Internal ID: CGI-RSR-000008 | We formulate a strict first-order terminal-closure criterion for the Riemann Hypothesis using a matrix-valued completed explicit formula.
Internal ID: CGI-RSR-000007 | We study a natural operator associated with the wedge product on exterior powers and show that its kernel admits a universal representation-theoretic structure.
Internal ID: CGI-RSR-000006 | We study terminal rank-one saturation mechanisms in a dyadic analysis of the three-dimensional incompressible Navier–Stokes equations. Starting from a high–high OBCI closure module for comparable high-frequency interactions, we analyze the remaining determining-scale paraproduct strain branch using localized output Gram matrices. No terminal nondepleted rank-one output-coherent saturation branch persists under the stated modules and criteria.
Internal ID: CGI-RSR-000005 | We study comparable high–high interactions in the three-dimensional incompressible Navier–Stokes nonlinearity.
Internal ID: CGI-RSR-000004 | We present a structured program relating the arithmetic and analytic structures appearing in the Birch–Swinnerton–Dyer conjecture for elliptic curves over Q. The construction proceeds through two parallel bridges. The arithmetic bridge reconstructs the NÅLeron–Tate height pairing from a system of local coherence pairings obtained via defect descent at all places of the curve. Summation of the local energies produces a global quadratic operator whose determinant yields the classical regulator. The analytic bridge constructs a quadratic operator from the spectral structure of the L–function.
Internal ID: CGI-RSR-000003 | We provide a structural classification of spectral gaps for local coherence functionals on periodic lattices.
Internal ID: CGI-RSR-000002 | We study a coherence-based dynamical representation of Boolean satisfiability in which clauses induce local pressures that generate a field over variables, and assignments evolve by aligning with this field.