Structural Coherence Beyond Modularity: Residual Dynamics Near Quantum Criticality

This work introduces the Structural Coherence Index (SCI), a new metric designed to distinguish coherent critical organization from stochastic fragmentation in complex systems. Using graph representations of the two-dimensional Ising model near criticality, we demonstrate that modularity alone may generate false-positive structural signals in randomized fragmented networks. SCI combines modularity, graph density, and largest connected component persistence to recover physically coherent structural regimes.