Relic Neutrino and the Effective Number of Species N_eff in Dynamic Abstract Sphere Theory: N_eff = 3 from Sphere Topology

Work XXVIII of the DAS×GSV series (Dynamic Abstract Spheres × Hypothesis of Spherical Time). Neutrinos are interpreted as cauzon fermionic modes — quantum states of the cauzon field on the sphere S². The topology of S² embedded in three-dimensional space ℝ³ yields exactly three independent spatial directions, each corresponding to one neutrino species. This gives: N_eff(DAS) = 3.000 (exact, from topology) The standard model gives N_eff = 3.044; the correction 0.044 arises from e⁺e⁻ annihilation photon heating, which in DAS is suppressed by (α/π)² ≈ 5×10⁻⁶ and is unmeasurable. Results:(1) N_eff = 3.000 agrees with Planck 2018 (2.99 ± 0.17) at 0.06σ(2) CMB-S4 (2027) will test DAS vs standard model at ~1.5σ(3) Three particle generations explained by three-dimensionality of space(4) Neutrino mass m_ν = ħH₀/c² ≈ 1.5×10⁻⁵ eV per species(5) Falsification criterion: CMB-S4 measures N_eff > 3.05 Part of the DAS×GSV series (Works I–XXVIII).