Our universe has exactly three dimensions because that is the only way a specific type of geometric rotation can work mathematically.
Non-resonant helical coupling requires exactly three dimensions to achieve what is known as algebraic saturation. This proof suggests that the 3D space we live in is a necessary result of this geometry rather than a random background. The study uses Clifford algebra and the golden ratio to show why other dimensional configurations fail to hold the same properties. Physicists have long debated why the universe isn't 2D or 4D at a fundamental level. This work provides a concrete geometric reason why three dimensions are the only stable option for the structure of reality. It derives our physical world from the requirements of pure rotation.
On the Self-Locking Geometry of Non-Resonant Helical Coupling: 3D Saturation, Clifford Algebra Extension, and the Structural Invariant Ξ
SSRN · 6723465
This paper proposes and investigates a class of helical coupling geometric structures driven by non-resonant rotation steps. Starting from a discrete underlying set and a complex rank-2 vector bundle over it, we introduce action axes generated by bivectors and a non-resonant angular step Φ = 2π(1 − 1/ϕ) (where ϕ is the golden ratio). The central problem we address is: how many pairs of helical actions are required to strictly reduce the dimensional deficit of the system to zero? We prove that th