Non-Linear Spectral Saturation and Clifford Unification: Mathematical Completeness, Non-Perturbative Unitarity, Anomaly Cancellation, and Moduli Rigidity

We present the mathematically complete formulation of the unified field theory governed by the quadratic operator saturation constraint X² - 3X = 0 over the Clifford bundle Cl(1,3) ⊗ Cl(6). The field operator X = 3P+ decomposes into scalar, gauge, and gravitational sectors within a flat MacDowell-Mansouri-Cartan super-connection where cross-grade interference vanishes identically off-shell under the Levi-Civita condition (zero torsion). The internal geometry M6 = T⁶/Z₃ inherits the algebraic triality of Spin(8) ⊃ Cl(6), naturally generating exactly three chiral fermionic generations. By computing explicit triple overlap integrals of internal harmonic spinor wavefunctions across orbifold fixed points, we derive the full rank-3 Yukawa tensors, the mass hierarchies (mt/me ~ 10⁵), and the complete CKM and PMNS matrices from first principles. Moduli fields are dynamically stabilized at the maximal symmetry point τ = exp(2πi/3) with Planckian mass, ensuring parameter rigidity. Gauge and mixed gravitational anomalies cancel via the Atiyah-Singer index theorem. The Lee-Wick gravitational sector features complex-conjugate poles, guaranteeing positive Hilbert space metrics (Θ = exp(-Q)), microcausality, and non-perturbative S-matrix unitarity. Spacetime singularities are replaced by regular de Sitter cores (K ≤ mp⁴) and a cosmological quantum bounce. The framework accounts for cold dark matter through a stable 4.8 TeV singlet, protects the proton (τp ~ 10³⁶ yr), and yields definitive cosmological predictions: r = 0.00167, ns = 0.9667, and αs = -0.00055, testable by LiteBIRD and the Simons Observatory.