On the log-local principle for the toric boundary

Let X be a smooth projective complex variety and let D = D-1 + ... + D-l be a reduced normal crossing divisor on.. with each component D-j smooth, irreducible and numerically effective. The log-local principle put forward in van Garrel et al. (Adv. Math. 350 (2019) 860-876) conjectures that the genus 0 log Gromov-Witten theory of maximal tangency of (X, D) is equivalent to the genus 0 local Gromov-Witten theory of X twisted by circle plus(1)(j=1) O(-D-j). We prove that an extension of the log-local principle holds for X a (not necessarily smooth) Q-factorial projective toric variety, D the toric boundary, and descendant point insertions.