It had been known since old times (works of Murakami–Ohtsuki, Cheptea–Le and the
second author) that there exists a universal finite type invariant (" an expansion") Z old for
knotted trivalent graphs (KTGs), and that it can be chosen to intertwine between some of the
standard operations on KTGs and their chord-diagrammatic counterparts (so that relative to
those operations, it is" homomorphic"). Yet perhaps the most important operation on KTGs is
the" edge unzip" operation, and while the behavior of Z old under edge unzip is well …

It had been known since old times ([MO],[Da]) that there exists a universal finite type
invariant (“an expansion”) Zold for Knotted Trivalent Graphs (KTGs), and that it can be
chosen to intertwine between some of the standard operations on KTGs and their chord-
diagrammatic counterparts (so that relative to those operations, it is “homomorphic”). Yet
perhaps the most important operation on KTGs is the “edge unzip” operation, and while the
behaviour of Zold under edge unzip is well understood, it is not plainly homomorphic as …