OS System / ε-Model — Chapter 29 -- Structural Closure Across Scales: Atomic Frequency, Earth, and Planetary Derivations

This work presents a complete, self-contained structural calculation set demonstrating invariant closure across atomic, terrestrial, and planetary scales using a single projection balance condition ε = 0.50. The document includes: atomic limit frequency extraction for hydrogen-like systems, Earth time–rotation–orbit closure based on the structural number 64, Earth 64–137–c structural reconstruction, full planetary structural derivations for Earth, Mars, Jupiter, and Saturn, explicit numerical closure without fitted parameters, assumptions, or reinterpretation. All calculations are shown step by step exactly as executed.No external theories, forces, curvature, or auxiliary models are introduced.The work is presented as a structural result set.