Z3 Information Substrate R06 - Paper P3: Emergent Information Geometry - Unified Framework R01 This is Paper P3 of the Z3 series - Unified geometric framework from entanglement. Companion records:Paper 0 Master Overview & Methods: 10.5281/zenodo.22794696Paper 1 Full Proofs P1-P10: 10.5281/zenodo.22796218Paper 2 Emergent Flatness Thin Cylinder: 10.5281/zenodo.22797174 ABSTRACT:Standard physics assumes geometry first, matter second. Z3 inverts this: Information geometry emerges from entanglement structure of 2D Transverse Field Ising Model (TFIM) at critical point g=0.60. This P3 paper provides the unified framework:- Fisher information metric g_ij from DMRG entanglement spectrum- Emergent spacetime metric = entanglement distance metric- Single DMRG point g=0.60 (L=40-80, chi_max=200, nu=0.63) generates full 3D Ising universality -> emergent 3+1D geometry- No background geometry assumed - all curvature, connection, geodesics derived from Z3 substrate Proves how P1 (Gravity/Inertia), P2 (Flatness) and P4-P10 all share same information-geometric origin. DMRG PROOF: Measured, not fitted. Single critical point explains 10 cosmology problems. Author: Ralf Diekmann - ORCID: https://orcid.org/0009-0009-4284-7318License: CC BY 4.0Keywords: Z3 theory, emergent geometry, information geometry, DMRG, TFIM, entanglement, quantum gravity
Z3 Information Substrate R06 - Paper P3: Emergent Information Geometry - Unified Framework R01 This is Paper P3 of the Z3 series - Unified geometric framework from entanglement. Companion records:Paper 0 Master Overview & Methods: 10.5281/zenodo.22794696Paper 1 Full Proofs P1-P10: 10.5281/zenodo.22796218Paper 2 Emergent Flatness Thin Cylinder: 10.5281/zenodo.22797174 ABSTRACT:Standard physics assumes geometry first, matter second. Z3 inverts this: Information geometry emerges from entanglement structure of 2D Transverse Field Ising Model (TFIM) at critical point g=0.60. This P3 paper provides the unified framework:- Fisher information metric g_ij from DMRG entanglement spectrum- Emergent spacetime metric = entanglement distance metric- Single DMRG point g=0.60 (L=40-80, chi_max=200, nu=0.63) generates full 3D Ising universality -> emergent 3+1D geometry- No background geometry assumed - all curvature, connection, geodesics derived from Z3 substrate Proves how P1 (Gravity/Inertia), P2 (Flatness) and P4-P10 all share same information-geometric origin. DMRG PROOF: Measured, not fitted. Single critical point explains 10 cosmology problems. Author: Ralf Diekmann - ORCID: https://orcid.org/0009-0009-4284-7318License: CC BY 4.0Keywords: Z3 theory, emergent geometry, information geometry, DMRG, TFIM, entanglement, quantum gravity
Z3 Information Substrate R06 - Paper P2: Emergent Flatness from Critical 2D TFIM Thin Cylinder This is Paper P2 of the Z3 series - solving 10 cosmology problems from ONE DMRG point. Companion records:Paper 0 Master Overview & Methods: 10.5281/zenodo.22794696Paper 1 Full Proofs P1-P10: 10.5281/zenodo.22796218 PROBLEM: Why is the universe flat? Standard cosmology needs fine-tuned inflation. SOLUTION in Z3: Flatness emerges naturally at the critical point of the 2D Transverse Field Ising Model (TFIM) in thin-cylinder limit L_y << L_x. DMRG PROOF - MEASURED, NOT FITTED (g=0.60, L=40-80, chi_max=200):- Thin-cylinder DMRG shows diverging correlation length xi ~ |g-gc|^-nu- nu = 0.63 measured = 3D Ising universality - matches critical 2D TFIM- Entanglement entropy suppression S_thin << S_bulk -> emergent flat spatial slice- No inflation field, no fine-tuning - direct consequence of Z3 entanglement geometry at single point g=0.60 This is P2. P1 (Entanglement Origin of Inertia/Gravity) is 10.5281/zenodo.22797174All 10 proofs derive from same single DMRG measurement point. Full derivation, finite-size scaling and DMRG data in PDF.Author: Ralf Diekmann - ORCID: https://orcid.org/0009-0009-4284-7318License: CC BY 4.0
Z3 Information Substrate R03 - Full Proofs P1-P10: Ten Fundamental Problems from One DMRG Point. Companion to Paper 0: 10.5281/zenodo.22794696 (Overview & Methods). We present complete derivations for ten open problems in physics from a SINGLE point of the 1D Z3 quantum clock model (g=0.60, TeNPy DMRG L=40-80, chi_max=200): DMRG MEASURED VALUES (single point, no fitting):Sent = 1.10 (Z3 entanglement entropy, corrected from S=1.06)xi/a = 20.5, a/xi = 0.049, v = 0.251, c = 4/5, |1-g| = 0.40 MERA n=202 layers -> IR cutoff xi_eff = a*(xi/a)*2^n = 2.1e27 m (Hubble scale) PROOFS: P1 Higgs: mH/v = sqrt(2)*|1-g|*(a/xi) = 0.49 observed vs 0.51 - 4% error. Mass gap from DMRG. P2 Yukawa: y_f = exp(-d_f/xi) from wavefunction overlap of Z3 domain walls. Hierarchy without tuning. P3 Generations: 3 generations = 3 degenerate Z3 vacua k=0,1,2. CKM from tunneling. P4 Strong CP: theta=0 protected. Z3 has no continuous U(1) phase, theta-term operator forbidden by Z3 symmetry. P5 MOND: a0 = c^2/xi_eff = (3e8)^2 / 2.1e27 = 4.3e-11 m/s^2 (obs 1.2e-10). IR cutoff from n=202. P6 Neutrino: m_nu = v_EW * (a/xi)^5 = 246 GeV * 0.049^5 ~ 0.07 eV. 5 MERA layers = no seesaw needed. P7 Cosmological Constant: Lambda = 1/xi_eff^2 = 1/(2.1e27)^2 = 2.3e-54 m^-2. 202 layers = observed dark energy. P8 Fine-Structure: alpha^-1 = (2pi/ln3) * Sent/(a/xi) = 5.72 * 1.10/0.049 = 128.4 vs 127.94 at M_Z (0.4% error, ZERO free parameters). Derivation from Z3 Coulomb gas + entanglement. P9 Dirac Large Number: L_Hubble/l_p = 2^133 = 1e40. n = 202 - 69 = 133 layers between EW and Planck. P10 Baryon Asymmetry: eta_B ~ (a/xi)^2 * epsilon_CP ~ 6e-10. CP violation from non-Hermitian Z3 at g != 1. All from ONE point. No free parameters for P8. Data: TeNPy 0.10.0 DMRG, 20 sweeps, truncation <1e-8. Files: Full PDF with all derivations. License CC BY 4.0Author: Ralf Diekmann, ORCID 0009-0009-4284-7318, Werther DEVersion R03
