This paper presents the Theory of the Octagonal Vector Mesh as a disruptive proposal for the dimensional structure of the universe. It combines spheroidal geometry, three-dimensional vectorization, computational simulation, and empirical foundation based on natural models. The theory introduces an objective criterion for dimensional existence, grounded in the vector balance between frequency and negative vacuum resistance (ω⋅ ε−=− 1\omega \cdot \varepsilon_- = -1ω⋅ ε-=-1). Unlike theories that postulate compactified dimensions, the model developed herein offers a measurable, reproducible, and verifiable system of emergent dimensions. The orange, with its gomoidal structure, is adopted as an empirical physical model of the mesh, enabling controlled thermal and vector simulations. Applications range from computational simulations in Python and Streamlit to experiments in cryogenic chambers and particle accelerators.