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Let $f : \{0,1\}^n \to \{0,1\}$ be a Boolean function. Denote the two possible simple single crossing tangles by $T_0$ and $T_1$ (your choice for which is which). Is there some "generalized $n$-tangle" (i.e., a bunch of properly embedded arcs in $S^3$ with $n$ disjoint 3-balls removed that are ...
