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.

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• This no-go theorem serves as a source of fitness pressure for biological phenomena like stigmergy and embodiment.claim0.909
  Interpretation that evolutionary solutions evolved to overcome topological constraints
• no-go theorem for long-range orderconcept0.825
  Result that certain topological interaction constraints prevent ordered phases; proposed as evolutionary fitness pressure
• Topological no-go theorem (Sacco-Sakthivadivel-Levin) will establish that autoregressive LLMs cannot maintain long-range coherence via local interactions alone within 6 months of widespread community prediction0.800
• The results generalise readily to non-equilibrium systems where scaling relationships remain similar (e.g., dynamic or localised scaling).claim0.800
  Claim about broader applicability of the scaling argument
• We hypothesize that a similar 'brutal' and purely geometric process always occurs somewhere in other kinds of unfolding that generate living order — in poetry, dance, social structure, planning, and family relationships.hypothesis0.773
  Extends the brutal geometry thesis beyond architecture into all creative and social domains; acknowledged as not yet confirmed with certainty
• 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.finding0.771
  Core result demonstrating topological constraints on self-organization
• We cannot create living order only by concentrating on appearance; we must characterize the geometry that comes from living process.claim0.767
• Darwinian selective advantage alone cannot explain the appearance of global geometric order in organisms; an internal geometric ordering tendency must act together with selective pressure.claim0.767
  Alexander's argument that neo-Darwinism needs supplementation by internal dynamical ordering principles