  We construct semiglobal singular spacetimes for the Einstein equations
coupled to a massless scalar field. Consistent with the heuristic analysis of
Belinskii, Khalatnikov, Lifshitz or BKL for this system, there are no
oscillations due to the scalar field. (This is much simpler than the
oscillatory BKL heuristics for the Einstein vacuum equations.) Prior results
are due to Andersson and Rendall in the real analytic case, and Rodnianski and
Speck in the smooth near-spatially-flat-FLRW case. Similar to Andersson and
Rendall we give asymptotic data at the singularity, which we refer to as final
data, but our construction is not limited to real analytic solutions. This
paper is a test application of tools (a graded Lie algebra formulation of the
Einstein equations and a filtration) intended for the more subtle vacuum case.
We use homological algebra tools to construct a formal series solution, then
symmetric hyperbolic energy estimates to construct a true solution
well-approximated by truncations of the formal one. We conjecture that the
image of the map from final data to initial data is an open set of anisotropic
initial data.
