Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.
Power laws, pareto distributions and zipf’s law.Contemporary physics, 46(5):323–351
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LLM agent societies develop power-law coordination cascades and intellectual elites through an integration bottleneck that grows with system size.
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Banach density of generated languages: Dichotomies in topology and dimension
Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.
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Do Agent Societies Develop Intellectual Elites? The Hidden Power Laws of Collective Cognition in LLM Multi-Agent Systems
LLM agent societies develop power-law coordination cascades and intellectual elites through an integration bottleneck that grows with system size.