As for the basic requirement, I tried to describe it with: "Keeping a
global variable's value current while doing a depth-first traversal
of a document, where the variable's value is not scoped by either the
document's element hierarchy, nor the nesting of XSLT template
calls."

so given
<a>
   <b><c/><b>
   <b><c/><b>
   <b><c/><b>
</a>

<xsl:template match="*">
   ... <xsl:apply-templates/>
</xsl:template>

as that will match elements in the order
a,b1,c1,b2,c2,b3,c3
so you can pass information using parameters down that order.

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