On optimal Wannier decay in dimension three

For a Chern nontrivial Bloch bundle over the three torus, we construct an orthonormal Wannier basis with the optimal pointwise decay $\mathcal{O}(\mathrm{\mid }x{\mathrm{\mid }}^{-5\mathrm{/}2})$. All but one of the generators decay exponentially. This resolves the question left open in arXiv:2505.01999.