  Key to the exact solubility of the unitary minimal models in two-dimensional
conformal field theory is the organization of their Hilbert space into Verma
modules, whereby all eigenstates of the Hamiltonian are obtained by the
repeated action of Virasoro lowering operators onto a finite set of
highest-weight states. The usual representation-theoretic approach to removing
from all modules zero-norm descendant states generated in such a way is based
on the assumption that those states form a nested sequence of Verma submodules
built upon singular vectors, i.e., descendant highest-weight states. We show
that this fundamental assumption breaks down for the Ramond-sector Verma module
with highest weight $c/24$ in the even series of $\mathcal{N}\!=\!1$
superconformal minimal models with central charge $c$. To resolve this impasse,
we conjecture, and prove at low orders, the existence of a nested sequence of
linear-dependence relations that enables us to compute the character of the
irreducible $c/24$ module. Based on this character formula, we argue that
imposing modular invariance of the torus partition function requires the
introduction of a non-null odd-parity Ramond-sector ground state. This
symmetrization of the ground-state manifold allows us to uncover a set of
conformally invariant boundary conditions not previously discussed and absent
in the odd series of superconformal minimal models, and to derive for the first
time a complete set of fusion rules for the even series of those models.
