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Chordal SLE$_\kappa(\underline{\rho})$ is a natural variant of chordal SLEcurve. It is a family of random non-crossing curves on the upper half planefrom 0 to $\infty$, whose law is influenced by additional force points on$\mathbb R$. When there are force points away from the origin, the law ofSLE$_\kappa(\underline{\rho})$ is not reversible as the ordinary chordalSLE$_\kappa$. Zhan (2019) give an explicit description of the law of the timereversal of SLE$_\kappa(\underline{\rho})$ when all force points lies on thesame sides of the origin, and conjectured that a similar result holds ingeneral. In this paper we prove his conjecture. In particular, based on Zhan'sresult, using the techniques from the Imaginary Geometry developed by Millerand Sheffield (2013), we show that when $\kappa\in(0,8)$, the law of the timereversal of non-boundary filling $\mathrm{SLE}_\kappa(\underline{\rho})$process is absolutely continuous with respect to$\mathrm{SLE}_\kappa(\underline{\hat{\rho}})$ for some $\underline{\hat{\rho}}$determined by $\underline{\rho}$, with the Radon-Nikodym derivative being aproduct of conformal derivatives.

Time-reversal of multiple-force-point chordal $\mathrm{SLE}_\kappa(\underline{\rho})$