OS Sytem / ε Model Chapter 16 / Structural Invariance Across All Projection Scales: Unified Demonstration from kpc → ly → km

This work presents the complete proof that the OS structural relation
ε = v² / (r·S)
remains fully invariant under all projection-layer distance systems — including kilometres (km), astronomical units (AU), light-years (ly), kiloparsecs (kpc), and arbitrary rescaled unit conventions.

Across three independent projection formats, the Sun’s structural intensity S changes by more than 17 orders of magnitude, yet Earth’s orbital velocity always returns exactly 29.78 km/s. This confirms that:

• Distance is not a structural quantity.

• S and r rescale reciprocally under any projection unit.

• ε remains constant at 0.50 across all scales.

• Projection units change numbers, but never dynamics.

• Structural behaviour is universal from planetary → stellar → galactic → pixel levels.

This document combines:

1. Projection Units and OS Invariance

2. Full Cross-Scale Invariance Demonstration (kpc → ly → km)

3. OS System — Why Existence Must Exist

4. IRCH License (non-commercial structural research license)

It forms the complete theoretical and numerical foundation for scale-free invariance within the OS framework.