A parameter-free derivation of the neutrino mass-squared ratio Δm²₃₁/Δm²₂₁ = 4π² cos²(π/8) in Quantum Traction Theory

A geometric neutrino mass-ratio prediction tested on the full joint oscillation likelihood The source statement is scale-free: \[ ρ=2πcos\!(π/8), R_νQTT ={Δ m₃₁²}{Δ m₂₁²} =ρ^2 =33.69693720145647. \] The current mass coordinate makes the cancellation of the common scale explicit: \[ (m_1,m_2,m_3) =m_Δ\!( 0,{1}{√ρ^2-1}, {ρ}{√ρ^2-1} ). \] Freezing this direction before opening the official NuFIT 6.1 normal-ordering tables gives \[ Δχ^2ᵣₐₜᵢₒ=0.187708 ({ IC23/no\ SK}), 0.387921 ({ IC24+SK}). \] A single external scale anchor then becomes a cross-prediction rather than a two-parameter fit: \[ Δ m₃₁2, QTT|A =ρ^2Δ m₂₁2,A =(2.5272703±0.0404363)×10⁻³\ { eV}^2, \] \[ Δχ^2one\ anchor=0.194936, 0.684704. \] The absolute source normalization is a separate observable. Under identity source-to-laboratory transport it gives \(Δχ^222.42\)--\(22.50\), so the ratio direction is profile-compatible while the absolute transport map remains an explicit test. A PMNS--Takagi theorem proves that mixing angles cannot alter the singular-value verdict. The sharp falsifiers are exclusion of the frozen ratio line at \(Δχ^2≥9\), inverted ordering, or a robustly nonzero lightest mass in the strict minimal branch. Stable anchors: paper concept DOI; QTT Main Book v10.01; QTT Observatory.