{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CO2K6NTVHALW7MDKJQ44YNNQQN","short_pith_number":"pith:CO2K6NTV","canonical_record":{"source":{"id":"1603.01311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T22:59:07Z","cross_cats_sorted":[],"title_canon_sha256":"188234aba148b87b5fabd8867bdf35aae296acd6514eb486665b7dd285ea3f2a","abstract_canon_sha256":"639183c89240cbed05d9d6c268ce39a465eafa46df56038c05412a3e2cacb7ce"},"schema_version":"1.0"},"canonical_sha256":"13b4af367538176fb06a4c39cc35b0836206a9a6d15bd9b81b4c52dcd74ea50b","source":{"kind":"arxiv","id":"1603.01311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01311","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01311v1","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01311","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"pith_short_12","alias_value":"CO2K6NTVHALW","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CO2K6NTVHALW7MDK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CO2K6NTV","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CO2K6NTVHALW7MDKJQ44YNNQQN","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T22:59:07Z","cross_cats_sorted":[],"title_canon_sha256":"188234aba148b87b5fabd8867bdf35aae296acd6514eb486665b7dd285ea3f2a","abstract_canon_sha256":"639183c89240cbed05d9d6c268ce39a465eafa46df56038c05412a3e2cacb7ce"},"schema_version":"1.0"},"canonical_sha256":"13b4af367538176fb06a4c39cc35b0836206a9a6d15bd9b81b4c52dcd74ea50b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:38.001245Z","signature_b64":"AX/uvcb5kXr1JN5kvjAxZT5pqv7qRfx+6nj3unq9EyqcYStVFZWsUK4t+REyxKp9j4U5yen3CfnciDAPiubuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13b4af367538176fb06a4c39cc35b0836206a9a6d15bd9b81b4c52dcd74ea50b","last_reissued_at":"2026-05-18T01:19:38.000438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:38.000438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01311","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cHgp5VW6j1rdit0rbwGuEnZVrxkMXUEq+skmd3IFbogwc45CTn77OfcLmzDinfA3tTwz2g6gaZET3lnHMFFNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:23:50.922069Z"},"content_sha256":"36f3a08a313527b7dc0bdab3ebceb29f0a69685d3266323d956a07998ca2bcf9","schema_version":"1.0","event_id":"sha256:36f3a08a313527b7dc0bdab3ebceb29f0a69685d3266323d956a07998ca2bcf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CO2K6NTVHALW7MDKJQ44YNNQQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Donghao Wang, Nan Ye, Xiang Ma","submitted_at":"2016-03-03T22:59:07Z","abstract_excerpt":"We generalize the Fenchel theorem to strong spacelike (which means that the tangent vector and the curvature vector span a spacelike 2-plane at each point) closed curves with index 1 in the 3-dimensional Lorentz space, showing that the total curvatures must be less than or equal to $2\\pi$. A similar generalization of the Fary-Milnor theorem is also obtained. We establish the Crofton formula on the de Sitter 2-sphere which implies the above results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01311","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HaiL2Dva6mOPqHe7hcWPmYBpFq3WU+kWS6MlZKzgBD5EEJ2fNQLC4Q0iKJ5LoD0C2DEKyM5dujSainYOaElvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:23:50.922638Z"},"content_sha256":"1c1808d9422ac10bc2867cccf648d957962252eaf7300ca3c7bf03ac8b2dbbfb","schema_version":"1.0","event_id":"sha256:1c1808d9422ac10bc2867cccf648d957962252eaf7300ca3c7bf03ac8b2dbbfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CO2K6NTVHALW7MDKJQ44YNNQQN/bundle.json","state_url":"https://pith.science/pith/CO2K6NTVHALW7MDKJQ44YNNQQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CO2K6NTVHALW7MDKJQ44YNNQQN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T17:23:50Z","links":{"resolver":"https://pith.science/pith/CO2K6NTVHALW7MDKJQ44YNNQQN","bundle":"https://pith.science/pith/CO2K6NTVHALW7MDKJQ44YNNQQN/bundle.json","state":"https://pith.science/pith/CO2K6NTVHALW7MDKJQ44YNNQQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CO2K6NTVHALW7MDKJQ44YNNQQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CO2K6NTVHALW7MDKJQ44YNNQQN","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":"639183c89240cbed05d9d6c268ce39a465eafa46df56038c05412a3e2cacb7ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T22:59:07Z","title_canon_sha256":"188234aba148b87b5fabd8867bdf35aae296acd6514eb486665b7dd285ea3f2a"},"schema_version":"1.0","source":{"id":"1603.01311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01311","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01311v1","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01311","created_at":"2026-05-18T01:19:38Z"},{"alias_kind":"pith_short_12","alias_value":"CO2K6NTVHALW","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CO2K6NTVHALW7MDK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CO2K6NTV","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:1c1808d9422ac10bc2867cccf648d957962252eaf7300ca3c7bf03ac8b2dbbfb","target":"graph","created_at":"2026-05-18T01:19:38Z","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"},"paper":{"abstract_excerpt":"We generalize the Fenchel theorem to strong spacelike (which means that the tangent vector and the curvature vector span a spacelike 2-plane at each point) closed curves with index 1 in the 3-dimensional Lorentz space, showing that the total curvatures must be less than or equal to $2\\pi$. A similar generalization of the Fary-Milnor theorem is also obtained. We establish the Crofton formula on the de Sitter 2-sphere which implies the above results.","authors_text":"Donghao Wang, Nan Ye, Xiang Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T22:59:07Z","title":"The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01311","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":"sha256:36f3a08a313527b7dc0bdab3ebceb29f0a69685d3266323d956a07998ca2bcf9","target":"record","created_at":"2026-05-18T01:19:38Z","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":"639183c89240cbed05d9d6c268ce39a465eafa46df56038c05412a3e2cacb7ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T22:59:07Z","title_canon_sha256":"188234aba148b87b5fabd8867bdf35aae296acd6514eb486665b7dd285ea3f2a"},"schema_version":"1.0","source":{"id":"1603.01311","kind":"arxiv","version":1}},"canonical_sha256":"13b4af367538176fb06a4c39cc35b0836206a9a6d15bd9b81b4c52dcd74ea50b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13b4af367538176fb06a4c39cc35b0836206a9a6d15bd9b81b4c52dcd74ea50b","first_computed_at":"2026-05-18T01:19:38.000438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:38.000438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AX/uvcb5kXr1JN5kvjAxZT5pqv7qRfx+6nj3unq9EyqcYStVFZWsUK4t+REyxKp9j4U5yen3CfnciDAPiubuCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:38.001245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36f3a08a313527b7dc0bdab3ebceb29f0a69685d3266323d956a07998ca2bcf9","sha256:1c1808d9422ac10bc2867cccf648d957962252eaf7300ca3c7bf03ac8b2dbbfb"],"state_sha256":"e155c2144f5c545a7e1a16c39b0e1dd8b40ca6f011a4cf1b5c252c56f6dd9ad8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8xUfMxiJ65nkr9PSYHE2zA3TI4xOqRRuvGF+ofs7CHykUNICVaYjeXel7CzxUcbyi0lZqbUiYpqTMaX/8YdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:23:50.925244Z","bundle_sha256":"13ec926272e4bf1c479ca02260db7a7f6731bc513216c1d1d5ded2c8dacacbca"}}