{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DEJ4RAAIU4BDLFHTP6JDNU3GNA","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":"66490100c44b70b30c06101d47a848768ef6aa390a6da3c54aafc60547657956","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-21T04:05:09Z","title_canon_sha256":"74a624560bd85cd0f490d49adb48978fdf036de446772d2fcc6277afee1d355f"},"schema_version":"1.0","source":{"id":"1009.3994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3994","created_at":"2026-05-18T04:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3994v1","created_at":"2026-05-18T04:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3994","created_at":"2026-05-18T04:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"DEJ4RAAIU4BD","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DEJ4RAAIU4BDLFHT","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DEJ4RAAI","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:4813583e94e23487bca313dce8895da473771dc3d5a2a54bfbeffc943cde5b2c","target":"graph","created_at":"2026-05-18T04:40:34Z","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":"In this paper, we parametrize the space of isometric immersions of the hyperbolic plane into the hyperbolic 3-space in terms of null-causal curves in the space of oriented geodesics. Moreover, we characterize \"ideal cones\" (i.e., cones whose vertices are on the ideal boundary) by behavior of their mean curvature.","authors_text":"Atsufumi Honda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-21T04:05:09Z","title":"Isometric Immersions of the Hyperbolic Plane into the Hyperbolic Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3994","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":"sha256:4f50950b85c3aa88d437dd71e23d233cfefe8c9b12a605d147347367cb6e93f8","target":"record","created_at":"2026-05-18T04:40:34Z","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":"66490100c44b70b30c06101d47a848768ef6aa390a6da3c54aafc60547657956","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-21T04:05:09Z","title_canon_sha256":"74a624560bd85cd0f490d49adb48978fdf036de446772d2fcc6277afee1d355f"},"schema_version":"1.0","source":{"id":"1009.3994","kind":"arxiv","version":1}},"canonical_sha256":"1913c88008a7023594f37f9236d36668299f0f16d9c5dd484da31a1d83825bd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1913c88008a7023594f37f9236d36668299f0f16d9c5dd484da31a1d83825bd4","first_computed_at":"2026-05-18T04:40:34.752996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:34.752996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3CUBGRU7Yhto0l/5RpBudVqSn1SlzlsSIfKNQETdJbwO8I7bZ+Rd3T/AFmaizMXvwsNIpwqhA+VJjof3MOuCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:34.753636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f50950b85c3aa88d437dd71e23d233cfefe8c9b12a605d147347367cb6e93f8","sha256:4813583e94e23487bca313dce8895da473771dc3d5a2a54bfbeffc943cde5b2c"],"state_sha256":"040a7c7d8d3e8a9acaf4dd00e5a55d29fa0432edaae7d1bc040dd863cdbbc469"}