The ADO limit formula for $\widehat Z$-invariants

Let $K$ be a knot, let $p$ be a positive integer, and let $\operatorname{ADO}_p(x;K)$ denote the Akutsu–Deguchi–Ohtsuki polynomial invariant associated with the quantum group $\mathcal U_q(\mathfrak{sl}_2)$ at the even $2p$-th root of unity. Let $\widehat Z(M_3,SU(2),q)$ denote the $q$-series invariant of the knot complement, and set $\zeta_p=e^{2\pi i/p}$. The ADO–$\widehat Z$ conjecture. For any knot $K$, the limit of the corresponding $\widehat Z$-invariant as $q\to\zeta_p$ is the ADO invariant:

$$\lim_{q\to\zeta_p}\widehat Z(S^3\setminus K,SU(2),q)=\operatorname{ADO}_p(x;K).$$

The supplied candidate contains only the opening sentence of the conjectural statement, so the exact normalization and any additional variables or summation over $\operatorname{Spin}^c$ structures cannot be recovered from the span; the relation is presented as evidence for knot complements, while general 3-manifolds are left for future work.