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: \[ \rho=2\pi\cos\!\left(\frac{\pi}{8}\right), \qquad R_\nu^{\rm QTT} =\frac{\Delta m_{31}^{2}}{\Delta m_{21}^{2}} =\rho^2 =33.69693720145647. \] The current mass coordinate makes the cancellation of the common scale explicit: \[ (m_1,m_2,m_3) =m_\Delta\!\left( 0,\frac{1}{\sqrt{\rho^2-1}}, \frac{\rho}{\sqrt{\rho^2-1}} \right). \] Freezing this direction before opening the official NuFIT 6.1 normal-ordering tables gives \[ \Delta\chi^2_{\rm ratio}=0.187708 \quad({\rm IC23/no\ SK}), \qquad 0.387921 \quad({\rm IC24+SK}). \] A single external scale anchor then becomes a cross-prediction rather than a two-parameter fit: \[ \Delta m_{31}^{2,\rm QTT|A} =\rho^2\Delta m_{21}^{2,A} =(2.5272703\pm0.0404363)\times10^{-3}\ {\rm eV}^2, \] \[ \Delta\chi^2_{\rm one\ anchor}=0.194936, \qquad 0.684704. \] The absolute source normalization is a separate observable. Under identity source-to-laboratory transport it gives \(\Delta\chi^2\simeq22.42\)--\(22.50\), 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 \(\Delta\chi^2\ge9\), 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.