Unified Coherence Geometry: A Common Action for Physical Fields
CGI-RSR-000011 | This work introduces the Unified Coherence Action with constrained forms that reproduce the major laws of physics.
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Mathematical Foundations of Coherence Formation and Stability
CGI-RSR-000010 | We establish a mathematical framework for coherence formation and stability in energy-minimizing phase systems. Introduces the UCCP, SCRC, and CS-SCT.
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A Multi-Phase Extension of Complex Numbers and the Global Coherence Theorem
CGI-RSR-000009 | This is the foundational document that introduces multi-phase numbers and the Global Coherence Theorem (GCT).
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A First-Order Terminal-Closure Criterion for the Riemann Hypothesis and the Exterior-Rank Source Boundary
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.
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Universal Kernel Operators and Seed Correspondences in the Direction of the Hodge Conjecture
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.
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Projective Rank-one Closure for Terminal Navier–Stokes Saturation
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.
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Rank-One Coherence Obstructions in High–High Navier–Stokes Interactions
Internal ID: CGI-RSR-000005 | We study comparable high–high interactions in the three-dimensional incompressible Navier–Stokes nonlinearity.
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An Operator Bridge Between Arithmetic Heights and Analytic Residues for Elliptic Curves
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.
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Local Coherence Hessians: A Structural Classification of Spectral Gaps
Internal ID: CGI-RSR-000003 | We provide a structural classification of spectral gaps for local coherence functionals on periodic lattices.
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Information & Computation | Clay Millennium Problems | Constraint Satisfaction and Computational Search | Mathematics | Research Papers
A Coherence Field Approach to SAT: Linear-Scale Defect Structure and Clause-Centered Repair
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.