RIFT: Relational Information Flow Theory A Pre-Geometric Ontological Framework for Emergent Spacetime and Self-Organized Criticality

RIFT: Relational Information Flow Theory A Pre-Geometric Ontological Framework for Emergent Spacetime and Self-Organized Criticality Harald Eugen Helling, MD, MBA Department of Geriatric Medicine; University Hospital of North Norway, Tromsø [email protected] | ORCID: 0009-0002-8383-5435 October 27, 2025 Abstract We propose Relational Information Flow Theory (RIFT), a pre-geometric framework in which reality is a network of information-bearing relations and spacetime geometry emerges via self-organized criticality (SOC). From three minimal postulates—relational priority, operational distance, and causal modesty—we define an an emergent interface with informational speed vinfo = v0e−σ and obtain (i) a causal cone bound, (ii) finite-speed vector-wave transport, and (iii) a weak-field bridge Φ = c2δσ recovering Newtonian acceleration and lensing. Numerical 2D +t experiments illustrate cone formation and weak-field bending. We position RIFT as complementary to entanglement-based programs: SOC generates the geometric phase; entanglement constrains its equilibrium structure. The framework suggests falsifiable targets (CMB lowℓ structure, mild w ( z )evolution from slow ¯σ ( z )drift, and correlated metric fluctuations) while postponing full GR/QFT derivations to future work. Keywords: emergent spacetime; self-organized criticality; relational ontology; weak-field gravity; information geometry; holography. 1 Introduction Modern work increasingly suggests that spacetime is not fundamental but emergent. The holographic link between entanglement and area (Ryu–Takayanagi), the view that connectivity arises from entanglement (Van Raamsdonk), and relational quantum mechanics (Rovelli) all point to a common claim: geometry reflects patterns of information and connection in an underlying network. What is still missing is a concrete, dynamical mechanism: how do discrete relations self-organize into a coherent geometric phase? RIFT proposes self-organized criticality (SOC) as that mechanism. SOC systems spontaneously evolve to scale-free states with long-range correlations—conditions under which geometric structure can crystallize from a pre-spatial substrate. RIFT complements entanglement-based programs rather than competes with them: SOC generates the geometric phase; entanglement constrains its equilibrium structure within that phase. We adopt three minimal postulates and define an emergent interface; from these follow a causal cone, finite-speed vector-wave transport, and a weak-field bridge Φ = c2δσ that recovers Newtonian behavior and lensing. 1 Check Point Threat Extraction secured this document Get Original 2 Framework (Postulates & Interface) P1 (Relation first). Let the substrate be a directed relational grid G = ( V, E ). Each edge e = ( u→v )carries capacity Ce> 0, informational cost Ve> 0, and plasticity σe∈R . Define the operational edge length ℓe=e−σeCeVe. P2 (Operational distance). For x, y ∈V,D(x, y) = minγ:x→yPe∈γℓe. P3 (Causal modesty). Updates are strictly local and contractive (a Dobrushin-type bound with parameter α < 1holds per step), implying finite-speed influence after coarse-graining. Emergent interface. There is a mapping I : ( G, σ ) 7→ ( M, g )to an effective continuum with informational speed vinfo(x, t) = v0e−σ(x,t),|∇T|=1 vinfo . On (M, g)the coarse-grained signal field uobeys finite-speed vector-wave transport ∂2 tu=∇·c2e−2σ∇u, with characteristics bounded by the vinfo-cone. Weak-field correspondence. For σ=σ0+δσ with |δσ|≪1, a=− ∇ 1 2v2 info≈ − c2∇δσ, c2:= v2 0e−2σ0, so identifying a=−∇Φyields the bridge Φ = c2δσ. Remark 1 (Conformal gauge).A constant shift σ→σ + const rescales v0 but leaves null cones and weak-field deflections invariant; cis a large-scale property of the emergent phase. 3 Results (very brief) Numerical experiments in 2D +t illustrate: (i) decay of anisotropy with scale toward a uniform cone; (ii) geodesic bending proportional to R∇⊥δσ ds , with near-unit slope and R2≈ 1in the weak-field regime. Parameters and scripts are provided in the supplementary archive. 