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I often wonder if the welded trees considered in the Childs, Cleve, Deotto, Farhi, Gutmann, Spielman [CCDFGS02] paper have any applicability to questions in (algorithmic) knot theory such as knot-identification or knot-canonization. For example, I envision labeling vertices of the welded tree with specific knot diagrams/grid diagrams, and labeling edges ...

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