{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FN5DCDCUMCTYQQQELLTT63RH6J","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":"92a333094f44689b4f5f0ea73f83dd50e4864e678c80c1c15287e43e3557654e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T18:51:29Z","title_canon_sha256":"9f01e19e79b3c8cf29b59e8910c7a8fb3502b78183d6070999728533d8167c14"},"schema_version":"1.0","source":{"id":"1503.07489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07489","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07489v2","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07489","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"FN5DCDCUMCTY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FN5DCDCUMCTYQQQE","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FN5DCDCU","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:dba5bce20f710c7a2ebee7ccb50c339ca1e2348afade750c20651ead79afe394","target":"graph","created_at":"2026-05-18T01:35:26Z","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":"We prove the existence of rotational hypersurfaces in $\\mathbb{H}^n\\times \\mathbb{R}$ with $H_{r+1}=0$ and we classify them. Then we prove some uniqueness theorems for $r$-minimal hypersurfaces with a given (finite or asymptotic) boundary. In particular, we obtain a Schoen-type Theorem for two ended complete hypersurfaces.","authors_text":"Barbara Nelli, Maria Fernanda Elbert, Walcy Santos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T18:51:29Z","title":"Hypersurfaces with H_{r+1}=0 in H x R"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07489","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:c7a1b0f8c658319724ddd4dd56f0827244beae8a45685f06e9d3c400ab37619a","target":"record","created_at":"2026-05-18T01:35:26Z","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":"92a333094f44689b4f5f0ea73f83dd50e4864e678c80c1c15287e43e3557654e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T18:51:29Z","title_canon_sha256":"9f01e19e79b3c8cf29b59e8910c7a8fb3502b78183d6070999728533d8167c14"},"schema_version":"1.0","source":{"id":"1503.07489","kind":"arxiv","version":2}},"canonical_sha256":"2b7a310c5460a78842045ae73f6e27f260be8efe50908f54677135eeae140142","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b7a310c5460a78842045ae73f6e27f260be8efe50908f54677135eeae140142","first_computed_at":"2026-05-18T01:35:26.807980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:26.807980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HKfkwR7Qe7iY77cR529q8HAMX6cl124XoRergqTrZBjSBVtWjnWvdj9JUS9RGcq0PnOVaAakEujNQQKtMoFlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:26.808625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a1b0f8c658319724ddd4dd56f0827244beae8a45685f06e9d3c400ab37619a","sha256:dba5bce20f710c7a2ebee7ccb50c339ca1e2348afade750c20651ead79afe394"],"state_sha256":"043a486032cf5e37137671cd7cdcda7889547d4831e5f46b14b5dd903f7b1e71"}