Logarithmic negative tangency and root stacks

We study stable maps to normal crossings pairs with possibly negative tangency orders. There are two independent models: punctured Gromov-Witten theory of pairs and orbifold Gromov-Witten theory of root stacks with extremal ages. Exploiting the tropical structure of the punctured mapping space, we define and study a new virtual class for the punctured theory. This is produced via refined intersections on the Artin fan, and gives rise to a distinguished sector of the punctured Gromov-Witten theory. Restricting to genus zero, we then show that the resulting invariants coincide with the orbifold invariants, first for smooth pairs, and then for normal crossings pairs after passing to a sufficiently refined blowup. This builds on previous work to provide a complete picture of the logarithmic-orbifold comparison in genus zero. This is compatible with splitting and thus allows for the wholesale importation of orbifold techniques: a consequence is a self-contained localisation formalism for logarithmic Gromov-Witten invariants. Contemporaneous work of Johnston uses this comparison to give a new proof of the associativity of the Gross-Siebert intrinsic mirror ring.