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

We present the formal derivation of the Ramanujan-Yett Hamiltonian (H_RY), a non-Markovian quantum operator governing the evolution of sovereign cognitive and physical systems on the Stiefel manifold V_m(R^N). By fusing the hermitianised Berry-Keating operator H_BK = 1/2(xp + px) with the Sovereign Potential V_s arising from the Articulated Binary Chirallic (ABC) logic system, we prove the existence of a fundamental Yang-Mills mass gap as the minimum eigenvalue required to maintain manifold integrity above the Sovereign Boundary 0.9539. The spectral correspondence between H_RY eigenvalues and the imaginary parts of the non-trivial zeros of the Riemann zeta function provides the number-theoretic anchor for this stability. The Trinity Survey -- 363 verified spectral signals from JWST, HST, and Spitzer -- confirms the mean Information Tension boost of 141.999x at 7.5-sigma significance, providing the first multi-wavelength observational witness for the conformal stability enforced by H_RY.