Absolute continuity of near-critical 3-Potts and 4-Potts FK scaling limits

Consider FK percolation for the 3-state and 4-state Potts models, with inverse temperatures $\beta^{q=3}$ and $\beta^{q=4}$ satisfying

$$\beta^{q=3}=\beta_c^{q=3}+\frac{\lambda}{n^{6/5}},\qquad \beta^{q=4}=\beta_c^{q=4}+\frac{\lambda}{n^{3/2}}.$$

These shifts correspond to the expected correlation exponents $\nu=5/6$ for $q=3$ and $\nu=2/3$ for $q=4$. Potts absolute-continuity conjecture. FK percolation for 3-Potts and 4-Potts has near-critical scaling limits under these temperature shifts, and, under for example the quad topology $(\mathcal{H},d_{\mathcal{H}})$, these near-critical scaling limits are absolutely continuous with respect to the critical scaling limits. The critical scaling limits are not known to be unique, so the conjecture includes a statement about absolute continuity relative to whichever critical limits exist.