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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Coherence Geometry Foundations, Part II: Physical Projections
CGI-BKS-0002 | Part II of the Coherence Geometry Foundations working reference text. It examines how quantum-like linear dynamics, causal and relativistic structure, residual coherence strain and cosmological background terms, electromagnetic field structure, thermodynamic behavior, and macroscopic transport can be represented as domain-level projections of the shared-amplitude, multi-phase coherence framework.
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Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations
CGI-BKS-0001 | Part I of the Coherence Geometry Foundations working reference text. It introduces multi-phase numbers, shared-amplitude phase structure, mathematical closure, projection, coherence relations, coherence matrices, coherence manifolds, projective coherence objects, morphisms, operators, and the canonical convergence and stability results governing coherent systems.
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A Variational–Relaxation Framework for Coherence-Driven Structure Formation
CGI-RSR-000013 | We develop a variational framework for coherence-driven structure formation, placing phase coherent self-organization within a unified geometric description compatible with variational principles used throughout physics.
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The Unified Coherence Functional: A Closed Generative Basis for Mathematics
CGI-RSR-000012 | We introduce the Unified Coherence Functional (UCF), a closed variational framework in which broad classes of mathematical structures arise as stationary projections.
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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…
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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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