{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:45VS3JNP7PBENJDJTSIDJUPG6I","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3ac095868ce70e523c731386eccfa8debb23d3c04302f50e38f989967ea9b03b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-02T17:17:32Z","title_canon_sha256":"38d8079f9671cf76fc512e8ea6ccb8828dc0f7d48b2337d8196874c41dbba231"},"schema_version":"1.0","source":{"id":"2608.01393","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01393","created_at":"2026-08-04T02:04:56Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01393v1","created_at":"2026-08-04T02:04:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01393","created_at":"2026-08-04T02:04:56Z"},{"alias_kind":"pith_short_12","alias_value":"45VS3JNP7PBE","created_at":"2026-08-04T02:04:56Z"},{"alias_kind":"pith_short_16","alias_value":"45VS3JNP7PBENJDJ","created_at":"2026-08-04T02:04:56Z"},{"alias_kind":"pith_short_8","alias_value":"45VS3JNP","created_at":"2026-08-04T02:04:56Z"}],"graph_snapshots":[{"event_id":"sha256:84ca86fe68fe059eb9d24f5ffeceb0a091eeb9113b35e463719cf3e360d760e8","target":"graph","created_at":"2026-08-04T02:04:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.01393/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a general formulation to address the problems of covering curves and polygonal chains with triangle, and fitting these curves into triangle. These problems can be formulated as special cases of Bellman's lost-in-a-forest problem (escaping triangular forest) and Moser's worm problem (covered by triangle). We model and reformulate the problem by keeping the curve stationary while allowing the triangle to translate and rotate. Subsequently, we derive the functional minimization formulation with support function constraints to solve. We also prove the equivalence and conv","authors_text":"Zhipeng Deng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-02T17:17:32Z","title":"Universal Triangle Covering Curve and Polygonal Chain: Escaping Forest and Fitting Worm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01393","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:227cbd7e7ae7b4fb9a3690febc4776df4288dc435f7ab29748be3b57c1a61d75","target":"record","created_at":"2026-08-04T02:04:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3ac095868ce70e523c731386eccfa8debb23d3c04302f50e38f989967ea9b03b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-02T17:17:32Z","title_canon_sha256":"38d8079f9671cf76fc512e8ea6ccb8828dc0f7d48b2337d8196874c41dbba231"},"schema_version":"1.0","source":{"id":"2608.01393","kind":"arxiv","version":1}},"canonical_sha256":"e76b2da5affbc246a4699c9034d1e6f2389a1dfe51f35e350586c21908c0f8cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e76b2da5affbc246a4699c9034d1e6f2389a1dfe51f35e350586c21908c0f8cf","first_computed_at":"2026-08-04T02:04:56.613840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:04:56.613840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NEcwf04SdvFCAtmvmkdhdCgR2pCA2vg+TbohXeXzDsbdMHw/fTU7iqlAZOkUF4WShBZzm4FyF7Vk5x51Ot4+DQ==","signature_status":"signed_v1","signed_at":"2026-08-04T02:04:56.615666Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.01393","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:227cbd7e7ae7b4fb9a3690febc4776df4288dc435f7ab29748be3b57c1a61d75","sha256:84ca86fe68fe059eb9d24f5ffeceb0a091eeb9113b35e463719cf3e360d760e8"],"state_sha256":"a347085da57467bae9bd5c387e8cb026c6369084177ef6963db20a4327c3f341"}