Logarithmic Gromov–Witten theory with expansions

We construct a version of relative Gromov-Witten theory with expanded degenerations in the normal crossings setting and establish degeneration formula for resulting invariants. Given simple pair $(X,D)$, we virtually smooth proper moduli spaces curves $X$ prescribed boundary conditions along $D$. Each point such space parameterizes maps from nodal to that are dimensionally transverse strata. use formalism reconstruct virtual class attached tropical map terms expansions vertices.