Phase-transition conjecture for SLE with a boundary force point

For each $\underline{\kappa}\in(0,4)$, let $\rho_c=\rho_c(\underline{\kappa})$ lie in $(-2-\underline{\kappa}/2,-2)\cap[\underline{\kappa}/2-4,-2)$, and let $\eta$ be an SLE$_{\underline{\kappa}}(\rho)$ curve from $0$ to $\infty$ in $\mathbb{H}$ with its force point always to the right of the tip. SLE boundary-force-point phase-transition conjecture. There exists such a $\rho_c$ for which, for $\rho\in(\rho_c,-2)$, the range of $\eta$ is almost surely conformally removable and the adjacency graph of $\mathbb{H}\setminus\eta$ is connected; while for $\rho\in(-2-\underline{\kappa}/2,\rho_c)\cap[\underline{\kappa}/2-4,\rho_c)$, the range is conformally non-removable, the graph is disconnected, and the range contains a topological Sierpiński carpet. This conjectures a parameter phase transition simultaneously governing conformal removability, bubble connectivity, and carpet containment; the source notes that these properties are not established throughout the indicated regimes.