Computational Falsification of Symmetrical Flow Constraints: The Emergence of Geometric Relaxation and the 1.63 Phase Shift

This paper presents a standalone computational falsification protocol demonstrating the breakdown of symmetrical flow constraints in finite-capacity topological networks. Classical physical models assume continuous, infinite-capacity environments where flow inherently distributes with rational symmetry. We test this assumption by routing discrete information packets through an Erdős-Rényi network topology subjected to a strict local capacity limit and varying density constraints. Our empirical results prove that when a saturated system is starved of parallel pathways, the thermodynamic cost of data compression—governed by Landauer's Principle—forces the system to abandon rational symmetry to prevent destructive interference. The network organically undergoes a geometric relaxation phase shift, violently bifurcating into an asymmetric survival state with a structural flow ratio approximating the Golden Ratio. By hard-coding a unified mathematical anchor (Seed 457), we provide a strictly reproducible framework establishing this 1. 63 phase shift not as an imposed constant, but as a universal scaling limit governing macro-scale structural deformations. Update (Version 1. 1): Resolved a Windows file-extension formatting issue. The primary computational script (Seed457WindTunnel. py) was updated to ensure it downloads as a pure, executable Python file for seamless command-line replication. No alterations were made to the underlying code, informational-geometric constraints, or mathematical outputs. AI Assistance Statement The author acknowledges the use of AI-assisted tools for structural formatting and text editing during the drafting of this manuscript. All scientific theory, mathematical modeling, and final content are solely the responsibility of the author. Math Typesetting Statement All mathematical expressions in the main body of this manuscript are presented using a dual-inline convention to ensure stability across software environments and archival formats. Each mathematical quantity appears first as a standard Unicode symbol in bold, which is provided solely for immediate visual readability. This is followed immediately by the archival text in LaTeX format, enclosed in brackets. The bracketed LaTeX represents the definitive, authoritative mathematical content for all purposes of citation, reproduction, and long-term preservation. No external MathType objects are utilized.