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

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• 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.quote0.800
  Final concluding statement linking the mathematical result to biological evolution
• no-go theorem for long-range orderconcept0.790
  Result that certain topological interaction constraints prevent ordered phases; proposed as evolutionary fitness pressure
• Purely local autoregressive systems cannot maintain long-range coherence at finite temperature.claim0.780
• This no-go theorem serves as a source of fitness pressure for biological phenomena like stigmergy and embodiment.claim0.768
  Interpretation that evolutionary solutions evolved to overcome topological constraints
• LLM tangential speech (derailment, formal thought disorder parallel) will be empirically demonstrated to trace to Peierls-Landau topological constraint on 1D local systems within 12 months.prediction0.758
• Lab shape (as independent institute) becomes weaker option after Sacco-Sakthivadivel-Levin no-go theorem on pure-text coherence.prediction0.747
• 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.finding0.744
  Core result demonstrating topological constraints on self-organization
• Any system that persists must minimise surprisal, thereby gathering evidence for its own generative model, a process known as self-evidencing.claim0.742
  Foundational claim of the paper, defining self-evidencing.