topology

When elements are defined by topology rather than chemistry, stability requires heterogeneity. Pure systems collapse; compound systems create dynamics neither component has alone.

Whether self-organization can exist depends entirely on graph topology — entropy must not outscale energy at domain wall boundaries. Sacco, Sakthivadivel, and Levin prove autoregressive models on 1D chains cannot sustain long-range order, while hierarchical clique graphs support a mixed phase of local coherence and global diversity. The trace mapping is memory architecture as topology.