Modularity conjecture for the listed lift-dual rank-four Nahm sums

For each triple $(A,B,C)$ listed in Tables 1–4 and Table 5 (the table labels are those used in the source), let $\mathcal{DL}_i(A,B,C)$ be its lift-dual triple and let the associated Nahm sum be defined by the Nahm-sum construction. Lift-dual modularity conjecture. The Nahm sums associated with all the listed lift-dual triples $\mathcal{DL}_i(A,B,C)$ are modular. Four sets of rank-four Nahm sums have been confirmed in the paper, while modularity of the remaining listed lift-dual triples is left open.