We present a hybrid OpenMP/Charm++ framework for solving the O(N ) Self-Consistent-Field eigenvalue problem with parallelism in the strong scaling regime, P 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 ∈ {30, 90, 150}, P/N ≈ {819, 273, 164}) and find support for an increasingly strong scalability with increasing system size N .