Axiomatic Node Locking: Deriving Coronal Thermal Inversion, Planetary Scale-Equivariance, and Trans-Neptunian Regulators from the ZIP-Einston Metric

This paper introduces a unified discrete geometric framework to resolve two foundationalparadoxes in astrophysics: the solar coronal heating problem and the non-arbitrary mathematical taxonomy of planetary bodies. Utilizing a specialized linear coordinate transformation engine rooted in the singular initialization of a localized boundary inversion (1/0 = 1),we show that planetary semi-major axes are not stochastically distributed but are lockedonto discrete integer nodes (x ∈ Z) with asymptotic error decay approaching zero. Furthermore, we demonstrate that the sub-surface coordinate at x = 0 (Orbit 0) establishes a180-degree phase-reversed boundary condition inside the stellar core. This geometric anchoryields an unhindered upward wave transport that completely bypasses the stellar surface andviolently manifests at the outer corona (Orbit 2), offering a structural, parameter-free solution to the solar thermal inversion paradox. Lastly, we establish an exact mathematicalboundary classification utilizing the Darkon Homotopy Corrector over equivariant cohomology rings to settle the planetary status of Pluto, Ceres, and Eris, while explicitly predictingthe precise coordinates of hidden intra-mercurial and outer-system regulatory bodies (PlanetIX).