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

A one-number neutrino test: the ratio is \(2\pi\cos(\pi/8)\)^2 Version: 4.0 Concept DOI: 10.5281/zenodo.19960813 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 The paper derives a dimensionless neutrino observable that does not depend on the absolute mass scale: \[ R_\nu \equiv {\Delta m_{31}^2\over\Delta m_{21}^2} = 4\pi^2\cos^2{\pi\over8} = 33.69694\ldots. \] The same number can be written as \[ R_\nu=\rho^2, \qquad \rho=2\pi I_{\mathrm{clk}}, \qquad I_{\mathrm{clk}}=\cos{\pi\over8}. \] The QTT construction uses the A1 two-clock half-angle and the A6/A7 minimal-holonomy mass-spectrum rule. The resulting Takagi singular values are \[ (m_1,m_2,m_3) = \left(0,{m_0\over\rho},m_0\right), \] so \[ \Delta m_{21}^2={m_0^2\over\rho^2}, \qquad \Delta m_{31}^2=m_0^2, \qquad {\Delta m_{31}^2\over\Delta m_{21}^2}=\rho^2. \] The normalization \(m_0\) cancels. No mixing angle or continuous flavor parameter is inserted into the ratio. The paper compares this with the global-fit neutrino ratio and reports a sub-sigma residual for the public fit used in the manuscript. Its forward-facing tests are sharp: future JUNO/DUNE/Hyper-K style convergence away from \(33.69694\), a confirmed inverted ordering, or a robustly nonzero lightest mass in the strict minimal branch would falsify this particular construction. What to audit in the paper: the metaplectic half-angle readout \(I_{\mathrm{clk}}=\cos(\pi/8)\); the loop factor \(\rho=2\pi I_{\mathrm{clk}}\); the minimal-holonomy spectrum \((0,m_0/\rho,m_0)\); the cancellation of \(m_0\) in the mass-squared ratio; the stated normal-ordering and lightest-mass falsifiers.