Duality conjecture for modular Nahm sums

Let $(A,b,c,d)$ be parameters of a Nahm sum, and suppose that the associated symmetrizable matrix has symmetrizer $D$. Define

$$A^*=A^{-1},\qquad b^*=A^{-1}b,$$ $$c^*=\frac12 b^{\mathsf T}(AD)^{-1}b-\frac{\operatorname{tr}D}{24}-c,\qquad d^*=d.$$

Duality conjecture. If the Nahm sum associated with $(A,b,c,d)$ is modular, then the Nahm sum associated with $(A^*,b^*,c^*,d^*)$ is also modular. The conjecture proposes a general modularity-preserving operation exchanging $A$ with its inverse; the source presents it as an expectation and gives no resolution status.