  We propose an intersection-theoretic method to reduce questions in genus zero
logarithmic Gromov-Witten theory to questions in the Gromov-Witten theory of
smooth pairs, in the presence of positivity. The method is applied to the
enumerative geometry of rational curves with maximal contact orders along a
simple normal crossings divisor and to recent questions about its relationship
to local curve counting. Three results are established. We produce
counterexamples to the local/logarithmic conjectures of van
Garrel-Graber-Ruddat and Tseng-You. We prove that a weak form of the conjecture
holds for product geometries. Finally, we explicitly determine the difference
between local and logarithmic theories, in terms of relative invariants for
which efficient algorithms are known. The polyhedral geometry of the tropical
moduli of maps plays an essential and intricate role in the analysis.
