{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QYCAATZNCYVOIG3XUYSYGENV5Y","short_pith_number":"pith:QYCAATZN","schema_version":"1.0","canonical_sha256":"8604004f2d162ae41b77a6258311b5ee062dbad78c59baa2ff046777a86bd1dd","source":{"kind":"arxiv","id":"1508.01186","version":1},"attestation_state":"computed","paper":{"title":"Legendrian curve shortening flow in $\\mathbb{R}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gregory Drugan, Micah W. Warren, Weiyong He","submitted_at":"2015-08-05T19:21:58Z","abstract_excerpt":"Motivated by Legendrian curve shortening flows in $\\mathbb{R}^{3}$, we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and curvature conditions, a figure-eight curve will shrink to a point at the first singular time."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.01186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-05T19:21:58Z","cross_cats_sorted":[],"title_canon_sha256":"b51b6f9cea02431f1f55b7f6b4527d2c7e55c44f8c5cf9e043fc8f30677ef14f","abstract_canon_sha256":"b1a0bb0716a6734a52e116a0f2a44a7df906f124aee17b0baa4e5fe355e13867"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:43.896634Z","signature_b64":"RRLeFukeHl+kqSgd4QJeflA0jI0v6VTnv8jqzMV1mEp3X0GauQE4Em/YvlPpJcZ23xc9vySQOnxA8752unUZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8604004f2d162ae41b77a6258311b5ee062dbad78c59baa2ff046777a86bd1dd","last_reissued_at":"2026-05-18T01:35:43.896237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:43.896237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Legendrian curve shortening flow in $\\mathbb{R}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gregory Drugan, Micah W. Warren, Weiyong He","submitted_at":"2015-08-05T19:21:58Z","abstract_excerpt":"Motivated by Legendrian curve shortening flows in $\\mathbb{R}^{3}$, we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and curvature conditions, a figure-eight curve will shrink to a point at the first singular time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01186","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.01186","created_at":"2026-05-18T01:35:43.896296+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01186v1","created_at":"2026-05-18T01:35:43.896296+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01186","created_at":"2026-05-18T01:35:43.896296+00:00"},{"alias_kind":"pith_short_12","alias_value":"QYCAATZNCYVO","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"QYCAATZNCYVOIG3X","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"QYCAATZN","created_at":"2026-05-18T12:29:39.896362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y","json":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y.json","graph_json":"https://pith.science/api/pith-number/QYCAATZNCYVOIG3XUYSYGENV5Y/graph.json","events_json":"https://pith.science/api/pith-number/QYCAATZNCYVOIG3XUYSYGENV5Y/events.json","paper":"https://pith.science/paper/QYCAATZN"},"agent_actions":{"view_html":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y","download_json":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y.json","view_paper":"https://pith.science/paper/QYCAATZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01186&json=true","fetch_graph":"https://pith.science/api/pith-number/QYCAATZNCYVOIG3XUYSYGENV5Y/graph.json","fetch_events":"https://pith.science/api/pith-number/QYCAATZNCYVOIG3XUYSYGENV5Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/action/storage_attestation","attest_author":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/action/author_attestation","sign_citation":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/action/citation_signature","submit_replication":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/action/replication_record"}},"created_at":"2026-05-18T01:35:43.896296+00:00","updated_at":"2026-05-18T01:35:43.896296+00:00"}