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An interesting conjecture, $\rm{Z_{BH}=|Z_{top}|^2}$,
as recently proposed by Ooguri, Strominger and
Vafa, connects the free energy of topological strings with the degeneracy of 4-dimensional
BPS black hole states arising in $\cal{N}$$=2$ compactifications of IIA(B) string theories.
In the original proposal the black hole ensemble is a \emph{mixed} ensemble, in the sense that
it treats the magnetic charges microcanonically while the electric charges canonically.
Consequently, the results for degeneracy of states as obtained from the ensemble
inverse-Laplace integration, suffer from prefactors which do not respect the
(relevant) \emph{electric-magnetic dualities}. One idea to overcome this deficiency, as
claimed recently,
is imposing a nontrivial measure for the ensemble sum.\ We address this problem and \emph{upon a redefinition of the OSV ensemble} whose variables
are as numerous as the electric potentials,
show that for restoring the symmetry \emph{no non-Euclidean measure is needful}. In detail,
we rewrite the OSV free
energy as a function of new variables which are combinations of the
electric-potentials and the black hole charges.
Subsequently the Legendre transformation which bridges between the entropy and the black
hole free energy in terms of these variables, points to a generalized
ensemble. In this context we will consider \emph{all} the cases of relevance: \emph{small}
and \emph{large} black holes, with
or without $D_6$-brane charge. For the case of vanishing
$D_6$-brane charge, the ensemble is \emph{pure canonical} and
the electric-magnetic duality is restored \emph{exactly}, leading to
the proper results for the black hole degeneracy of states. For
more general cases, the construction still works well \emph{as far
as} the violation of the duality by the corresponding OSV result
is restricted to a \emph{prefactor}. In a concrete example we
shall show that for black holes with non-vanishing $D_6$-brane
charge, there are cases where the duality violation \emph{goes
beyond this restriction}, thus imposing non-trivial measures is
\emph{incapable} of restoring the duality. This observation
signals for a \emph{deeper modification} in the OSV proposal.
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