We develop a topological framework for proving lower bounds on sign-rank via $\mathbb{Z}_2$–equivariant topology, and use it to resolve the sign-rank of the Gap Hamming Distance problem up to lower-order terms.

For every (partial) sign matrix $A$, we associate a free $\mathbb{Z}_2$–simplicial complex $S(A)$ and show that sign-rank of $A$ ... more >>>