Stable $U_{d4e4}(d4f0d4f1_2)$-action conjecture for quantum annular spectra

Let $L$ be an annular link, let $Kh_{\mathbb{A}_\mathfrak{q}}(L)$ denote its quantum annular homology, and let ${\mathcal X}^r_{\mathbb{A}_\mathfrak{q}}(L)$ be the associated spectrum. The quantum group $U_\mathfrak{q}(\mathfrak{sl}_2)$ acts on $Kh_{\mathbb{A}_\mathfrak{q}}(L)$. Stable quantum-group action conjecture. This action can be lifted to an action on ${\mathcal X}^r_{\mathbb{A}_\mathfrak{q}}(L)$. The conjecture proposes a spectrum-level refinement of the quantum-group symmetry of quantum annular homology; the paper does not establish such a lift.