The Neutrino Mass-Squared Ratio from T₁u Geometry: Δm²₃₁/Δm²₂₁ = 33

Proves that Δm²₃₁/Δm²₂₁ = 33 as a Tier 1 algebraic theorem of the Unified Foam Field Theory. The result follows from ‖M−I‖²_F = (r₁−1)²+(r₂−1)² = 49−18+2 = 33, where r₁ = (9−√17)/2 and r₂ = (9+√17)/2 are the roots of the master equation λ²−9λ+16=0. Given m₁ = 0 (proven theorem) and m₂ = m₃/√33, the ratio Δm²₃₁/Δm²₂₁ = m₃²/m₂² = 33 exactly. Observed value 33.57 ± 0.7 → 0.8σ from prediction. Corrects a notation error in earlier UFFT documents: Δm²₃₂/Δm²₂₁ = 32 (also exact), not 33. The neutrino sector is now algebraically complete: m₁ = 0, m₂ = m₃/√33, m₃ = mₑ exp(−(11+13√17)/4), tan²θ₁₂ = √17/9, sin²θ₂₃ = 1/2+√17/81, sin²θ₁₃ = (√17/27)²(1−√17/162)², all Tier 1 or Tier 2. Zero free parameters.