Topological Surgery as Universal Interface Constraint
Year: 2026
Type: article
Abstract: For decades, the mathematical community treated the resolution of 3D singularities in geometry and fluid dynamics as two distinct problems. In geometry, the Poincar´e Conjecture was finally resolved by Perelman using Ricci Flow and Topological Surgery. In fluid dynamics, the Navier-Stokes Millennium Prize remains open, stalled on the potential for a finite-time blow-up (singularity). In this paper, we demonstrate that these are structurally isomorphic problems. Using the Golden Rule of Structural Rationalism, we argue that any 3D dynamical system governed by curvature or advection will inevitably produce singularities (ghosts) due to unconstrained Scalar Drives. The resolution in both domains is not analytical, but topological: the system requires an Open Interface that performs deterministic topological surgery (cutting, capping, and folding) to preserve the fundamental identity of the manifold. The Golden Rule is thus revealed as a universal meta-algorithm for detecting and resolving ghosts in any projection, regardless of the mathematical domain.
Authors: Theriault, Eric, DeepSeek A.I.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225332075