Data for CP-conserving SO(3) parameterization of the neutrino mixing matrix

Structure of SO(3) hypothesis mixing matrix CP-conserving SO(3) parameterization of the neutrino mixing matrix Jarosław Duda(Jagiellonian U. (main)), Janusz Gluza(Silesia U.), Biswajit Karmakar(Silesia U.) Supporting Mathematica file for : https://arxiv.org/abs/2509.25328 SO3 Generators In[ ]:= Gx = 0 0 0 0 0 -1 0 1 0 ; Gy = 0 0 1 0 0 0 -1 0 0 ;Gz= 0-1 0 100 000 ; Rotation vector and matrix exponent In[ ]:= A= -θx*Gx -θy*Gy -θz*Gz; A// MatrixForm UExpA =FullSimplifyMatrixExp[A] /.θx 2+θy 2+θz 2-> θ2,(θx)2+θy2+ (θz)2>1; Out[ ]//MatrixForm= 0θz-θy -θz0θx θy-θx0 SO(3) mixing matrix In[ ]:= USO3 =MatrixFormUExpA[[1, 1]] /. θx 2+θy 2+θz 2 -> θ, UExpA[[1, 2]] /.θx 2+θy 2+θz 2-> θ, UExpA[[1, 3]] /.θx 2+θy 2+θz 2-> θ, UExpA[[2, 1]] /.θx 2+θy 2+θz 2-> θ, UExpA[[2, 2]] /.θx 2+θy 2+θz 2-> θ, UExpA[[2, 3]] /.θx 2+θy 2+θz 2-> θ,UExpA[[3, 1]] /.θx 2+θy 2+θz 2-> θ, UExpA[[3, 2]] /.θx 2+θy 2+θz 2-> θ, UExpA[[3, 3]] /.θx 2+θy 2+θz 2-> θ; USO3 // MatrixForm Out[ ]//MatrixForm= θx 2+Cos[θ]θy 2+θz 2 θ2 -((-1+Cos[θ]) θxθy)+θSin[θ]θz θ2-θSin[θ]θy+(-1+Cos[θ]) θxθz θ2 -(-1+Cos[θ]) θxθy+θSin[θ]θz θ2 θy 2+Cos[θ]θx 2+θz 2 θ2 θSin[θ]θx-(-1+Cos[θ]) θyθz θ2 θSin[θ]θy-(-1+Cos[θ]) θxθz θ2-θSin[θ]θx+(-1+Cos[θ]) θyθz θ2 Cos[θ]θx 2+θy 2+θz 2 θ2 2SO3.nb