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The aim is to extend geometric control principles to the continuum mechanics of incompressible Navier-Stokes equations.

April 12, 2026Open Access

Omega-Sigma Control: From Discrete H3 Geometric Admissibility to Quantum Delta Continuum Mechanics

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The aim is to extend geometric control principles to the continuum mechanics of incompressible Navier-Stokes equations.
Constructed a finite chiral coordinate realization based on the Coxeter system H3.
Embedded into a hyperbolic triangle group to create a 60-vertex dodecahedral frame.
Utilized the Kato-Rellich theorem and a higher-order Schatten-class framework for continuum mechanics.
Applied the framework to the Navier-Stokes Millennium problem using a new coordinate system.
Established that the hyperbolic embedding provides structural coercivity, preventing blow-up under perturbations.
Reclassified fluid blow-up as a topological rupture in spectral space rather than a loss of smoothness.
Absorbed classical bounds while defining spectral admissibility as crucial for fluid transport.

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This manuscript formulates a unified framework for fluid dynamics, suggesting new interpretations of singularities in 3D fluid transport.

Andrew Kim (2026) studied this question.

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