Mathematics
Coherence Geometry provides a structural framework for investigating mathematical systems through coherence-governed structure, constraint, and stability. Research in this domain currently focuses on foundational mathematical formulation, unifying functional structures, and selected major problem settings where coherence-based methods provide new organizing principles.
Research Topics
Foundational Structure
Canonical Foundations
Formal definitions, named results, and structural principles underlying Coherence Geometry.
Unified Coherence Functional (UCF)
Development of a framework for relating mathematical structures through coherence, constraint, and variational organization.
Major Problem Settings
Clay Millennium Problems
Applications of coherence-geometric methods to selected Clay Millennium Prize Problems, including structured investigations of problem-specific constraints, stability conditions, and formal closure mechanisms.
Publications List
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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…
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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…
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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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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.
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