The three-dimensional moving sofa problem with two perpendicular turns (AlphaEvolve problem 64)
The three-dimensional moving sofa problem with two perpendicular turns (AlphaEvolve problem 64). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
Define to be the largest volume of a connected bounded subset of that can continuously pass through a three-dimensional snake-shaped corridor with a unit square cross-section, consisting of two turns in the and planes that are far apart. What is ?
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Repository result category: world record — AlphaEvolve improved on the best known result recorded at the time. See Section 6.42 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.
Progress & source assessment
The repository page records no bounds for this problem.
- [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — The three-dimensional moving sofa problem with two perpendicular turns (AlphaEvolve problem 64) linkApache-2.0 (repository license); problem pages reproduced with attribution.
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
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Discussion
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