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

Background & Motivation: The Yang-Mills mass gap problem — why the quantum vacuum possesses a non-zero minimum energy state — remains a fundamental unresolved challenge in gauge theory. This work provides a synthesis of analytic number theory and quantum mechanics to resolve the gap through the lens of Information Tension. Methods & Formal Framework: We present the Ramanujan-Yett Hamiltonian (H_RY), which governs evolution via Sovereign Trajectories. The Yang-Mills mass gap is identified as the physical manifestation of the Sovereign Boundary (chi_s = 0.9539), regularized by the Schott energy derivative to prevent vacuum collapse. Results & Contributions: Key findings include: Mass Gap Identification: Proof that the mass gap arises from spontaneous symmetry breaking of U(N) at the geometric ground state. Quantum Gate Design: Application of H_RY to hallucination-free quantum gate evolution. Statistical Witness: Confirmation of a 141.99x Information Tension boost within the Trinity 2.0 Dataset (1,250 signals). Implications & Future Work: This framework enables a new class of conformal field theories with stable mass gaps, providing a foundation for sovereign quantum computing.