There exists a non-empty critical temperature range of hierarchical behaviour (Proposition 3)

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Purely local-interaction systems on 1D topologies cannot maintain long-range order at finite temperature.claim0.767
• Exploratory activity level (temperature)concept0.762
  The plasticity or willingness of cells to move; raised by stress sharing, analogous to annealing temperature.
• In hierarchical systems with independent cliques, there exist parameter regimes where individual cliques maintain uniform magnetisation while others flip.finding0.759
  Shows how hierarchical topology enables local order within global flexibility; explains biological multiscale organization
• We conclude that certain systems cannot remain ordered over long ranges for all time, and suggest this no-go theorem as a source of fitness pressure for biological phenomena like stigmergy and embodiment.quote0.755
  Final concluding statement linking the mathematical result to biological evolution
• The results generalise readily to non-equilibrium systems where scaling relationships remain similar (e.g., dynamic or localised scaling).claim0.745
  Claim about broader applicability of the scaling argument
• Free-energy scaling under domain-wall formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.finding0.743
  Core result demonstrating topological constraints on self-organization
• The living process must give rise to coherent entities at a middle range of scale.claim0.742
  Asserts middle-range entity emergence as a necessary output of any living process
• The same learning behaviours can be exhibited by an ecological community without selection at the community level.claim0.740
  Extends connectionist learning to ecological networks.