OS System / ε-Model — Chapter 37 — Structural Closure and Cross-Scale Balance (ε ≈ 0.5)

This work presents a complete numerical closure structure connecting atomic-scale systems, planetary-scale relations, and light-scale reconstruction through invariant balance conditions. All calculations are explicitly shown and originate from independently verifiable numeric inputs. No assumptions, no omitted steps, and no parameter tuning are introduced. Key results: • Independent closure of atomic systems to ε ≈ 0.5• Earth-scale transition node (13.8477) and its internal return path• Cross-scale structural propagation through identical operators (×3600, ×1.2)• Emergence of partial and full light-channel regimes• Reconstruction of light-scale values through intermediate nodes (499.68, 600)• Multi-path convergence producing identical structural values The work demonstrates that: A single invariant relationε = v² / (r · S) remains consistent across all tested scales. The hierarchy changes only the projection format — not the underlying structure. This document is part of the ε-Model / OS System research series and is released in its final, non-modifiable form under IRCH Public Research License 1.0.