no-go theorem for long-range order

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

• 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.quote0.825
  Final concluding statement linking the mathematical result to biological evolution
• long-range orderconcept0.823
  Persistence of a macroscopic pattern across large scales; necessary for maintaining coherent outputs or structures
• 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 prediction0.790
• This no-go theorem serves as a source of fitness pressure for biological phenomena like stigmergy and embodiment.claim0.757
  Interpretation that evolutionary solutions evolved to overcome topological constraints
• long-range coherenceconcept0.732
  Ability to maintain structural consistency over extended sequences
• Long-range coherence in sequencesconcept0.731
  Ability to maintain organized behavior over extended scales; shown limited in flat autoregressive models, enabled in hierarchical/biological systems.
• Middle-Range Orderframework0.729
  Coherent entities at the scale of rooms and bays — roughly halfway between building volume and smallest elements — whose existence and beautiful pattern of arrangement is essential for profound building order; first noted by Ingrid King
• Purely local-interaction systems on 1D topologies cannot maintain long-range order at finite temperature.claim0.715