  It was recently shown how to account for all instantons of hermitian matrix
models via (anti-) eigenvalue-tunneling -- including both
exponentially-suppressed and exponentially-enhanced transseries-transmonomials
which are predicted by resurgence. Matrix-model eigenvalue-tunneling
corresponds to ZZ-branes. The present work shows how matrix-model
anti-eigenvalues correspond to negative-tension ZZ-branes; and how to compute
generic nonperturbative sectors -- with both ZZ and negative-tension-ZZ branes
-- in the minimal-string free-energy. Negative-tension D-branes are herein a
requirement of resurgence. This results in the construction of minimal-string
free-energy transseries and the analytic computation of their resurgent Stokes
data. Calculations are presented via Liouville boundary conformal field theory
and via (matching) matrix model analysis. Minimal-string results are extended
to Jackiw-Teitelboim gravity. Building on the matrix model analysis, one
extension towards topological string theory is obtained via the
remodeling-conjecture -- which allows for addressing one-cut, toric Calabi-Yau
geometries. Building on the Liouville theory calculation, one other extension
towards critical string theory is obtained via the H3+ - Liouville
correspondence -- which allows for addressing negative-tension D-instantons in
AdS spacetime. Throughout, checks of the construction and formulae are made in
several examples, against both Borel resurgent analysis and string-equation
transseries data.
