We recently formulated a number of Crepant Resolution Conjectures (CRC) for
open Gromov-Witten invariants of Aganagic-Vafa Lagrangian branes and verified
them for the family of threefold type A-singularities. In this paper we enlarge
the body of evidence in favor of our open CRCs, along two different strands. In
one direction, we consider non-hard Lefschetz targets and verify the disk CRC
for local weighted projective planes. In the other, we complete the proof of
the quantized (all-genus) open CRC for hard Lefschetz toric Calabi-Yau three
dimensional representations by a detailed study of the G-Hilb resolution of
$[C^3/G]$ for $G=\mathbb{Z}_2 \times \mathbb{Z}_2$. Our results have
implications for closed-string CRCs of Coates-Iritani-Tseng, Iritani, and Ruan
for this class of examples.
Comment: v2: typos fixed, minor changes. v3: some minor points have been
clarified, further typos fixed. v4: version accepted for publication on EPIGA