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 structure constant formula. The S³ metric includes a position-dependent lapse function f(χ) = 1/(1+z), which produces both redshift and time dilation as inseparable geometric effects. This explains the observed (1+z)^(1.003±0.005) supernova time dilation (White et al. 2024, DES) — a test that classical tired light fails but lattice redshift passes. Over 10⁴¹ cells at the QCD confinement scale, the total redshift is z = e⁷ − 1 ≈ 1096, matching the CMB. JWST observations support this framework: high-redshift galaxies have normal sizes at lattice redshift distances, resolving the "impossible early galaxy problem" (Raikov et al. 2025). This framework eliminates the need for spacetime expansion, inflation, and dark energy while explaining all major cosmological observations through static icosahedral geometry.