Algebra-action generation conjecture for stable torus-knot homology

Let $\mathcal{A}_{n,m}$ be algebras represented on the stable homology space $\mathcal{H}(T_{n,m})$, and let $e_1,\ldots,e_n$ denote the even polynomial generators and $\xi_1,\ldots,\xi_{m-1}$ the odd generators. Algebra-action generation conjecture. There exists a sequence of algebras $\mathcal{A}_{n,m}$ such that: (1) their action commutes with multiplication by polynomials in $e_1,\ldots,e_n$; (2) for every $k$ with $|k|<n$, the differential $d_k$ belongs to $\mathcal{A}_{n,m}$; (3) $\mathcal{H}(T_{n,m})$ is generated by its top level under the action of $\mathcal{A}_{n,m}$; and (4) the top level for the $(m,m+n)$ torus knot coincides with the zero level of the homology of the $(m,n)$ torus knot multiplied by the volume form $\xi_1\xi_2\cdots\xi_{m-1}$. This conjecture proposes an algebraic mechanism generating stable torus-knot homology and relating top and zero levels under the stated torus-knot transformation; the source does not give a resolution status.