{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SUWYWC4UEFT52SHISAUEELVOFW","short_pith_number":"pith:SUWYWC4U","schema_version":"1.0","canonical_sha256":"952d8b0b942167dd48e89028422eae2d84843cfcd880fe8afd871dbecb59763e","source":{"kind":"arxiv","id":"1603.03335","version":1},"attestation_state":"computed","paper":{"title":"Concentration of total curvature of minimal surfaces in H^2xR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eric Toubiana, Ricardo Sa Earp","submitted_at":"2016-03-10T17:11:19Z","abstract_excerpt":"We prove a phenomenon of concentration of total curvature for stable minimal surfaces in the product space H^2xR; where H^2 is the hyperbolic plane. Under some geometric conditions on the asymptotic boundary of an oriented stable minimal surface immersed in H^2xR, it has infinite total curvature. In particular, we infer that a minimal graph M in H^2xR whose asymptotic boundary is a graph over an arc of the asymptotic boundary of H^2, different from the asymptotic boundary of the boundary of M, has infinite total curvature. Consequently, if M is a stable minimal surface immersed into H^2xR with"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.03335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-10T17:11:19Z","cross_cats_sorted":[],"title_canon_sha256":"6f2abba260991be910e6f69a70a1f0792d2f5e28ab8f6d157cd07e34476a7beb","abstract_canon_sha256":"af39c411e00f8d6bd30b6a6b1f684b7fceda5a1f8c6b7f02948574cebd2f8baa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:16.597625Z","signature_b64":"GaTuLPV59+f9T41sIMKcwuCguGlEVIaAB7H2r/3QoqXzvn8iuglZIulq7CbG/Qk3Y9dFrHqgJ36UjstAZiX7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"952d8b0b942167dd48e89028422eae2d84843cfcd880fe8afd871dbecb59763e","last_reissued_at":"2026-05-18T01:19:16.597224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:16.597224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration of total curvature of minimal surfaces in H^2xR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eric Toubiana, Ricardo Sa Earp","submitted_at":"2016-03-10T17:11:19Z","abstract_excerpt":"We prove a phenomenon of concentration of total curvature for stable minimal surfaces in the product space H^2xR; where H^2 is the hyperbolic plane. Under some geometric conditions on the asymptotic boundary of an oriented stable minimal surface immersed in H^2xR, it has infinite total curvature. In particular, we infer that a minimal graph M in H^2xR whose asymptotic boundary is a graph over an arc of the asymptotic boundary of H^2, different from the asymptotic boundary of the boundary of M, has infinite total curvature. Consequently, if M is a stable minimal surface immersed into H^2xR with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03335","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.03335","created_at":"2026-05-18T01:19:16.597287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03335v1","created_at":"2026-05-18T01:19:16.597287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03335","created_at":"2026-05-18T01:19:16.597287+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUWYWC4UEFT5","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUWYWC4UEFT52SHI","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUWYWC4U","created_at":"2026-05-18T12:30:44.179134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW","json":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW.json","graph_json":"https://pith.science/api/pith-number/SUWYWC4UEFT52SHISAUEELVOFW/graph.json","events_json":"https://pith.science/api/pith-number/SUWYWC4UEFT52SHISAUEELVOFW/events.json","paper":"https://pith.science/paper/SUWYWC4U"},"agent_actions":{"view_html":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW","download_json":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW.json","view_paper":"https://pith.science/paper/SUWYWC4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03335&json=true","fetch_graph":"https://pith.science/api/pith-number/SUWYWC4UEFT52SHISAUEELVOFW/graph.json","fetch_events":"https://pith.science/api/pith-number/SUWYWC4UEFT52SHISAUEELVOFW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW/action/storage_attestation","attest_author":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW/action/author_attestation","sign_citation":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW/action/citation_signature","submit_replication":"https://pith.science/pith/SUWYWC4UEFT52SHISAUEELVOFW/action/replication_record"}},"created_at":"2026-05-18T01:19:16.597287+00:00","updated_at":"2026-05-18T01:19:16.597287+00:00"}