Conjectural presentation of the first-order calculus for the Kronecker foliation spectral triple

Let $\cA=C^\infty(\mathbb{T}^2)\rtimes\mathbb{R}$, with generators $u_1,u_2$ for the torus part and $v_t$ for the crossed-product action, and let $D$ be the Dirac-type operator defining the spectral triple. Let $\Omega_D^1(\cA)$ denote its first-order differential bimodule. First-order-calculus conjecture. The bimodule $\Omega_D^1(\cA)$ is generated by $du_1$ and $du_2$, subject precisely to the relations

$$v_tdu_1=e^{iat}du_1v_t,\qquad v_tdu_2=e^{ibt}du_2v_t.$$

This gives an explicit proposed description of the first-order calculus after the paper explains that no further relations of the relevant type were derived. Its status is not resolved in the supplied text.