{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DHCZMGMPCVVAWU3M6GDDULUGH4","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":"50a9227fe5a295011dbd21d3b854cba45372b89932037b1583aabb742220f591","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T18:03:43Z","title_canon_sha256":"2cb12d5bb7f46b7046271ef4b7a15e7c026bf01d92cdeeec527ea8fcc363b4c5"},"schema_version":"1.0","source":{"id":"1510.08399","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08399","created_at":"2026-05-18T01:28:36Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08399v1","created_at":"2026-05-18T01:28:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08399","created_at":"2026-05-18T01:28:36Z"},{"alias_kind":"pith_short_12","alias_value":"DHCZMGMPCVVA","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DHCZMGMPCVVAWU3M","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DHCZMGMP","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:42a49cb3694a9862daadede135c67d1077d8927480c6e0c4608f27607796eb0d","target":"graph","created_at":"2026-05-18T01:28:36Z","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 work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere $\\mathbb{S}^4_s(1)$ with index s, $s=1, 2$, and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere $\\mathbb{S}^{m-1}_s(1)\\subset\\mathbb{E}^m_s$ with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space $\\mathbb{S}^4_1(1)\\subset\\mathbb{E}^5_1$ with 1-type p","authors_text":"Burcu Bekta\\c{s}, Elif \\\"Ozkara Canfes, U\\u{g}ur Dursun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T18:03:43Z","title":"Pseudo-spherical submanifolds with 1-type pseudo-spherical Gauss map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08399","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":"sha256:87d7f6a403b884e15c4b74179320004324c8162e49cbabbce296df57eac4c3b9","target":"record","created_at":"2026-05-18T01:28:36Z","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":"50a9227fe5a295011dbd21d3b854cba45372b89932037b1583aabb742220f591","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T18:03:43Z","title_canon_sha256":"2cb12d5bb7f46b7046271ef4b7a15e7c026bf01d92cdeeec527ea8fcc363b4c5"},"schema_version":"1.0","source":{"id":"1510.08399","kind":"arxiv","version":1}},"canonical_sha256":"19c596198f156a0b536cf1863a2e863f1ec0ae124f835b349025fb7c560fd14b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19c596198f156a0b536cf1863a2e863f1ec0ae124f835b349025fb7c560fd14b","first_computed_at":"2026-05-18T01:28:36.109012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:36.109012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lIQuOHgP36U4gmcDKsWIB1wHFZ77D+gZPIZ3ljf1L7eGSVDrA1ey+SpfZVf6BLQMybdsR29eevKZ9rOsLbk8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:36.109676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08399","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87d7f6a403b884e15c4b74179320004324c8162e49cbabbce296df57eac4c3b9","sha256:42a49cb3694a9862daadede135c67d1077d8927480c6e0c4608f27607796eb0d"],"state_sha256":"56b209eb9a1e6e7064d63aae80c3ff419cc5b6b2680802a33af5edded5c192f3"}