  Romelsberger's index has been argued to be an RG-invariant and, therefore,
Seiberg-duality-invariant object that counts protected operators in the IR SCFT
of an N=1 theory. These claims have so far passed all tests. In fact, it
remains possible that this index is a perfect discriminant of duality. The
investigation presented here bolsters such optimism. It is shown that the
conditions of total ellipticity, which are needed for the mathematical
manifestation of duality, are equivalent to the conditions ensuring
non-anomalous gauge and flavor symmetries and the matching of (most) 't Hooft
anomalies. Further insights are gained from an analysis of recent results by
Craig, et al. It is shown that a non-perturbative resolution of an apparent
mismatch of global symmetries is automatically accounted for in the index. It
is then shown that through an intricate series of dynamical steps, the index
not only remains fixed, but the only integral relation needed is the one that
gives the "primitive" Seiberg dualities, perhaps hinting that the symmetry at
the core is fundamental rather than incidental.
