From Dual‑Lattice Geometry to Cosmic Expansion: An Effective Friedmann Equation

Paper 3 of 8 This paper derives an effective Friedmann‑like expansion law directly from the dual‑lattice geometry of the Honeyverse. By analyzing how the HU/ghost mismatch shapes large‑scale curvature, the paper shows that the cosmic expansion rate emerges naturally from the underlying combinatorial structure, without invoking vacuum energy or dynamical dark‑energy fields. The resulting expansion law links the Hubble radius, the doubling depth k, and the HU/ghost ratio λ in a closed feedback loop. This provides a geometric explanation for the observed acceleration of the universe and demonstrates that the Friedmann equation is an emergent large‑scale approximation of a deeper discrete architecture. v1