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The three-dimensional moving sofa problem with two perpendicular turns

AlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open.

問題
Problem 64 in the AlphaEvolve repository: The three-dimensional moving sofa problem with two perpendicular turns
貢献
AlphaEvolve (Google DeepMind) · LLM-guided evolutionary code search, with Georgiev, Gómez-Serrano, Tao and Wagner
検証
Construction can be checked directlyPreprint (arXiv, 2025)
経緯
Paper submitted 2025-11-03
出典
Problem page (AlphaEvolve repository)Paper (arXiv:2511.02864)
部分的
結果Improved bound · new construction

The problem

Define CC to be the largest volume of a connected bounded subset S3S_3 of R3\R^3 that can continuously pass through a three-dimensional snake-shaped corridor with a unit square cross-section, consisting of two turns in the x−yx-y and y−zy-z planes that are far apart. What is CC?

Statement quoted from problem 64 of the AlphaEvolve repository of problems (Google DeepMind, CC BY 4.0).

What AI did

AlphaEvolve found a construction that improved on the best bound known at the time; the problem itself remains open. Status in the repository: New result. See Section 6.42 in "Mathematical Exploration and Discovery at Scale" paper. Records may have moved since; the repository's notes below list the latest bounds it knows of.

How it was checked

The results are explicit constructions or programs; the repository's notebooks include the verification code used to score them.

Limitations

An improved bound is progress, not a solution: the exact answer to the problem is still unknown. The authors report that results were better when experts set up and guided the search.

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