# Improved upper bounds in the moving sofa problem

## TL;DR

This paper presents a new, tighter upper bound of 2.37 for the moving sofa problem's maximal shape area using a computer-assisted proof scheme, advancing understanding of this longstanding geometric challenge.

## Contribution

The authors develop a computer-assisted method to derive improved upper bounds for the moving sofa problem, which can be iteratively refined to approach the true maximum area.

## Key findings

- Established an upper bound of 2.37 for the problem
- Introduced a computer-assisted proof scheme for bounds
- Method can be extended for further improvements

## Abstract

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 $2\sqrt{2}=2.82...$, 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.