Derivation of Standard Model Mixing Angles from a 44-Vector Discrete Vacuum Lattice

We derive the mixing angles and CP-violating phases of the PMNS and CKM matrices from a 44-vector discrete vacuum lattice—the 3D flavor-space projection of a 19-dimensional $\mathbb{Z}_3$-graded Lie superalgebra. The central prediction is the Cabibbo angle: $\lambda = |V_{us}| = 73/324 = 0.22530864$, obtained as $\lambda = (2/9)(1+\varepsilon_q^2/2)$ with $\varepsilon_q=1/6$ and the $\mathrm{SU}(3)$ quadratic Casimir $C_2=4/3$, matching the experimental value $0.225300(700)$ to $+0.01\sigma$—a precision of 8 parts per million, with zero free parameters. The PMNS predictions—compared against current global fit data—are: $\sin^2\theta_{12}=1/3-\lambda/9=0.30830$ ($-0.10\sigma$), $\sin^2\theta_{23}=0.54609$ ($+0.00\sigma$), $\sin^2\theta_{13}\in[1/46,1/44]$ (within interval). The CP phases are $\delta_{\rm CP}=240^\circ$ ($+0.26\sigma$) and $\delta_{\rm CKM}=65.3^\circ$. Projected future measurements by JUNO (targeting $\sim0.3\%$ precision on $\theta_{12}$) and DUNE (mass ordering) will provide decisive tests of these predictions. The perturbation strengths—$\varepsilon_{\nu_2}=1/36$, $\varepsilon_{\nu_3}=1/12$, $\varepsilon_q=1/6$—are obtained from the algebra's Frobenius norms and the $\mathfrak{u}(3)$ projection structure, with the Hybrid norm-filtered subclass rigorously proven to contain exactly 24 vectors. Every formula is presented with complete symbolic definitions and step-by-step derivations.