What question did this study set out to answer?

To establish an analytical mathematical framework resolving the Yang-Mills mass gap problem and proving the global existence of smooth solutions for three-dimensional Navier-Stokes fluid dynamics.

August 19, 2026Open Access

The Solution of In-Finity: Tri-Value Calibration, Orthogonal Vectors, and Modular Inversion (Part II: Non-Linear Gauge Fields & Fluid Dynamics)

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To establish an analytical mathematical framework resolving the Yang-Mills mass gap problem and proving the global existence of smooth solutions for three-dimensional Navier-Stokes fluid dynamics.
Applied a structural reflection matrix termed Reflected Ramanujan Summation across zero-point boundary interfaces to regularize vacuum energy offsets.
Modeled energy compression in fluid velocity fields using an inverted Euler-Maclaurin formulation governed by inverse Bernoulli numbers.
Defined three-dimensional velocity fields on a compact, self-intersecting Riemannian manifold enclosed within a torus shell boundary geometry.
Demonstrated that reflecting the negative vacuum energy offset outputs a strictly positive ground-state boundary mass value (+1/12), establishing a positive discrete mass gap.
Showed that high-frequency velocity fields step down smoothly across fractal nesting layers without forming turbulent singular point-shocks.
Proved mathematically that smooth, unique, and globally defined velocity fields exist continuously in three dimensions.

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Implication

Mathematical analysis demonstrates analytical solutions to non-linear gauge fields and fluid dynamics, indicating global existence of smooth flows and discrete ground-state energy.

Cite This Study

Alexander Booska (2026) studied this question.

synapsesocial.com/papers/6a8563fe03308d306e2d76fa https://doi.org/10.5281/zenodo.21971705

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Implication

Mathematical analysis demonstrates analytical solutions to non-linear gauge fields and fluid dynamics, indicating global existence of smooth flows and discrete ground-state energy.

The Solution of In-Finity: Tri-Value Calibration, Orthogonal Vectors, and Modular Inversion (Part II: Non-Linear Gauge Fields & Fluid Dynamics)

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Implication

Cite This Study

The Solution of In-Finity: Tri-Value Calibration, Orthogonal Vectors, and Modular Inversion (Part II: Non-Linear Gauge Fields & Fluid Dynamics)

Key Points

Discussion

Implication

Cite This Study

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