Title: Weighted $1\times1$ cut-and-project sets in bounded distance to a lattice,
Abstract: Recent results of Grepstad and Lev are used to show that weighted
cut-and-project sets with one-dimensional physical space and one-dimensional
internal space are bounded distance equivalent to some lattice if the weight
function $h$ is continuous on the internal space, and if $h$ is either
piecewise linear, or twice differentiable with bounded curvature.