OS System / ε-Model — Degree of Information Compression and Structural Inseparability: Mathematical Analysis of Scale Invariance in Physical Invariants (Universe OS Matrix Framework) ( part 7 )

Abstract

This paper presents a formal numerical test series and theoretical analysis examining the integration of the fine-structure constant reciprocal (α⁻¹ ≈ 137.035) with fundamental space-time parameters, planetary dimensions, orbital dynamics, and invariant geometric system operators within the "Universe OS Matrix Framework." Standard physical frameworks conventionally separate quantum electrodynamics from macro-scale celestial dynamics, treating them under isolated unit systems. This work explores an alternative deterministic paradigm: since all measuring instruments, physical units, and observers are inherently bound by atomic structure and electromagnetic (light) interaction constants, the foundational ratio 137.035 functions as a core invariant operator linking structural states across micro and macro scales. Key features of this research include:- Closed-Loop Operator Dynamics: Demonstrating how incorporating α⁻¹ (137.035) alongside light propagation parameters (c) systematically folds macro-scale distance and temporal metrics back into planetary orbital velocities, axial rotation periods, and gravitational acceleration constants.- Multi-Planetary Test Expansion: Mathematical verification across Earth, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune, demonstrating high-precision convergence on physical invariants (e.g., Sun-Earth light travel time of ~499 s, standard gravity g ≈ 9.81 m/s²), geometric constants (π), and base temporal cycles (3600 s / 24 h).- Observer-Interaction System Unity: Proposing that physical constants describe an interconnected informational-geometric framework where micro-atomic parameters translate directly into celestial mechanics through scale matrix compression and expansion.