{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5FP667N5PDI4VL6242IJSS6KZS","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":"84eaf0f40cffba7a13daee75cc1ef5fcc1d67cd61855212d6ca6fd29f3779b8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-14T03:48:31Z","title_canon_sha256":"38b1c070860d693f8aae105ec88e93faf11a593d4b856084842de54f978497dc"},"schema_version":"1.0","source":{"id":"0907.2284","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2284","created_at":"2026-05-18T04:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2284v3","created_at":"2026-05-18T04:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2284","created_at":"2026-05-18T04:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"5FP667N5PDI4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5FP667N5PDI4VL62","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5FP667N5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:33fedb3f9d2cb9a95b16a21af3ce563db19ea81c6a46bed21773a431f81cec5a","target":"graph","created_at":"2026-05-18T04:18:43Z","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 several topological properties of linear Weingarten surfaces of Bryant type, as wave fronts in hyperbolic 3-space. For example, we show the orientability of such surfaces, and also co-orientability when they are not flat. Moreover, we show an explicit formula of the non-holomorphic hyperbolic Gauss map via another hyperbolic Gauss map which is holomorphic. Using this, we show the orientability and co-orientability of CMC-1 faces (i.e., constant mean curvature one surfaces with admissible singular points) in de Sitter 3-space. (CMC-1 faces might not be wave fronts in general, but belon","authors_text":"Masaaki Umehara, Masatoshi Kokubu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-14T03:48:31Z","title":"Orientability of linear Weingarten surfaces, spacelike CMC-1 surfaces and maximal surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2284","kind":"arxiv","version":3},"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":"sha256:1a68ba123b3ec0492691dc73dea78ab93d50cad09cc0fe79102cf54cf4f48dad","target":"record","created_at":"2026-05-18T04:18:43Z","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":"84eaf0f40cffba7a13daee75cc1ef5fcc1d67cd61855212d6ca6fd29f3779b8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-14T03:48:31Z","title_canon_sha256":"38b1c070860d693f8aae105ec88e93faf11a593d4b856084842de54f978497dc"},"schema_version":"1.0","source":{"id":"0907.2284","kind":"arxiv","version":3}},"canonical_sha256":"e95fef7dbd78d1caafdae690994bcaccb507c7771c7f6e2b4d10a284dd5ab468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e95fef7dbd78d1caafdae690994bcaccb507c7771c7f6e2b4d10a284dd5ab468","first_computed_at":"2026-05-18T04:18:43.849459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:43.849459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yga955zEClY3WTk/0avfCME4Q0AweR4BDZGVwd2I7SJfmIYnblCZGvoewQ8lOFsx1rT4J5oYPS2Tw9P/6So5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:43.849878Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2284","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a68ba123b3ec0492691dc73dea78ab93d50cad09cc0fe79102cf54cf4f48dad","sha256:33fedb3f9d2cb9a95b16a21af3ce563db19ea81c6a46bed21773a431f81cec5a"],"state_sha256":"bc66e03ea246aff6b7a21342e2bb503913ebc4daf9e75bc53097aa700d9a9c82"}