The Universe as Zoll Manifold: Lattice Redshift from Icosahedral Geometry

We show that uniform matter distribution with icosahedral lattice structure necessarily produces a Zoll S³ geometry. The derivation chain is: uniform matter → uniform gravity → S³ topology → Zoll property (automatic). The universe radius R = rₛ/√3 = 13.8 Gly, where √3 is the dimensional RMS factor for 3D isotropic closure versus 1D radial closure — a result from standard dimensional analysis, not numerology. Lattice rigidity (α = constant) provides stability without requiring a cosmological constant. The cosmological redshift — termed "lattice redshift" — arises from photon-lattice coupling with energy loss ε = α¹⁹ = α⁵⁺¹¹⁺³ per cell, where the exponents encode the same geometric structure as the fine…