Abstract

The author introduces the Meyenburg Algebra, a generalization of classical arithmetic that resolves singularities by extending the rules of multiplication and division to include the axioms 0 ⋅ 0 = 𝜔 and 𝜔 0 =0. This framework reduces to standard arithmetic addition and subtraction in the limit omega tending to infinity, but in finite regimes, the algebra provides a consistent framework that regularizes otherwise undefined operations. It demonstrates compatibility with relativistic velocity addition, Wheel Algebra axioms, and Lorentz invariance, thereby establishing its physical relevance. When embedded into Hilbert space and extended to SU(2)×SU(2), the algebra naturally generates a positive mass gap, satisfying the criteria of Yang Mills theory. Cosmologically, the algebraic structure resolves the Schwarzschild singularity by complexifying the radial coordinate, leading to stable vacuum cores inside black holes. The algebraic vacuum contributes a nonzero energy density corresponding to dark energy, while hidden mass contributions emerge as a natural candidate for dark matter. Altogether, the Meyenburg Algebra provides a unifying algebraic foundation that connects mathematics, physics, and information theory to describe nature properly. It offers a coherent resolution of singularities and an intrinsic mechanism for mass generation, thereby addressing some of the most fundamental open problems in contemporary science.

Keywords

Meyenburg Algebra, Wheel Algebra, Yang–Mills Theory, Mass gap, Dark energy, Dark matter.

References

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