  We use insights from string field theory to analyze and cure the divergences
in the cylinder diagram in minimal string theory with both boundaries lying on
a ZZ brane. We focus on theories with worldsheet matter consisting of the
$(2,p)$ minimal model plus Liouville theory, with total central charge 26,
together with the usual $bc$-ghosts. The string field theory procedure gives a
finite, purely imaginary normalization constant for non-perturbative effects in
minimal string theory, or doubly non-perturbative effects in JT gravity. We
find precise agreement with the prediction from the dual double-scaled
one-matrix integral. We also make a few remarks about the extension of this
result to the more general $(p',p)$ minimal string.
