Artian LIA Neutrino Family-Rank Reference Theorem

Abstract

One frozen mass-gap direction, one external scale anchor, and a complete minimal neutrino spectrum The neutral-family constructor is written as a finite source compiler: \[ (D_\nu,G_\nu,\mathcal A_\nu^{\rm rank}) \longrightarrow \rho_\nu=2\pi\cos\!\left(\frac{\pi}{8}\right) \longrightarrow (m_1,m_2,m_3) =m_\Delta\!\left( 0,\frac{1}{\sqrt{\rho_\nu^2-1}}, \frac{\rho_\nu}{\sqrt{\rho_\nu^2-1}} \right). \] Its scale-free face is \[ \frac{\Delta m_{31}^2}{\Delta m_{21}^2} =\rho_\nu^2 =33.69693720145647. \] Official NuFIT 6.1 joint-profile execution gives \(\Delta\chi^2=0.187708\) and \(0.387921\) after profiling only the common mass scale. Using the JUNO reactor solar gap once gives \[ \Delta m_{31}^{2,\rm QTT|A} =(2.5272703\pm0.0404363)\times10^{-3}\ {\rm eV}^2, \] \[ (m_1,m_2,m_3) =(0,8.660254,50.271963)\ {\rm meV}, \qquad \sum m_\nu=58.932217\ {\rm meV}. \] The same branch supplies a non-gravitational Artian ruler: \[ \ell_A^{(\nu)} =\frac{\hbar c}{(2\pi)^5v^2} \sqrt{(\rho^2-1)\Delta m_{21}^2}. \] The framework keeps source geometry and laboratory scale transport distinct: \[ M_\nu^{\rm lab}=Z_\nu M_\nu^{\rm src}, \qquad \frac{\Delta m_{31}^{2,\rm lab}}{\Delta m_{21}^{2,\rm lab}} =\frac{\Delta m_{31}^{2,\rm src}}{\Delta m_{21}^{2,\rm src}} =\rho^2. \] Thus the ratio and one-anchor population are joint-profile compatible, while the raw identity-transport source normalization is separately stressed at \(\Delta\chi^2\simeq22.4\)--\(22.5\). No transport coefficient is selected from that residual. Stable anchors: paper concept DOI; QTT Main Book v10.01; Derivation Atlas.

The authors' abstract, as published at the source. arXiv (Cornell University), 2024 · DOI ↗