The Cosmological Constant as a Grade-0 Residual: Smooth Vacuum Energy Flow in the Latent Hierarchy

We identify the cosmological constant \(\Lambda\) as the grade-0 component of the gravitational Latent hierarchy and show that the double grade seesaw — two consecutive grade-2 → grade-0 projections — closes the cosmological constant problem. The first projection (SUSY cancellation) reduces the vacuum energy from \(\sim M_P^4\) to \(\sim M_{\text{SUSY}}^4\); the second projection (gravitational grade coupling) introduces a further \((M_{\text{SUSY}}/M_P)^4\) suppression. Using the SUSY spectrum predicted by the smooth \(\alpha\)-flow (bino \(\sim 1060\) GeV through squarks \(\sim 6354\) GeV), the self-consistent effective SUSY mass \(M_{\text{eff}} = 5604\) GeV gives \(\rho_\Lambda = M_{\text{eff}}^8 / (\sqrt{3} \, M_P^4) \times (1 - \alpha_{\text{GUT}}/\pi) = 2.524 \times 10^{-47}\) GeV\(^4\), within 0.11% of the observed \(2.527 \times 10^{-47}\) GeV\(^4\). We discover the UV-IR grade duality: the SUSY factor determined by \(\alpha\) (UV, through RG flow) and by \(\Lambda\) (IR, through the seesaw) agree to 0.14%, despite \(\Lambda\) being \(2062\times\) more sensitive to the SUSY factor than \(\alpha\). The \(1/\sqrt{3}\) geometric coefficient receives an \(O(\alpha_{\text{GUT}})\) perturbative correction that reduces the deviation from 1.09% to 0.11%. The predicted dark energy scale \(m_\Lambda \approx 2.6\) meV coincides with the neutrino mass scale. We prove 16 structural theorems in Lean 4 and verify scaling behavior numerically in Rust. All computations are reproducible.