## Introduction: To consolidate all the concepts developed in our work, we present a unified axiomatic equation that integrates: - **The Dual-Non-Dual (D-ND) model** - **Unified Information Theory** - **The principles of emergent gravity and polarization dynamics** - **The key components of the quantum operating system, including non-relational potential, possibilistic density, quantum fluctuations, NT (Null-All) states, and non-local transitions** ## Unified Axiomatic Equation

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## Abstract: We present a novel approach to improving the Barnes-Hut algorithm for N-body simulations by integrating it with a Dual-Non-Dual (D-ND) quantum framework within a Quantum Operating System (QOS). This integration incorporates concepts from Unified Information Theory, particularly the emergent gravity paradigm and the dynamics of polarization. By introducing quantum fluctuations, possibility densities, and non-relational potentials, we enhance both the performance and accuracy of the algorithm. The framework utilizes a proto-axiomatic state to guide spatial decomposition and force calculations, potentially improving computational efficiency without compromising physical precision.

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