  A novel application of lattice QCD spectral reconstruction is presented, in
which euclidean correlation function data in a fixed time range are used to
infer values outside the range, enabling a model-independent investigation of
the asymptotic large-time behavior. Moments of the correlator are also
determined, and reconstructed correlation matrices between different moments
are included in a variational optimization similar to the standard Generalized
Eigenvalue Problem (GEVP). These ideas are illustrated using a single-nucleon
correlation function determined on an $N_{\rm}=2+1$ ensemble of gauge
configurations at $m_{\pi} = 200{\rm MeV}$.
