{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6PVJSPWB7AEZBMYVAKAVCSJID6","short_pith_number":"pith:6PVJSPWB","canonical_record":{"source":{"id":"1012.4352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T15:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"73d91489a4311e8363978299990387b7838a8363625e2786a194e1642d90787a","abstract_canon_sha256":"45f4c86c63e5457b231ced6e19c1a7a4c4f896391e8d07a7b162817910b440ce"},"schema_version":"1.0"},"canonical_sha256":"f3ea993ec1f80990b31502815149281fa8e4411cd8f94dbef8d61fed6f11af49","source":{"kind":"arxiv","id":"1012.4352","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4352","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4352v2","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4352","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"pith_short_12","alias_value":"6PVJSPWB7AEZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6PVJSPWB7AEZBMYV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6PVJSPWB","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6PVJSPWB7AEZBMYVAKAVCSJID6","target":"record","payload":{"canonical_record":{"source":{"id":"1012.4352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T15:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"73d91489a4311e8363978299990387b7838a8363625e2786a194e1642d90787a","abstract_canon_sha256":"45f4c86c63e5457b231ced6e19c1a7a4c4f896391e8d07a7b162817910b440ce"},"schema_version":"1.0"},"canonical_sha256":"f3ea993ec1f80990b31502815149281fa8e4411cd8f94dbef8d61fed6f11af49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:26.418470Z","signature_b64":"sNMLiXJkz/HhzV0zeYdB4lVA6vc909bxOk+xNDIoASeZ4rBLR+yIPksdVAmnsnyz/NhYl/hHRCXsTwvkJzJDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3ea993ec1f80990b31502815149281fa8e4411cd8f94dbef8d61fed6f11af49","last_reissued_at":"2026-05-18T04:27:26.417945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:26.417945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.4352","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JEyo1xXwqM4NqLxxJxwnJrFpnSXvkVMYOqxtnGlTvQoaBr5FRpWLWSQKWP/TZcSSC12e7WzEcWJUfWVVZTtRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:27:13.591065Z"},"content_sha256":"dde78a37c90546593a943bb87c455112a5977c515196d85af2fce336d62548e0","schema_version":"1.0","event_id":"sha256:dde78a37c90546593a943bb87c455112a5977c515196d85af2fce336d62548e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6PVJSPWB7AEZBMYVAKAVCSJID6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rotational Linear Weingarten Surfaces into the Euclidean Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abd\\^enago Barros, Juscelino Silva, Paulo Sousa","submitted_at":"2010-12-20T15:13:46Z","abstract_excerpt":"The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and Gaussian curvatures, respectively, whereas a; b and c are real constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4352","kind":"arxiv","version":2},"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":"2026-05-18T04:27:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSdUxEjRX4cshra0VVQHOJGBYthC/9InQk1OgaET38pgt/l2oCGd4HOfCPiVDNlXM/8Z+MLa3Usq20pjU7pxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:27:13.591432Z"},"content_sha256":"94d8f6c18a576f526d9bd6b1a3fed12dc13c7ff04ab1d260c32ccb0c39bb3c86","schema_version":"1.0","event_id":"sha256:94d8f6c18a576f526d9bd6b1a3fed12dc13c7ff04ab1d260c32ccb0c39bb3c86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PVJSPWB7AEZBMYVAKAVCSJID6/bundle.json","state_url":"https://pith.science/pith/6PVJSPWB7AEZBMYVAKAVCSJID6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PVJSPWB7AEZBMYVAKAVCSJID6/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":"2026-05-28T00:27:13Z","links":{"resolver":"https://pith.science/pith/6PVJSPWB7AEZBMYVAKAVCSJID6","bundle":"https://pith.science/pith/6PVJSPWB7AEZBMYVAKAVCSJID6/bundle.json","state":"https://pith.science/pith/6PVJSPWB7AEZBMYVAKAVCSJID6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PVJSPWB7AEZBMYVAKAVCSJID6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6PVJSPWB7AEZBMYVAKAVCSJID6","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":"45f4c86c63e5457b231ced6e19c1a7a4c4f896391e8d07a7b162817910b440ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T15:13:46Z","title_canon_sha256":"73d91489a4311e8363978299990387b7838a8363625e2786a194e1642d90787a"},"schema_version":"1.0","source":{"id":"1012.4352","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4352","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4352v2","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4352","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"pith_short_12","alias_value":"6PVJSPWB7AEZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6PVJSPWB7AEZBMYV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6PVJSPWB","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:94d8f6c18a576f526d9bd6b1a3fed12dc13c7ff04ab1d260c32ccb0c39bb3c86","target":"graph","created_at":"2026-05-18T04:27:26Z","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":"The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and Gaussian curvatures, respectively, whereas a; b and c are real constants.","authors_text":"Abd\\^enago Barros, Juscelino Silva, Paulo Sousa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T15:13:46Z","title":"Rotational Linear Weingarten Surfaces into the Euclidean Sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4352","kind":"arxiv","version":2},"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:dde78a37c90546593a943bb87c455112a5977c515196d85af2fce336d62548e0","target":"record","created_at":"2026-05-18T04:27:26Z","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":"45f4c86c63e5457b231ced6e19c1a7a4c4f896391e8d07a7b162817910b440ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T15:13:46Z","title_canon_sha256":"73d91489a4311e8363978299990387b7838a8363625e2786a194e1642d90787a"},"schema_version":"1.0","source":{"id":"1012.4352","kind":"arxiv","version":2}},"canonical_sha256":"f3ea993ec1f80990b31502815149281fa8e4411cd8f94dbef8d61fed6f11af49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3ea993ec1f80990b31502815149281fa8e4411cd8f94dbef8d61fed6f11af49","first_computed_at":"2026-05-18T04:27:26.417945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:26.417945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sNMLiXJkz/HhzV0zeYdB4lVA6vc909bxOk+xNDIoASeZ4rBLR+yIPksdVAmnsnyz/NhYl/hHRCXsTwvkJzJDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:26.418470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4352","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dde78a37c90546593a943bb87c455112a5977c515196d85af2fce336d62548e0","sha256:94d8f6c18a576f526d9bd6b1a3fed12dc13c7ff04ab1d260c32ccb0c39bb3c86"],"state_sha256":"3430ec2d954d755ca0c2bfa6cce2090cd14cc5b9e4ff9f76ee490f3951a0a474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQBuZt6N5BIOpNBHqeLsqW73HBh73DImwCjshlRJgtdiHg4p7D5ZeMC5ktjcEyXVXwcqhd3vL0uljm27Q/NYBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:27:13.593552Z","bundle_sha256":"ea328b0625891e9cd08faa81198abc0494c24cf02347d3a379555ccc1790eee9"}}