An Exact Z₃-Graded Algebraic Framework Underlying Observed Fundamental Constants

We propose an algebraic framework constructed from a finite-dimensional 19-dimensional Z³-graded Lie superalgebra g = g₀ ⊕ g₁ ⊕ g₂ (dimensions 12+4+3), featuring exact closure of the graded Jacobi identities (verified symbolically in key sectors and numerically in a faithful matrix representation, with residuals ≲ 10⁻¹² across 10⁷ random combinations) and a unique (up to scale) invariant cubic form on the grade-2 sector, driving a triality symmetry on the vacuum sector. Interpreting the grade-2 sector as the physical vacuum state, we explore whether representation-theoretic invariants and contractions within this algebraic structure can account for observed Standard Model parameters—including fermion masses, mixing angles, and gauge couplings—as well as the magnitude of the cosmological constant, black-hole entropy scaling, and certain qualitative features of quantum entanglement. The framework yields twelve quantitative predictions amenable to experimental scrutiny at forthcoming facilities such as the High-Luminosity LHC, Hyper-Kamiokande, DARWIN/XLZD, and LiteBIRD.