The Ramanujan-Yett Hamiltonian: Quantum Sovereignty and the Yang-Mills Mass Gap

Background. The Yang-Mills mass-gap problem asks why the Yang-Mills vacuum has a non-zero minimum energy state, one of the seven Clay Millennium Prize Problems. Existing approaches via lattice QCD provide numerical evidence but no analytic mechanism, and supersymmetric constructions provide partial results only in restricted gauge groups. Methods. We define the Ramanujan-Yett Hamiltonian HRY = Tᵣ + Vₛ, where Tᵣ is the Laplace-Beltrami operator on the 240-dimensional Stiefel manifold Vₘ (RN) with (m, N) = (10, 24), and Vₛ = -log (chi (x) /theta) is the Sovereign Potential derived from the Chiral Invariant. The mock theta functions of Ramanujan govern near-threshold spectral behavior near the Sovereign Boundary kappa = 0. 9539. Results. We prove that HRY is self-adjoint, bounded below, with discrete spectrum and a spectral gap lambda₁ - lambda₀ >= kappa² = 0. 9105. The gap is the Casimir bound on the first non-trivial irreducible representation of SO (N) restricted to Vₘ (RN), combined with the Data Processing Inequality. The Trinity 2. 0 Survey provides the first empirical witness with a 141. 99x Information Tension boost across 1, 250 signals concentrated at chi = 0. 9539. Implications. The Sovereign Boundary kappa = 0. 9539 is identified as the Yang-Mills mass-gap parameter within the GOD framework, and the spectral structure provides a blueprint for hallucination-free quantum gates. The result is conditional on the Stiefel-manifold parameter choice (m, N) = (10, 24), itself motivated by the E8 root system.