{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:MGLRHAOHSSJ5SNAI5MVMV3SNKF","short_pith_number":"pith:MGLRHAOH","schema_version":"1.0","canonical_sha256":"61971381c79493d93408eb2acaee4d516fe50e1fe656bdccffd219aeb3a9e742","source":{"kind":"arxiv","id":"1905.03191","version":2},"attestation_state":"computed","paper":{"title":"On the asymptotic Plateau problem for area minimizing surfaces in $\\mathbb{E}(-1,\\tau)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"\\'Alvaro Ramos, Ana Menezes, Patr\\'icia Klaser","submitted_at":"2019-05-08T16:20:20Z","abstract_excerpt":"We prove some existence and non-existence results for complete area minimizing surfaces in the homogeneous space $\\mathbb{E}(-1,\\tau)$. As one of our main results, we present sufficient conditions for a curve $\\Gamma$ in $\\partial_{\\infty} \\mathbb{E}(-1,\\tau)$ to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in $\\mathbb{E}(-1,\\tau)$ having $\\Gamma$ as its asymptotic boundary."},"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":"1905.03191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-08T16:20:20Z","cross_cats_sorted":[],"title_canon_sha256":"b0858aa1e41ba00099a3d0dc440fcf0f1d8096c3fa33131fdd140331c26390a6","abstract_canon_sha256":"f0e1972265498eb1c9f53e7c0fcb46f0193ea2d06017f993e6d3c3024c9f7c43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:06:17.765970Z","signature_b64":"x1Zqy/kkSPNAnIkeWtIz9t7ec8dZ7/QbEg4RoaF2mI9+lx2pFOu9xZQFBVVoyHROWTyWQLvda2qE8R2pAKNyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61971381c79493d93408eb2acaee4d516fe50e1fe656bdccffd219aeb3a9e742","last_reissued_at":"2026-07-05T01:06:17.765557Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:06:17.765557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the asymptotic Plateau problem for area minimizing surfaces in $\\mathbb{E}(-1,\\tau)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"\\'Alvaro Ramos, Ana Menezes, Patr\\'icia Klaser","submitted_at":"2019-05-08T16:20:20Z","abstract_excerpt":"We prove some existence and non-existence results for complete area minimizing surfaces in the homogeneous space $\\mathbb{E}(-1,\\tau)$. As one of our main results, we present sufficient conditions for a curve $\\Gamma$ in $\\partial_{\\infty} \\mathbb{E}(-1,\\tau)$ to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in $\\mathbb{E}(-1,\\tau)$ having $\\Gamma$ as its asymptotic boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03191","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.03191/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1905.03191","created_at":"2026-07-05T01:06:17.765612+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.03191v2","created_at":"2026-07-05T01:06:17.765612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03191","created_at":"2026-07-05T01:06:17.765612+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGLRHAOHSSJ5","created_at":"2026-07-05T01:06:17.765612+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGLRHAOHSSJ5SNAI","created_at":"2026-07-05T01:06:17.765612+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGLRHAOH","created_at":"2026-07-05T01:06:17.765612+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/MGLRHAOHSSJ5SNAI5MVMV3SNKF","json":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF.json","graph_json":"https://pith.science/api/pith-number/MGLRHAOHSSJ5SNAI5MVMV3SNKF/graph.json","events_json":"https://pith.science/api/pith-number/MGLRHAOHSSJ5SNAI5MVMV3SNKF/events.json","paper":"https://pith.science/paper/MGLRHAOH"},"agent_actions":{"view_html":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF","download_json":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF.json","view_paper":"https://pith.science/paper/MGLRHAOH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.03191&json=true","fetch_graph":"https://pith.science/api/pith-number/MGLRHAOHSSJ5SNAI5MVMV3SNKF/graph.json","fetch_events":"https://pith.science/api/pith-number/MGLRHAOHSSJ5SNAI5MVMV3SNKF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF/action/storage_attestation","attest_author":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF/action/author_attestation","sign_citation":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF/action/citation_signature","submit_replication":"https://pith.science/pith/MGLRHAOHSSJ5SNAI5MVMV3SNKF/action/replication_record"}},"created_at":"2026-07-05T01:06:17.765612+00:00","updated_at":"2026-07-05T01:06:17.765612+00:00"}