{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WNBTIR6HOLPOO2T3ARQELUYWIT","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":"f61221cd23f2bc7cfab2105259ed2ff3094ca40e533eed1bd5ef339b72081e74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-06T14:24:00Z","title_canon_sha256":"f7f5cc888ad4a1993b60e970532887c0cd054a9da0efae81e4ca7190ad893b2d"},"schema_version":"1.0","source":{"id":"1405.1280","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1280","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1280v3","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1280","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"WNBTIR6HOLPO","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WNBTIR6HOLPOO2T3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WNBTIR6H","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:039909067c664e8a3974c5f3012ec5d2d4c7ecab3b7c0ec439ae2f1d74975de9","target":"graph","created_at":"2026-05-18T02:52:13Z","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":"This paper extends, in a sharp way, the famous Efimov's Theorem to immersed ends in $\\real^3$. More precisely, let $M$ be a non-compact connected surface with compact boundary. Then there is no complete isometric immersion of $M$ into $\\Bbb R^3$ satisfying that $\\int_M |K|=+\\infty$ and $K\\le-\\kappa<0$, where $\\kappa$ is a positive constant and $K$ is the Gaussian curvature of $M$. In particular Efimov's Theorem holds for complete Hadamard immersed surfaces, whose Gaussian curvature $K$ is bounded away from zero outside a compact set.","authors_text":"S\\'ergio Mendon\\c{c}a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-06T14:24:00Z","title":"Complete negatively curved immersed ends in $\\Bbb R^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1280","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":"sha256:850e5f68bf16c1b2b00cd4aa7fb1fdb542ab877b70774fb8627157e69877f54b","target":"record","created_at":"2026-05-18T02:52:13Z","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":"f61221cd23f2bc7cfab2105259ed2ff3094ca40e533eed1bd5ef339b72081e74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-06T14:24:00Z","title_canon_sha256":"f7f5cc888ad4a1993b60e970532887c0cd054a9da0efae81e4ca7190ad893b2d"},"schema_version":"1.0","source":{"id":"1405.1280","kind":"arxiv","version":3}},"canonical_sha256":"b3433447c772dee76a7b046045d31644c2e6353a366a1725151494710739da86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3433447c772dee76a7b046045d31644c2e6353a366a1725151494710739da86","first_computed_at":"2026-05-18T02:52:13.780083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:13.780083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5hGA1GBfA7aRFx7d1n/dNaeav+Zmy2tPwxHRTKoIXGhaoVp6JMSFZQzF1HWgqBxJ5bgYn4xQuNvX/SM57vriDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:13.781850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1280","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:850e5f68bf16c1b2b00cd4aa7fb1fdb542ab877b70774fb8627157e69877f54b","sha256:039909067c664e8a3974c5f3012ec5d2d4c7ecab3b7c0ec439ae2f1d74975de9"],"state_sha256":"55eb48a409298dc1cfefc38da9e7db69d12c9cb839b3da954ab38763bdfda747"}