{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZN7TM7UAKN7W337OF3RZLFVIJM","short_pith_number":"pith:ZN7TM7UA","schema_version":"1.0","canonical_sha256":"cb7f367e80537f6defee2ee39596a84b220b6fcf1ffc48ba7f80efdd58c97653","source":{"kind":"arxiv","id":"1603.07793","version":1},"attestation_state":"computed","paper":{"title":"Closed strong spacelike curves, Fenchel theorem and Plateau problem in the 3-dimensional Minkowski space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nan Ye, Xiang Ma","submitted_at":"2016-03-25T01:03:12Z","abstract_excerpt":"We generalize the Fenchel theorem for strong spacelike closed curves of index $1$ in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to $2\\pi$. Here strong spacelike means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve $\\gamma$ under consideration. The assumption of index 1 is equivalent to saying that $\\gamma$ winds around some timelike axis with winding number 1. We prove this reversed Fenchel-type inequality by constructing a ruled spacelike surface with the given curve as boundary and apply"},"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":"1603.07793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-25T01:03:12Z","cross_cats_sorted":[],"title_canon_sha256":"c24b49000144ee42dc04b880305406990b2a4873cd8968dbf26ea37a77b37758","abstract_canon_sha256":"56ec35061cabaa1731446302325a99f2aeab5fd7485df8d6a77e91e8df4e3583"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:17.823587Z","signature_b64":"MuamgjyTOB4jFEjSpnsJspPRdFHLOSevThXtJlSdQp/4Hkm75QwLdBIX30aOtRq3uv1vzG4gUDjS2SpH9D4tBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb7f367e80537f6defee2ee39596a84b220b6fcf1ffc48ba7f80efdd58c97653","last_reissued_at":"2026-05-18T01:18:17.822940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:17.822940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed strong spacelike curves, Fenchel theorem and Plateau problem in the 3-dimensional Minkowski space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nan Ye, Xiang Ma","submitted_at":"2016-03-25T01:03:12Z","abstract_excerpt":"We generalize the Fenchel theorem for strong spacelike closed curves of index $1$ in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to $2\\pi$. Here strong spacelike means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve $\\gamma$ under consideration. The assumption of index 1 is equivalent to saying that $\\gamma$ winds around some timelike axis with winding number 1. We prove this reversed Fenchel-type inequality by constructing a ruled spacelike surface with the given curve as boundary and apply"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07793","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":"1603.07793","created_at":"2026-05-18T01:18:17.823035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.07793v1","created_at":"2026-05-18T01:18:17.823035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07793","created_at":"2026-05-18T01:18:17.823035+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZN7TM7UAKN7W","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZN7TM7UAKN7W337O","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZN7TM7UA","created_at":"2026-05-18T12:30:55.937587+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/ZN7TM7UAKN7W337OF3RZLFVIJM","json":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM.json","graph_json":"https://pith.science/api/pith-number/ZN7TM7UAKN7W337OF3RZLFVIJM/graph.json","events_json":"https://pith.science/api/pith-number/ZN7TM7UAKN7W337OF3RZLFVIJM/events.json","paper":"https://pith.science/paper/ZN7TM7UA"},"agent_actions":{"view_html":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM","download_json":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM.json","view_paper":"https://pith.science/paper/ZN7TM7UA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.07793&json=true","fetch_graph":"https://pith.science/api/pith-number/ZN7TM7UAKN7W337OF3RZLFVIJM/graph.json","fetch_events":"https://pith.science/api/pith-number/ZN7TM7UAKN7W337OF3RZLFVIJM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM/action/storage_attestation","attest_author":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM/action/author_attestation","sign_citation":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM/action/citation_signature","submit_replication":"https://pith.science/pith/ZN7TM7UAKN7W337OF3RZLFVIJM/action/replication_record"}},"created_at":"2026-05-18T01:18:17.823035+00:00","updated_at":"2026-05-18T01:18:17.823035+00:00"}