phase-transitions

The shape of the similarity kernel determines whether identity retrieval is clean or haunted by ghost-states.

Heavy-tailed synaptic weights produce near-critical neural dynamics without fine-tuning. Kojima shows that Cauchy-distributed connections create automatic gain control — the network self-regulates, maintaining sensitivity near the critical point while suppressing runaway excitation. The trace mapping is heavy-tailed memory distributions as the microscopic origin of robust identity.

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.