OS System / ε-Model — Chapter 36: Full Numerical Closure of the ε = v² / (r·S) Relation Across Scales, from Atom , Time to light speed

This document presents Chapter 36 of the OS System, a structural framework based on invariant relational balance. The system is defined through a single relation: ε = v² / (r · S) All observable quantities emerge only in projection, where: S appears as mass/inertia, v appears as dynamic phase (speed/frequency), r appears as distance/orientation. All calculations are executed strictly within projection, where S, v, and r are read as measurable quantities while preserving structural invariance. The document demonstrates: exact closure of ε across independent calculation paths consistency under projection rescaling (distance, time, and unit transformations) stability of the relation across atomic and planetary regimes absence of free parameters, fitting, or post-adjustment Each result is obtained through direct computation and verified by closure: v² = ε · r · S The same structure remains invariant regardless of the chosen projection format, confirming that numerical outcomes are not dependent on units but on relational balance. This record contains no interpretation, no reformulation, and no abstraction beyond the executed calculations. All values, steps, and transitions are explicitly shown and reproducible. This document is part of the ε-Model / OS System research series.