The tipping point where a liquid turns into solid glass is mathematically identical to how a 'committed minority' changes a society's opinion.
March 31, 2026
Original Paper
Topological-Mechanical Degeneracy and Phenomenological Mapping in the Rigidity Percolation of Covalent Networks
arXiv · 2603.27352
The Takeaway
Scientists found a 'deeper universality' in how networks transition from loose to rigid. The exact moment a microscopic backbone of atoms locks together to form a solid glass happens at the same 12.5% threshold that social scientists use to predict when a small group of people can flip a majority opinion.
From the abstract
We study rigidity percolation in random covalent networks to establish the pure topological baseline of the floppy-to-rigid transition. Using a generating-function mean-field theory on configuration-model graphs, we report three results. First, we prove that the onset of the topological giant rigid component (GRC) coincides with the mechanical Maxwell isostatic point (_c = 2.4) -- a topological-mechanical degeneracy that holds in the locally tree-like limit and provides a clean reference frame,