Relational Model of Informational Geometry (RMIG): Emergent gravity, Standard Model, and cosmological constant from the entanglement budget on the 18/27 qubit fractal

Abstract

We present the Relational Model of Informational Geometry (RMIG) — a theory proposing a common mechanism for the emergence of spacetime, gravity, gauge interactions, and the cosmological constant from the finite quantum entanglement budget on a qubit network embedded on the self-similar 18/27 fractal. Of the 27 neighboring positions in a 3×3×3 cube, only 18 generate a nonzero entanglement surface, yielding a fractal with Hausdorff dimension d_H = log 18/log 3 ≈ 2.631. The metric is constructed from fractal diffusion as an effective gravitational potential. **Key results:** - **Cascading gravitational constant:** the amplitude a = 0.168 is proposed by a candidate spectral ansatz based on graph invariants, not fitted. The tanh⁺ cascade with one fitted scale parameter reproduces the NGC 3198 rotation curve (χ² = 13.8; 7× better than NFW with dark matter) and the dynamical mass of galaxy clusters (Coma, Bullet Cluster: ~100% match).- **SPARC population verification:** test on 171 galaxies from the Lelli 2016 database — median χ²/N = 2.94; 38% of galaxies with χ²/N < 2; 64% with χ²/N < 5; median rotation curve slope +0.063 (approximately flat). Reproduction of the McGaugh radial acceleration relation (RAR).- **Interaction complementarity (hypothesis):** the entanglement budget motivates a partition into nuclear, gravitational, and cosmological interactions, proposing a conditional mechanism for the hierarchy problem (g_nucl/g_grav ~ 10³⁹) and a model estimate of the order of magnitude of the cosmological constant (Λ/Λ_Planck ~ 10⁻¹²²).- **Multi-level mass hierarchy:** the effective tunneling amplitude decreases geometrically with fractal level; lepton mass ratios reproduced to 11% accuracy.- **Chiral graph structure and gauge symmetries:** the graph topology admits candidate representation spaces compatible with SU(3) × SU(2)_L × U(1)_Y; identification of the stabilizer as the gauge group remains an open problem.- **GR consistency:** PPN β = γ = 1 to accuracy Δp < 10⁻⁷; the effective energy-momentum tensor satisfies the Bianchi identity. **Open problems:** exact mass hierarchy (p ≈ 1.36 is an RG hypothesis), dwarf galaxies (DDO 154), universality of the reference density ρ_ref, CMB/BBN analysis, derivation of ξ_grav from axioms, status of the combinatorial observation sin²θ_W = 3/13, formal identification of the gauge group. RMIG is a research program with falsifiable predictions. This work constitutes a mathematical formalization of the author's intuitive assumptions. It was created with AI assistance. It does not claim the status of a verified scientific theory at the present stage.