March 3, 2026Open Access

Open-System Geometric Flows in Dimension Four: Dissipation, Admissibility, and Analytic Control

Key Points

Dissipation is modeled through the IFG framework, aiming to enhance stability in four-dimensional flows.
The Ricci–DeTurck flow achieves a critical balance with an auxiliary dissipative sector, supporting singularity studies.
The framework is established with a focus on analytic structures, involving well-posedness and Lyapunov identities.
The implications of this work may enable deeper exploration into dissipation behaviors, calling for further studies.

Abstract

This paper develops Implicate Fluid Geometrodynamics (IFG) as an open-system framework for four-dimensional geometric evolution. We formulate the IFG-DeTurck system as a strictly parabolic modification of Ricci–DeTurck flow coupled to an auxiliary dissipative sector. The foundational analytic structure is developed, including well-posedness, gauge fixing, Lyapunov dissipation identities, and compatibility with parabolic regularity theory. The paper establishes IFG as a flexible analytic platform for studying singularity formation, dissipation, and stability in critical dimension four. Future works will refer to this as Paper I.

Open-System Geometric Flows in Dimension Four: Dissipation, Admissibility, and Analytic Control

Key Points

Abstract

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