Topological-Mechanical Degeneracy and Phenomenological Mapping in the Rigidity Percolation of Covalent Networks
This study employs generating-function mean-field theory on configuration-model graphs to demonstrate that rigidity percolation in random covalent networks exhibits a topological-mechanical degeneracy at the Maxwell isostatic point, identifies a specific topological milestone (12.5% giant rigid component) within the intermediate phase, and reveals a universal connection between this structural threshold and committed-minority tipping points in social and biological systems.