Note that pxdom(v) [not an element of] micro(v): since the arc ([p.sub.D] (root(micro(v))), root(micro(v))) catenated with the tree path root(micro(v)) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] v forms a PXDOM path to v, we have that pxdom(v) [is less than or equal to] [p.sub.D] (root(micro(v))).
The tree path root(G) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] u catenated with the arc (u, v) and the subpath in P from v to x gives a path in G to x that avoids z, again giving a contradiction.
P catenated with the tree path from w to v, however, forms a PXDOM path from y to v, contradicting the assumption that pxdom(v) = x.
Hence the disavowal that Europe's capitalist-industrial transition was the catenated
outcome of successive turns and developments that unfolded over the longue duree, and the accompanying homogenizing claim that Eurasian civilizational histories were marked by enduring continuities and isomorphisms--in mercantile cultures, commercial dynamism, technological inventiveness, scientific rationalism, demographic patterns, etc.--dating from the Bronze Age.