  We discuss the quantum numbers of domain walls of minimal length induced by
doping Mott insulators, carefully distinguishing between holon and hole walls.
We define a minimal wall hypothesis that uniquely correlates the observed
spatial structure with the doping level for the low-temperature commensurate
insulating state of La$_{2-x}$Ba$_x$CuO$_4$ and related materials at $x={1\over
8}$. We remark that interesting walls can be supported not only by conventional
antiferromagnetic but also by orbital antiferromagnetic (staggered flux phase,
$d$-density) bulk order. We speculate on the validity of the minimal wall
hypothesis more generally, and argue that it plausibly explains several of the
most striking anomalous features of the cuprate high-temperature
superconductors.