4 Discussion RIFT is best understood as a complement to entanglement-based approaches: SOC supplies a nonequilibrium route to geometries that admit entanglement extremization; entanglement then constrains equilibrium information geometry within that phase. The present model is narrowly scoped; discrete intrinsic formulations, parameter derivations from edge statistics, and high-precision tests (e.g., redshift/time-delay framed in δσ ) are natural next steps. Predictions concern small, correlated metric fluctuations (“informational noise”) rather than departures from established weak-field phenomenology. 2 Quantum evidence for a pre-geometric substrate. EPR entanglement and double-slit interference provide empirical support for RIFT’s pre-geometric ontology. Bell-inequality–violating correlations that show no decay with spatial separation are natural if entangled systems share direct relational connections (low Ve ) in the substrate, independent of emergent spatial distance. Likewise, single-photon double-slit interference—where each detection reflects “knowledge” of both apertures—follows if the informational state is encoded on the relational grid before geometric positions are assigned. In this view, quantum “weirdness” is expected behavior at Layer 0: these phenomena operate prior to space, and appear nonlocal only after geometry emerges at the interface. Recent reports of quantum-like behavior arising at classical interfaces are consistent with this picture, suggesting that standard quantum mechanics may itself be an interface phenomenon between relational and geometric descriptions. Philosophical implications. By grounding geometry in relational ontology, RIFT dissolves the traditional subject–object dichotomy: properties exist only relationally, echoing Rovelli’s perspectivedependent quantum mechanics while extending it to spacetime itself. What appears as “absolute” geometric structure is a coarse-grained description of underlying relational patterns, resolving Wheeler’s “it from bit”/“bit from it” tension through bidirectional emergence in which information and geometry co-create each other at interfaces. Dimensionality and figures. RIFT is pre-geometric: the substrate is a graph of relations with no background manifold, coordinates, or metric; dimensionality appears only after the interface mapping I ( G, σ ) → ( M, g ). Our numerical demonstrations visualize emergent 2D +t geometries solely for computational tractability. The mechanism and statements (cone bound, vector-wave transport, and the bridge Φ = c2δσ ) are dimension-agnostic; a 3D +t phase follows from richer network topologies under the same local, contractive rules. No conclusion relies on any prior spatial embedding of the substrate. Data and code availability. Minimal scripts reproducing the cone and weak-field fits are provided as a Zenodo attachment (source.zip). 3 A Sketches Cone bound. Unfold influence along paths; bound by products of local Lipschitz constants and e−σweights; control with the spectral radius ρ(Wt). Bridge. Optical Lagrangian L = 1 2v2 info|˙x|2 ; Euler–Lagrange yields ¨x = −∇ ( 1 2v2 info ); linearize in δσ. B Robust derivation of the bridge Φ = c2δσ Assumptions. (i) Interface speed vinfo = v0e−σ with σ = σ0 + δσ and |δσ| ≪ 1; (ii) locality/contractivity so that rays follow stationary paths of the Fermat functional; (iii) weak-field, slowly varying δσ. Step 1 — Ray bending (eikonal/Fermat). For a path γ , the travel time is T [ γ ] = Rds vinfo = 1 v0Reσds. Stationarity gives the optical (ray) equation; linearizing in δσ yields δθ ≈Zγ ∇⊥δσ ds, the lensing law used in the main text. Step 2 — Jacobi–Maupertuis identification. Newtonian trajectories at fixed energy E extremize Rp2(E−Φ) |d x | (Jacobi metric). To represent the same curves (up to reparameterization) as the optical geodesics, identify 2 (E−Φ(x)) ≡κ e−2σ(x)(κ>0). Expanding around σ0gives Φ(x) = Φ0+c2δσ(x)+O(δσ2), c2:= κ e−2σ0, where the additive constant Φ0is irrelevant. Step 3 — Acceleration and Poisson corollary. Newtonian kinematics a=−∇Φimplies a=−c2∇δσ +O(δσ2). If one further imposes ∇2Φ=4πGρ in the weak field, then ∇2σ= (4πG/c2)ρ. References [1] C. 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