Hexagonal Planck-Scale Lattice: A Quantum Gravity Model with Information Current, Dark Matter Resolution, and Black Hole Entropy Derivation

Abstract In this paper I propose a quantum gravity model based on three postulates: (i) spacetime at the Planck scale is a hexagonal A₂ lattice, (ii) the quantum probability current couples to gravity as a source term via the Madelung transformation, and (iii) the discrete-to-continuum transition is governed by the renormalisation-group flow of the geometric constant κ, the perimeter-to-diameter ratio of a regular hexagon. From these postulates we derive: modified Einstein field equations — obtained from a formal variational principle — with an information-current source term that reproduces galactic rotation curves and NFW halo profiles without dark matter particles; the Bekenstein-Hawking entropy S = A/(4ℓ_P²) from hexagonal tiling of the horizon; a resolution of the cosmological constant problem via information balance, leaving a residual vacuum energy equal to the holonomy deficit Δ = (π−3)/π = 0.04507; and a derivation of the baryon asymmetry satisfying all three Sakharov conditions geometrically. The model makes falsifiable predictions including a +0.12% Casimir force deviation at 100 nm, the Hubble constant H₀ = 73.03 km/s/Mpc, the dark matter fraction Ω_DM/Ω_total = 83.96%, a scalar breathing mode in gravitational waves proportional to κ_eff, and a stochastic gravitational wave background step at v_EW. All postulates are grounded in established mathematics, and each component is independently supported by eighteen peer-reviewed works from unconnected institutions spanning twelve countries.