Hypothesis of Informational geometric gravitation

Abstract We present an informational-geometric theory of gravity (IGG) in which the fundamental structure is a quantum graph with fixed coordination number d=8. From the graph topology we derive the dark matter to baryon ratio \Omega_{\text{DM}}/\Omega_b = 6, the number of fermion generations N_{\text{gen}} = 3, and the Standard Model gauge group SU(3)\times SU(2)\times U(1). A variational principle yields a self-consistent description of galactic rotation curves, leading to the baryonic Tully-Fisher relation M_b \propto V_f^4. From the quantum potential and holographic scaling we obtain the dark energy density \rho_\Lambda = \hbar c/(2L_{\text{horizon}}^4) \approx 5.3\times10^{-10} J/m³ and the inflationary parameters n_s \approx 0.967, r \approx 0.002. The theory contains a single free parameter (d=8) fixed by minimal embedding of the Standard Model. A test on SPARC data (84 galaxies) shows that the model scatter (0.173 dex) is 24% smaller than the empirical power-law scatter (0.219 dex). Derivation of general relativity, computation of Standard Model couplings, and explanation of the perturbation amplitude remain open problems. All code and data are provided for reproducibility.