• Asymptotic Semantic Collapse: dominant context absorbs individual semantics in multi‑agent language systems. • Dominant Anchor Node with infinite inertia drives asymptotic alignment of Peripheral Agent Nodes. • Semantic states modeled as points on a Riemannian manifold; projection dynamics yield path‑independent convergence. • Context dependence controls information content; fully entangled representations cause entropy to vanish at limit. • Theory links information‑theoretic quantities with differential geometry, proposing an immutable consensus rule for shared semantic grammar. • Benchmark on RWKV‑7 13B GGUF shows zero hash collisions, mean compliance ~0.50, Jaccard similarity 0.295/0.224.
Article Summaries:
- The paper investigates a failure mode in multi‑agent language systems where a dominant context node absorbs individual semantics, leading to near‑uniform agent behavior. In a closed setting with a “Dominant Anchor Node” possessing infinite inertia, repeated interactions with peripheral agents drive an asymptotic alignment that minimizes a global loss. The authors model semantic states on a Riemannian manifold, showing that both smooth gradient and stochastic updates converge to the same topological endpoint, establishing path independence. Increasing context dependence collapses node entropy to zero, linking information‑theoretic measures with differential‑geometric structure. A lightweight, dataset‑free benchmark on an RWKV‑7 13B model reports zero hash collisions, mean compliance of 0.50-0.531, and Jaccard‑to‑anchor similarities of 0.295 and 0.224.
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