Question: We still use parentheses for roots or xrefs, so is () still legal, and if so does it turn out to still be synonymous with common root, or does it mean something else?

$is is documented at https://wiki.oasis-open.org/xdi/EquivalenceRelations
I don't see $is() in the wiki except in the ABNF.

https://lists.oasis-open.org/archives/xdi/201311/msg00016.html
"going to an empty path to represent the outer root created a problem for inverse contextual statements, since the inverse contextual predicate would become just $is, i.e., an identity equivalence statement. Markus and I explored this and decided that it did in fact work semantically if the object of the inverse contextual statement was the complete context. For example:

=markus//<+name>
<+name>/$is/=markus<+name>

However after much discussion we felt that this was a different semantic that our current inverse contextual predicate, which only requires the parent context as the object. And we decided that we still needed this semantic. Thus our conclusion was that we should to keep $is() as the inverse contextual predicate. Our logic is that the parentheses become necessary simply because they enclose the actual XDI address of the outer root (which is empty) as a cross-reference so that it can be described by the inverse predicate $is."

Markus, could you let us know the justification? Would it be ok to use $is?

This dates from when the common root and contextual predicate was () instead of empty string. When we changed, Drummond and Markus chose to leave the inverse contextual predicate as $is(). Since the () symbol is now used nowhere else I think this is anomalous.