field, geometry, and quantum state — are coupled into a closed, well-posed dynamical system on the phase space M_EFIR = {I, θ, ρ}. A reconstruction tensor R_μν is derived from first principles and shown to satisfy a variance bound expressible in terms of the Fisher–Ricci scalar, establishing a direct link between information curvature and reconstruction noise. In the Gaussian limit, the framework reduces exactly to the Kalman–Bucy filter, providing a non-trivial consistency check against classical optimal filtering theory. For a network of N observers, the synchronisation cost is proven to scale as O(N²), and decoherence is shown to grow monotonically with observer density. The paper includes three independently falsifiable scaling laws, a complete simulation protocol validated on a two-qubit toy model, and a discussion of the connection to emergent gravity via the Hessian of the von Neumann entropy. Keywords: information field theory, Fisher–Rao geometry, open quantum systems, Lindblad equation, CPTP maps, Kraus operators, information reconstruction, Kalman–Bucy filter, multi-agent systems, emergent gravity, variational methods, gauge symmetry.
This article presents a critical–propositional examination of Marco Galli’s Effective Field Theory of Information Reconstruction: A Unified Variational, Information-Geometric, and Open Quantum System Framework in confrontation with the Theory of Objectivity (TO). The study investigates the extent to which Galli’s Effective Field Theory of Information Reconstruction (EFIR) is compatible with the modal axioms, cosmogonic commitments, phenomenic structure, and testability criteria developed in the Theory of Objectivity. The paper argues that EFIR constitutes a rigorous and valuable formal framework for describing processes of informational reconstruction in already constituted universes, especially through its unification of variational field theory, Fisher–Rao information geometry, and open quantum system dynamics. Particular attention is given to the informational field, gauge structure, reconstruction tensor, multi-agent synchronization, decoherence growth, Gaussian reduction to Kalman–Bucy filtering, and the framework’s falsifiable predictions. From the standpoint of the Theory of Objectivity, the article identifies important areas of compatibility, including the relational constitution of observable states, the plurality of observers, the compositional structure of reconstructed phenomena, and the operational relevance of informational mediation. At the same time, it highlights decisive points of tension: EFIR does not begin from Nothing as a primitive and eternal mathematical essence, does not explicitly formulate modal necessity, does not deduce cosmic origin, and does not fully develop the transcendent status of information as required by TO. The article concludes that EFIR may be read as a highly relevant operational and phenomenological bridge for the Theory of Objectivity, especially in discussions of empirical contact, informational reconstruction, observer networks, and emergent geometrical organization, while TO remains the deeper modal-ontological framework concerning the constitution and intelligibility of the universe. Authors’ note: This article benefited from the analytical support of ChatGPT in bibliographic organization, comparative structuring, and the systematization of compatibilities, tensions, and critical propositions. Keywords Theory of Objectivity; Effective Field Theory of Information Reconstruction; EFIR; information reconstruction; modal ontology; Fisher–Rao geometry; open quantum systems; decoherence; gauge symmetry; reconstruction tensor; phenomenic elements; Inductive Effects; operational bridges; testability; emergent geometry; entropic gravity; observer networks; cosmology; philosophy of physics; Marco Galli
ISA v5f (Informational Systemic Actualization, final release) is a mathematically rigorous effective field theory that reconstructs General Relativity (GR) and Quantum Theory (QT) from a single variational principle defined on a statistical manifold of logical states M_ISA. Addressing the ontological fragmentation of standard physics, this framework replaces disjoint primitives (spacetime metrics, wavefunctions, ad hoc measurement postulates) with two operatized quantities: the logical bandwidth W_max(μ) and the density of actualized connections ρ_ISA(x). Reality is modeled as a network of logical correlations whose actualization rate is fundamentally bounded by W_max. When correlation density exceeds a critical threshold Θ, abstract probabilistic potentials transition to actualized relational facts. From the master functional S_ISA, Einstein’s field equations are derived via metric variation, while the Schrödinger equation and canonical commutation relations emerge from constrained geodesic flow under finite W_max. The measurement process is formalized as a nonlinear stochastic Lindblad dynamics, from which the Born rule is rigorously derived via martingale convergence, eliminating ad hoc collapse postulates. The framework resolves several foundational and cosmological tensions: • Hubble tension: Alleviated via a dynamic logarithmic dark energy equation of state w(a), shifting inferred H_0 to 72.8 ± 0.9 km/s/Mpc when fitted to Planck+SH0ES data. • Dark matter: Emerges as a geometric response to background logical density gradients, naturally explaining galactic rotation curves and Bullet Cluster separation without new particle species. • Black hole entropy: Predicts a rigid logarithmic correction α_ISA = −1, distinct from standard quantum gravity estimates. • Baryon asymmetry: Framed as a topological bias during the ρ_ISA → ρ_eq phase transition. All phenomenological deviations scale with W_max^(−2) or the dimensionless factor Z(μ). No free parameters are introduced per phenomenon. Explicit falsifiability thresholds, experimental calibration protocols (based on Margolus–Levitin bounds in superconducting transmons and optical clocks), and a cross-validation matrix are provided. The theory preserves microcausality, ensemble unitarity, and reduces exactly to standard GR and QT in the limits W_max → ∞ and ħ → 0. This release contains the complete theoretical manuscript, supplementary derivations (Appendices A–I), calibration protocols, cross-validation matrices, and numerical implementation details. All code, version history, and supplementary materials are openly accessible. ISA v5f represents a unified, mathematically closed, and empirically confrontable architecture for fundamental physics.
We present a complete, mathematically rigorous formulation of the Information Geometry Unification Principle (IGUP). Starting from three fundamental axioms establishing quantum information as the primary ontological substrate, we construct the Bures–Fisher–Rao metric on the manifold of density matrices, derive covariant derivatives, curvature tensors, and the universal information action. We perform full variational derivations for both the quantum state ρ\rhoρ and the information metric gμνg_{\mu\nu}gμν​, obtaining closed-form unified field equations that govern quantum dynamics, thermodynamics, and gravitational geometry. We show explicitly how the Schrödinger, Liouville, Boltzmann, and Einstein equations arise as limiting cases. This paper constitutes the foundational core of a complete theory of physics based on the identification of geometry with information.
This paper provides a rigorous functional-analytic foundation for the Shadow Theorem within the Effective Field Theory of Information Reconstruction (EFIR). The author establishes a formal mathematical structure for the theory by equipping the EFIR phase space with a Banach manifold structure based on Sobolev spaces. The work delivers several key proofs, including the Fréchet differentiability and strict log-concavity of the shadow operator in the Gaussian regime. Furthermore, it provides an explicit computation of the proportionality constant for the decoherence rate and a rigorous Cramér-Rao derivation for the reconstruction tensor. This research upgrades the Shadow Theorem from a conceptually coherent framework to a mathematically complete theory.
This work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on Geometry=Information\text{Geometry} = \text{Information}Geometry=Information.
We present a fundamental unified framework based on information geometry, in which quantum mechanics, statistical thermodynamics, and general relativity emerge from a single information-theoretic ontology. Starting from three rigorous axioms that establish quantum information as the primary physical substrate, we construct the universal information action functional using the Bures–Fisher–Rao metric on the manifold of quantum density matrices. Full variational derivation yields a unified field equation that governs the evolution of quantum information and emergent spacetime geometry. In appropriate limiting regimes, we recover the Schrödinger equation, equilibrium statistical mechanics, and the Einstein field equations. This work provides the foundational layer of a complete theory of everything based on the principle: geometry is information.