{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OE4KZOWIR7VWVJE372L25GN3QZ","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":"e7471f45371c539453c01e3492e97894c8d158fff153d0ba1b90c4f3e1360341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-13T02:42:06Z","title_canon_sha256":"9dcab48382ebdafe6ed731e3139492f6814a0e5f0fd7ab8ce090a4656140a965"},"schema_version":"1.0","source":{"id":"1201.2732","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2732","created_at":"2026-05-18T04:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2732v1","created_at":"2026-05-18T04:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2732","created_at":"2026-05-18T04:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"OE4KZOWIR7VW","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OE4KZOWIR7VWVJE3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OE4KZOWI","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:8cd6681441290911e2d650e2b051b2402b79a414f5dc44f2013c576cc4c670f5","target":"graph","created_at":"2026-05-18T04:04:43Z","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":"Let $\\Sigma$ be a $k$-dimensional complete proper minimal submanifold in the Poincar\\'{e} ball model $B^n$ of hyperbolic geometry. If we consider $\\Sigma$ as a subset of the unit ball $B^n$ in Euclidean space, we can measure the Euclidean volumes of the given minimal submanifold $\\Sigma$ and the ideal boundary $\\partial_\\infty \\Sigma$, say $\\rvol(\\Sigma)$ and $\\rvol(\\partial_\\infty \\Sigma)$, respectively. Using this concept, we prove an optimal linear isoperimetric inequality. We also prove that if $\\rvol(\\partial_\\infty \\Sigma) \\geq \\rvol(\\mathbb{S}^{k-1})$, then $\\Sigma$ satisfies the classi","authors_text":"Keomkyo Seo, Sung-Hong Min","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-13T02:42:06Z","title":"Optimal isoperimetric inequalities for complete proper minimal submanifolds in hyperbolic space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2732","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:c17523f1f347824e5e0faed346cb7ca9270749ede42ed6c989d7222d5206eae8","target":"record","created_at":"2026-05-18T04:04:43Z","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":"e7471f45371c539453c01e3492e97894c8d158fff153d0ba1b90c4f3e1360341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-13T02:42:06Z","title_canon_sha256":"9dcab48382ebdafe6ed731e3139492f6814a0e5f0fd7ab8ce090a4656140a965"},"schema_version":"1.0","source":{"id":"1201.2732","kind":"arxiv","version":1}},"canonical_sha256":"7138acbac88feb6aa49bfe97ae99bb867e7464e491893f91bf22331d668499dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7138acbac88feb6aa49bfe97ae99bb867e7464e491893f91bf22331d668499dc","first_computed_at":"2026-05-18T04:04:43.219510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:43.219510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k5NtpFohZG2FRCl6qq8KGvKQ+JxkmSQGWf3u7eUJ4ygcbNg2F9BXsHcsPztySm+YGKI+eJZOnklIp2p4O3kDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:43.219979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c17523f1f347824e5e0faed346cb7ca9270749ede42ed6c989d7222d5206eae8","sha256:8cd6681441290911e2d650e2b051b2402b79a414f5dc44f2013c576cc4c670f5"],"state_sha256":"12188a86264356f6dff75907cbbd7f3093f0e03b134cadb162b3e487ba24ca36"}