Beyond Convergence: W* = e⁻¹ as a Universal Structural Threshold for Complex System Coherence — A Multi-Domain Empirical Assessment

Key Points

• This research aims to establish a universal threshold for assessing structural coherence in complex systems.
• Utilized the Local Entropic Stability Engine framework to derive W* = e⁻¹ analytically.
• Applied empirical analysis across diverse domains, including nuclear safety and cognitive decision-making.
• Assessed the stability of systems by comparing W_min to the universal threshold W*.
• Identified a clear structural boundary: W_min > W* indicates stable systems, while W_min < W* indicates fragility across various fields.
• Demonstrated that the threshold is consistent without parameter adjustments across the studied domains.
• Provided a minimum coherence principle indicating functional capability without total internal convergence.