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: \ =2\! (8), R_^ QTT = m₃₁^₂ m₂₁^{2} =² =33. 69693720145647. \ The current mass coordinate makes the cancellation of the common scale explicit: \ (m₁, m₂, m₃) =m_\! (0, 1²-1, ²-1). \ Freezing this direction before opening the official NuFIT 6. 1 normal-ordering tables gives \ ² ₑ₀ₓ₈₎=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: \ m₃₁^2, QTT|A =² m₂₁^2, A = (2. 52727030. 0404363) 10^-3\ eV², \ \ ² ₎₍₄\ ₀₍₂₇₎ₑ=0. 194936, 0. 684704. \ The absolute source normalization is a separate observable. Under identity source-to-laboratory transport it gives \ (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 \ (²9\), 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.