  We present a hybrid OpenMP/Charm++ framework for solving the $\mathcal{O}
(N)$ Self-Consistent-Field eigenvalue problem with parallelism in the strong
scaling regime, $P\gg{N}$, where $P$ is the number of cores, and $N$ a measure
of system size, i.e. the number of matrix rows/columns, basis functions, atoms,
molecules, etc. This result is achieved with a nested approach to Spectral
Projection and the Sparse Approximate Matrix Multiply [Bock and Challacombe,
SIAM J.~Sci.~Comput. 35 C72, 2013], and involves a recursive, task-parallel
algorithm, often employed by generalized $N$-Body solvers, to occlusion and
culling of negligible products in the case of matrices with decay. Employing
classic technologies associated with generalized $N$-Body solvers, including
over-decomposition, recursive task parallelism, orderings that preserve
locality, and persistence-based load balancing, we obtain scaling beyond
hundreds of cores per molecule for small water clusters ([H${}_2$O]${}_N$, $N
\in \{ 30, 90, 150 \}$, $P/N \approx \{ 819, 273, 164 \}$) and find support for
an increasingly strong scalability with increasing system size $N$.
