WARNING : bad format for reading This chapter presents a complete structural closure of planetary-scale relations using a single invariant relation: ε = v² / (r · S) All calculations are performed strictly within projection using observed values, while preserving structural invariance across hierarchy levels. The work demonstrates that: Planetary systems maintain a constant equilibrium ratio ε ≈ 0.50 Structural parameter S can be derived directly from observed v and r Rescaling of r automatically enforces inverse rescaling of S Numerical closure is achieved without introducing additional constants The chapter provides full step-by-step calculations, ensuring that: Every transformation preserves ε No scale mixing occurs All results close numerically This document is part of a continuous structural calculation record and contains no interpretative or theoretical claims, only verified numeric closures.