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Euclidean Embeddings of Acyclic Hypergraph Line Metrics
We study Euclidean embeddings of higher-order line metrics arising from hypergraphs. For a fixed threshold \(s\geq 1\), the \(s\)-line graph \(L_s(H)\) has one vertex for each hyperedge of \(H\), with two hyperedges adjacent when they intersect in at least \(s\) vertices; its shortest-path metric is
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