Universe OS & ϵ-Model: 3D Geometric Folding Engine, Fine constant 137.035 role , Boundary Metrics, and Scale-Invariant Systemic Relational Framework

This publication presents the structural and mathematical framework of the Universe OS and ϵ-Model, formalizing reality as a pre-physical, deterministic 3D geometric information network. Rather than treating spatial distance, physical forces, or time as independent empirical properties, this work demonstrates how macroscopic planetary dynamics, universal speed limits (c), and subatomic quantum parameters (such as the Bohr electron velocity factor v0) emerge from a single, scale-invariant spatial folding engine. Key theoretical and mathematical derivations within this record include: The 3D Geometric Folding Engine: The transformation of 1D scalar time durations into 3D volumetric wave boundaries using the fine-structure constant reciprocal (α−1≈137.035) and dual-orthogonal projection (π2). Bidirectional Boundary Metrics: Derivation of the 223.53 1D boundary vector (c/6) and closed-loop reconstruction of a 1-hour temporal block from the speed of light. Multi-Planetary Dynamics: Derivation of independent planetary base nodes (Earth, Mars, Jupiter) and scale-invariant geometric ratios without empirical fitting parameters. Macro-to-Micro Integration: A closed mathematical derivation chain connecting solar light transit time (tlight=499.65 s) directly to quantum atomic velocity states (v0≈2.1877×106 m/s) via universal relational operators (137.035, 1.2008, and 11.576). All materials in this publication are protected under the IRCH Public Research License 1.0.