T₃宇宙学 多级嵌套正交破缺与天体轨道偏心率的超欧拉生成定律 T₃ Cosmology Multi‑level Nested Orthogonality Breaking and the Hyper‑Euler Generation Law of Celestial Orbital Eccentricity

Classical celestial mechanics attributes planetary orbital eccentricity and orbital‑plane inclination mainly to initial conditions of primordial nebula collapse and many‑body gravitational perturbations. Based on the axiom of the upper bound of three‑dimensional orthogonal degrees of freedom and the axiom of velocity‑field projection coupling proposed within the T₃ Vortex Unified Field Theory, this report establishes the theory of multi‑level nested orthogonality breaking. It reconstructs the dynamical generation mechanism of celestial orbits by means of the T₃ three‑dimensional number system and hyper‑Euler exponential mapping. The core proposition of this report: the imperfection of cosmic orbits is not a random accident, but a geometric inevitability imposed by the fact that three‑dimensional space can carry at most three mutually orthogonal independent motion basis vectors. Once the nesting hierarchy exceeds three layers (planetary system – stellar system – galaxy – supercluster, etc.), high‑order velocity fields cannot generate additional orthogonal bases and must project onto low‑order orbital planes, producing quantifiable projection residuals. From this premise, a novel T₃ multi‑level nested eccentricity law is derived, presented in both standard T₃ algebraic form and unified hyper‑Euler exponential form. The orbital deformation variable is determined as a deterministic algebraic function of the planetary orbital radius , the distance from the host star to the galactic centre , and the dihedral angle between the two orbital planes. The law provides a self‑consistent explanation for the eccentricity distribution of planets in the Solar System and establishes an independent geometric criterion for predicting orbital properties of exoplanetary systems.