Shi–Wang's triple Nahm sum identity

Let $t$ be a formal variable. For $n\geq 0$, write $(t^4;t^4)_n=\prod_{r=1}^{n}(1-t^{4r})$, and use $(x,y;Q)_\infty=(x;Q)_\infty(y;Q)_\infty$ for products of $q$-Pochhammer symbols. Then

Shi–Wang's conjecture.

$$\sum_{a,b,d\geq 0}\frac{t^{4a^2+4ab+3b^2-2bd+d^2+4a+2b}}{(t^4;t^4)_a(t^4;t^4)_b(t^4;t^4)_d}=\frac{(t^6;t^6)_\infty(t^8;t^8)_\infty(t^2,t^{10};t^{12})_\infty}{(t^4;t^4)_\infty^2(t,t^{11};t^{12})_\infty(t^5,t^7;t^{12})_\infty}.$$

The paper introduces this identity as the conjecture stated in Shi and Wang and discusses its connection with one of the paper's proved identities. The supplied text does not state that the identity itself has been resolved.