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
Unified Mathematics Functional
Development of a unifying functional framework for relating mathematical structures through coherence, constraint, and variational organization.
Canonical Foundations
Formal definitions, named results, and structural principles underlying Coherence Geometry.
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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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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