  We generalize the methods in previous work to provide a program for proving
Singer's Conjecture for Coxeter systems. Specifically, we consider even Coxeter
systems with nerves that are flag triangulations of $\BS^{n-1}$, $n=2k$. We
prove that Singer's Conjecture in dimensions $n-2$ and $n-1$, along with the
vanishing of the $\ltwo$-homology of certain subspaces called "two-letter"
ruins above dimension $k+1$, imply Singer's Conjecture in dimension $n$. This
is, so far, an incomplete program. The author intends this paper to serve as a
reference for those inquiring about Singer's Conjecture and about even Coxeter
systems.
