What was already known
Romik constructed the candidate sofa and computed M, but left global optimality open; Georgiev, Gómez-Serrano, Tao and Wagner still listed the ambidextrous problem as open in 2025. The earlier formal-conjectures entry stated the conjecture without a proof.
AI involvement
The-Anh Vu-Le chose the problem and publication scope. The metadata says ChatGPT Pro 6 found the proof and drafted Lean; Claude Opus 5.5 made it compile and simplified it, while Codex later wrote and revised the explanatory manuscript.
The-Anh Vu-Le chose the problem and scope; the metadata says ChatGPT Pro 6 discovered the proof and drafted Lean, Claude Opus 5.5 made it compile and simplified it, and Codex wrote the paper.
Importance
Resolves the ambidextrous moving-sofa optimization and uniquely identifies every maximizing shape within the exact motion model.
Limitations
The theorem concerns compact connected sets and continuous proper rigid motions starting in the same orientation. Its proof imports a completed Lean formalization of Baek’s known ordinary moving-sofa theorem. The source reports agent review and kernel checks, with no human mathematical review.
Technical verification
The source reports nine completed lean challenge statements checked against solution, including optimality and uniqueness; standard-axiom audit and included proof of the needed ordinary-sofa theorem. This applies to the selected claim and is not an independent reproduction by AIProofWatch.
Formal checking
The repository reports nine completed Lean statements, axiom audit and Comparator checking of Challenge definitions and Solution proofs. Its included ordinary-sofa formalization proves the Baek result used by two steps.
- Checker
- Lean 4 kernel and documented Comparator or independent-kernel replay run by repository authors
- Scope
- Every compact connected planar set that can be moved continuously through both a right-turning and left-turning unit-width hallway from the same starting orientation has area at most M=1+4Y²+arctan(Y), where Y>0 solves 4Y³+3Y=1. Equality holds exactly for rotated and translated copies of Romik’s sofa, and the sofa attains M.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The author explicitly states no person checked the proof or statements. Agent reviews and an AI-written paper do not establish human understanding; Few is supported by that reported gap.
Correction and publication history
Claim-level primary-source review of exact theorem, prior baseline, AI contribution and documented checking scope.
Read this published revision