Bellman's Lost-in-a-Forest Problem for the Golden Gnomon
Statement
What is the shortest curve guaranteed to reach the boundary of the golden gnomon - the isosceles triangle with equal sides and apex angle - from an unknown starting position and heading? The optimum is a symmetric seven-piece path of segments, circular shoulders and tangents, of exactly determined transcendental length - the first proved exact optimum for an isosceles triangle with base angle below .
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Claude Fable 5, GPT-5.6 Sol, Claude Opus 5, with Alexander Temerev and Alessio DoriaThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
The models were used throughout: to search out the extremal curve, to draft the arguments, and to write the accompanying Lean 4 development. The paper states precisely which steps are machine-checked, and notes those checks hold regardless of how the statements were found.
Bellman's problem for general regions remains open
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