#### Kallus, Y., Komik, D.

The moving sofa problem, posed by L. Moser in 1966, asks for the planar shape of maximal area that can move around a right-angled corner in a hallway of unit width. It is known that a maximal area shape exists, and that its area is at least 2.2195... -the area of an explicit construction found by Gerver in 1992-and at most 2 root 2 approximate to 2.82, with the lower bound being conjectured as the true value. We prove a new and improved upper bound of 2.37. The method involves a computer-assisted proof scheme that can be used to rigorously derive further improved upper bounds that converge to the correct value.