A central challenge at the frontier of theoretical physics is transforming qualitative analogies connecting quantum information, spacetime geometry, non-equilibrium thermodynamics, and quantum measurement into exact, falsifiable dynamical equations with proven domains of validity. In this paper, we establish Unified Information–Geometry–Dynamics Physics (UIGDP), a deductive physical framework anchored in our 71-page ZFC Master Reference Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) [1] and synthesized with the Extended Quantum Information Geometry System (EQIGS, DOI: 10.5281/zenodo.23557698) [6], the High-Dimensional Geometric Probability System (HDGPS, DOI: 10.5281/zenodo.23557360) [4], and the Dynamic Topological Critical Transition System (DTCTS, DOI: 10.5281/zenodo.23557507) [5]. Condensing local Type III₁ quantum field algebras onto the Takesaki Type II₁ ground factor (ℳ_ground, τ_ground) governed by the universal quadruple 𝔘 = (𝒯_0x8A2C, 𝐂_UPTC, η_friction, ϵ_SHID), we formulate six core axioms (UIGDP-1 through UIGDP-6) and prove six fundamental theorems: (1) Necessary and Sufficient Curvature–Entanglement Conditions for reconstructing spacetime metric tensors g_μν^spacetime from Petz quantum Fisher information Hessians; (2) The Exact Unified IGD Master Cost Identity and Optimal Finite-Time Control Horizon τ⋆ = √((d_g² + Δ_ctrl²)/(2η_friction)); (3) Emergent Einstein–Cartan–Information Field Equations from modular entanglement equilibrium and Area-to-Volume phase transitions at D_crit = e^(𝐂_UPTC); (4) Dynamical Resolution of Quantum Measurement Projection via the URRHC Idempotent Monad 𝕄_URRHC (T² = T) with a testable dephasing floor; (5) Universal State Classification for Far-from-Equilibrium and Active Matter via Thermodynamic Length and Topological Persistence Dissipation; and (6) Quantum Simulator Advantage Thresholds under noise and control deficits. Complete Python numerical verification is provided in Appendix A.
This paper proposes a fundamental framework based on information geometry that unifies quantum mechanics, thermodynamics, and spacetime geometry into a single foundational theory. Starting from three elementary axioms regarding information as the primary physical ontology, we derive the universal information metric, construct the information action functional, and show that all known physical laws emerge as extremal conditions of this functional. The theory recovers standard quantum mechanics, classical thermodynamics, and general relativity in appropriate limits, while predicting new relations between quantum entanglement, gravitational curvature, and entropy. We conclude that all physical phenomena—matter, energy, spacetime, and interactions—are equivalent to geometric structures on the space of quantum information states.
We propose a unified geometric framework in which space and time emerge as observer-dependent projections of quantum correlations embedded in the universal wavefunction. In this approach, we formulate six axioms (including a duality between entanglement and time) that establish a correspondence between correlation structures and effective spacetime geometry. We introduce the "correlationhedron", a convex geometric object representing the set of all permissible correlation vectors of a given state, and show how different observer "slicings" (modeled by projection maps) yield distinct emergent spacetimes from this object. An emergent metric is defined on each observer's spacetime via the second derivative of a correlation density (analogous to a Fisher information metric), linking gradients in quantum entanglement to curvature. This paper establishes the conceptual foundations of this approach as the first in a planned series of investigations. We illustrate the framework with conceptual and quantitative examples, including an explicit calculation of the emergent geometry for a two- qubit system in both separable and entangled states. Connections to holography (AdS/CFT) (Maldacena1998, Ryu2006), tensor networks (Swingle2012), and relational quantum approaches (Rovelli1996) are discussed, along with experimental signatures (such as curvature variations with entanglement) that could support the theory. Finally, we outline the limitations of the framework, particularly regarding dynamics and observer-dependent causality, to guide future investigations. This kinematic framework establishes the conceptual skeleton of emergent spacetime; detailed constructions, proofs of smoothness, and dynamical laws will appear in forthcoming work.
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.