Information-Based Unification Model

IBU: Information-Based Unification Model A Pre-Geometric Framework for Spacetime, Spectral Dimensionality (3 + n), and Temporal Ordering Jiyoung Choi1 1Independent Researcher November 29, 2025 Abstract We propose the Information-Based Unification (IBU) model, a pre-geometric framework in which all observable physical structures emerge from a continuous information field I(x) defined on a non-geometric domain. Spacetime, locality, causality, and the arrow of time arise as emergent properties induced by entanglement connectivity and information-density gradients. A key prediction of the model is the distinction between the macroscopic effective spatial dimension deff = 3 and the microscopic spectral dimension dspec = 3 + n, with n>0 encoding additional informational degrees of freedom revealed only at high energy. We further introduce a measurable short-distance spectral index DSD(E) and provide numerical protocols and astrophysical constraints for testing the IBU model. Contents 1 Motivation and Conceptual Overview 2 2 Pre-Geometric Information Field 2 3 Emergent Metric 2 4 Lagrangian Dynamics 2 5 Dimensional Stability 2 6 Spectral Dimensionality and the (3+n)Hierarchy 2 6.1 Extraction of n....................................... 3 7 Short-Distance Spectral Index DSD 3 8 Numerical Verification and Spectral Flow 3 9 Distinguishing IBU from CDT and Asymptotic Safety 3 9.1 Complementarity...................................... 3 10 Time as Entanglement Ordering 4 1 11 Conclusion 4 A Spectral Dimension Summary 4 B Numerical Analysis and Observational Constraints 4 B.1 SimulationPseudo-Code.................................. 4 B.2 NumericalEstimates.................................... 5 B.3 UHECRConstraints .................................... 5 1 Motivation and Conceptual Overview Modern approaches to quantum gravity increasingly view spacetime as emergent. The IBU model posits: deff = 3, dspec =3+n. This contrasts sharply with dimensional reduction in CDT and Asymptotic Safety. 2 Pre-Geometric Information Field We postulate: I:X→C, with no prior geometry. Locality emerges from the entanglement proto-distance: dij =−log Tr(ρiρj).(1) 3 Emergent Metric gµν =α1∂µd ∂νd+α2∂µρI∂νρI. 4 Lagrangian Dynamics LI=α(∂µI)(∂µI)−λ(|I|2−η2)2.(2) Euler–Lagrange yields: □I+1 2α dV dI= 0. 5 Dimensional Stability S(d) = alog d−bd2−c d2.(3) 6 Spectral Dimensionality and the (3+n)Hierarchy dspec(σ) = −2dln P dln σ. UV: P(σ)∼σ−(3+n)/2. 2 123456 Dimension d 3 2 1 0 1 Stability Functional ( d ) Figure 1: Dimensional Stability ( d ) d eff = 3 Figure 1: Stability functional S(d) showing deff = 3. 6.1 Extraction of n n=−2dln P dln σσ→0 −3.(4) 7 Short-Distance Spectral Index DSD DSD(E) = dspec(E)−3. Phenomenological running: dspec(E) = 3 + nEk Ek+Ek crit . 8 Numerical Verification and Spectral Flow 9 Distinguishing IBU from CDT and Asymptotic Safety The IBU prediction is opposite to CDT/AS: CDT/AS: dspec →2,IBU: dspec →3+n. Approach UV dspec Interpretation CDT / AS →2 Dimensional reduction IBU (this work) →3+nInformational revelation 9.1 Complementarity IBU does not claim to replace CDT/AS. Instead, IBU may describe a pre-geometric substrate, while CDT/AS describe the emergent geometric regime. Both may coexist as descriptions of different layers of the same physical system. 3 1086420 log( ) 10 15 20 25 30 35 40 log( P ( )) Figure 2: Spectral Dimension Slopes n = 1.0 n = 0.5 IR Slope Figure 2: Expected UV/IR slopes of log P(σ). 10 Time as Entanglement Ordering dSent dt >0. 11 Conclusion IBU provides: •emergent 3D geometry, •UV signature dspec =3+n, •direct extraction formula for n, •numerical and astrophysical tests, •clear distinction from CDT/AS. A Spectral Dimension Summary P(σ)∼σ−(3+n)/2. B Numerical Analysis and Observational Constraints B.1 Simulation Pseudo-Code FUNCTION IBU_Spectral_Dimension_Test(N_nodes, T_max, dt, n_expected): Initialize Information_Field I[N] FOR t = 0 to T_max: 4 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 log10 ( E ) (GeV) 3.0 3.2 3.4 3.6 3.8 4.0 d spec( E ) Figure 3: Spectral Dimension Flow d spec( E ) IR Limit (3D) UV Limit (4D) E crit Figure 3: Spectral dimension flow from 3 to 3 + n. Update I[i] using EOM Compute Entanglement_Matrix E[i,j] Construct Adjacency A[i,j] from E FOR sigma in [sigma_min, sigma_max]: Perform Random Walks Compute P(sigma) slope = Fit(log P vs log sigma in UV regime) n_extracted = -2*slope - 3 RETURN n_extracted B.2 Numerical Estimates For (n= 1, k = 2, Ecrit = 1016 GeV): DSD(103GeV) ≈10−26,DSD(1016 GeV) ≈0.5,DSD(1019 GeV) ≈0.999. B.3 UHECR Constraints ∆c c<10−15 (E∼1019 GeV). IBU predicts: ∆c c∝E Ecrit n . 5 Thus, E Ecrit n <10−15. 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