Driving-function reconstruction for a chordal Loewner chain ($U_t=g_t(z)-2/{\partial }_t{g}_t(z)$)

The domains of a capacity-parametrized Loewner chain determine their hydrodynamically normalized mapping-out functions of compact H-hulls. At a surviving point, the Chordal Loewner equation gives $U_t=g_t(z)-2/{\partial }_t{g}_t(z)$. For a continuous driver and $t>0$, the left derivative uses only the hull past. High points $in$, $n\in \mathbb{N}$, survive up to any fixed finite time for sufficiently large $n$, making this a countable local reconstruction of the driver and its past filtration.