  The records of a clinical encounter can be extensive and complex, thus
placing a premium on tools that can extract and summarize relevant information.
This paper introduces the task of generating discharge summaries for a clinical
encounter. Summaries in this setting need to be faithful, traceable, and scale
to multiple long documents, motivating the use of extract-then-abstract
summarization cascades. We introduce two new measures, faithfulness and
hallucination rate for evaluation in this task, which complement existing
measures for fluency and informativeness. Results across seven medical sections
and five models show that a summarization architecture that supports
traceability yields promising results, and that a sentence-rewriting approach
performs consistently on the measure used for faithfulness
(faithfulness-adjusted $F_3$) over a diverse range of generated sections.
