{"paper":{"title":"The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alessio Doria, Alexander Temerev","submitted_at":"2026-07-27T14:18:28Z","abstract_excerpt":"We solve Bellman's lost-in-a-forest problem for the golden gnomon $G$, the isosceles triangle with equal sides $1$ and apex angle $108^\\circ$: the shortest curve guaranteed to reach the boundary of $G$ from an unknown starting position and heading is a symmetric seven-piece path of segments, circular shoulders, and tangents, of exactly determined length $C=1.282676025459\\ldots$. To our knowledge, this is the first proved exact optimum for an isosceles triangle whose base angle is below $45^\\circ$. The curve's parameters come from one isolated quartic root, and $C$ is transcendental. Equivalent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24483","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24483/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}