For Heaven's sake. Sofas are 3d objects and hallways are 3d spaces. The default sofa is also much closer to a truncated box shape than the curved 'Gerver sofa' chosen for the original problem.
Yay for finally coming up with a proof on an outstanding problem, but it also seems like a pointlessly abstracted and arbitrarily defined one. I was disappointed, because back in my youth I worked as a mover for a couple of years and found the challenges of moving large objects through tight spaces without damaging anything quite enjoyable.
Incidentally, if any mathematicians are looking for a hard problem of this type, mattresses are exponentially harder to move around than sofas.
