Optimality, uniqueness and stability of Gerver’s moving sofa
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Among compact connected planar shapes movable around a right-angle unit corridor, is Gerver’s sofa the unique maximum-area shape up to rigid motion? A stability question asks how close a near-maximizer must be to Gerver’s shape in the specified Hausdorff-distance model.
Why it matters and what counts as progress
Why it matters: Uniqueness and stability refine an area optimum by classifying exact and near-extremal sofa shapes.
What counts as progress: Classify all maximizers and prove an optimal C√ε closeness bound for area deficit ε, with the permitted rigid motions stated precisely.
How the problem developed
- 1966 · Problem formulation [1]
Leo Moser Posed the question of the largest area shape that can move through a unit-width right-angled hallway.
- 1992 · Candidate [2]
Joseph Gerver Constructed the 18-piece sofa of area about 2.2195 and conjectured it was optimal.
- 29 Nov 2024 · Optimality proof [3]
Jineon Baek Posted a preprint proving Gerver’s construction attains the maximum area for the ordinary one-corner moving sofa problem.
The-Anh Vu-Le; ChatGPT Pro 6 and Claude Opus 5.5 The project reports uniqueness up to rigid motion and sharp square-root stability for near-maximal sofas, alongside a Lean formalization of the optimality result.
AI contribution
Vu-Le reports: uniqueness and stability of Gerver’s moving sofa
The-Anh Vu-Le’s project reports that Gerver’s sofa is the unique area-maximizing moving sofa up to rigid motion, and that sofas with area deficit ε are within C√ε after translation in its Hausdorff-distance model, with exponent 1/2 optimal.
Sources
Website timeline
Publication dates and editorial changes.
Vu-Le reports: uniqueness and stability of Gerver’s moving sofa