= 2.5$ was simply too small. There was of course an alternative possibility: that the simple picture we found at lower $\beta$ failed as one approached the continuum limit. Clearly it is important to distinguish between these two possibilities, and this is what we propose to do in this paper. The cluster size scaling relations referred to above imply that an $L=32$ lattice at $\beta=2.5115$ should have a large enough volume. Such gauge fixed lattice fields were made available to us by G. Bali and we have used them, supplemented by calculations on an intermediate $L=20$ volume at $\beta=2.5$, to obtain evidence, as described in Secs. \[sec\_cl\_str\] and  \[sec\_mon\_vor\_K\], that the monopole picture we found previously is in fact valid at these lattice spacings and that the deviations we found previously were due to too small a lattice size.

The fact that one has to go to space-time volumes that are ever larger, in physical units, as the lattice spacing decreases, hints at some kind of breakdown of ‘monopole dominance’ in the continuum limit. We finish Sec. \[sec\_cl\_str\], with a discussion of the form that this breakdown might take.

An attractive alternative to the dual superconducting vacuum as a mechanism 