All-Genus Open Mirror Symmetry for Toric Calabi-Yau 3-Orbifolds with Multiple Branes

We prove the all-genus open mirror symmetry of a toric Calabi-Yau 3-orbifold where the boundary condition is given by multiple Aganagic-Vafa branes. Each brane could be either inner or outer, and admit a fractional framing. The B-model is given by the Chekhov-Eynard-Orantin topological recursion expanded in local coordinates specified by the brane data.