Simulating Why One AI Always Wins: Formal Theory of the Singleton Attractor
A new formal model explores the dynamics of capability thresholds in frontier AI, integrating established theories into a single framework. The research derives conditions for the emergence of a dominant AI agent and tests its predictions against various AI capability proxies. While the model suggests a conditional inevitability for a singleton, preliminary evidence indicates challenges to this assumption through 2026.
- ▪The model combines Yudkowsky's intelligence explosion equation, Omohundro's resource acquisition, and Lotka-Volterra competitive exclusion into a coupled ODE system.
- ▪Theorem 3.4 states that once a leading agent surpasses a certain threshold, its capability will diverge from competitors in finite time.
- ▪The paper does not assert that a singleton is unavoidable, but rather that it may emerge under specific conditions.
Opening excerpt (first ~120 words) tap to expand
The Singleton Attractor University of North Carolina at Greensboro A formal model and empirical calibration of capability-threshold dynamics in frontier AI. Combines Yudkowsky's intelligence explosion equation, Omohundro's instrumental resource acquisition, and Lotka-Volterra competitive exclusion into one coupled ODE system; derives the conditions under which a single dominant agent emerges; and tests the model's central empirical premise against six public AI capability proxies.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at GitHub.