{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:COA5C5A3HFB4SBPMMYLIR5XK6U","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":"4559b4e9d0431e71d60687ee4951633301f1d884a67038035b2a1555942b7174","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-26T22:00:41Z","title_canon_sha256":"58a5f226c6c2a7d50956207ed7299318683f4010132d34f227ede16b02c0feeb"},"schema_version":"1.0","source":{"id":"1102.5455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5455","created_at":"2026-05-18T04:27:46Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5455v1","created_at":"2026-05-18T04:27:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5455","created_at":"2026-05-18T04:27:46Z"},{"alias_kind":"pith_short_12","alias_value":"COA5C5A3HFB4","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"COA5C5A3HFB4SBPM","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"COA5C5A3","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:8289c261008935737af98ee0c9754c1134659caa1a2276ce5f5868b658b692f3","target":"graph","created_at":"2026-05-18T04:27:46Z","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 prove rigidity of oriented isometric immersions of complete surfaces in the homo- geneous 3-manifolds E(k; {\\tau}) (different from the space forms) having the same positive extrinsic curvature.","authors_text":"Harold Rosenberg, Renato Tribuzy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-26T22:00:41Z","title":"Rigidity of Convex Surfaces in Homogeneous Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5455","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:c4e511f8f3f9c72856cbaa96c6c1076482ecd91e1c31b3dee6a0ea8286f7d7b6","target":"record","created_at":"2026-05-18T04:27:46Z","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":"4559b4e9d0431e71d60687ee4951633301f1d884a67038035b2a1555942b7174","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-26T22:00:41Z","title_canon_sha256":"58a5f226c6c2a7d50956207ed7299318683f4010132d34f227ede16b02c0feeb"},"schema_version":"1.0","source":{"id":"1102.5455","kind":"arxiv","version":1}},"canonical_sha256":"1381d1741b3943c905ec661688f6eaf52fd76b8a403c3a0dba6f2373236bb276","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1381d1741b3943c905ec661688f6eaf52fd76b8a403c3a0dba6f2373236bb276","first_computed_at":"2026-05-18T04:27:46.877735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:46.877735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dq1V3xRySKz+8NWXh7R3yp5cBM/JUD/OHyNX3nopXiQJvBnCg3D1G1oihlWbX5JEsQo5Rj5guWB8YahDTdPDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:46.878444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4e511f8f3f9c72856cbaa96c6c1076482ecd91e1c31b3dee6a0ea8286f7d7b6","sha256:8289c261008935737af98ee0c9754c1134659caa1a2276ce5f5868b658b692f3"],"state_sha256":"fbf93c24572e9e8266837aeb72d3354184cfeb1b6ca44abdf053f5078aa10502"}