  We investigate torus actions on logarithmic expansions in the context of
enumerative geometry. Our main result is an intrinsic and coordinate-free
description of the higher-rank rubber torus appearing in the boundary of the
space of expanded stable maps. The rubber torus is constructed canonically from
the tropical moduli space, and its action on each stratum of the expanded
target is encoded in a linear tropical position map. The presence of
2-morphisms in the universal target forces expanded stable maps differing by
the rubber action to be identified. This provides the first step towards a
recursive description of the boundary of the expanded moduli space, with future
applications including localisation and rubber calculus.

Algebraic Geometry