{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XBNAGE2QWN4Y6COD3T64TFJOJT","short_pith_number":"pith:XBNAGE2Q","schema_version":"1.0","canonical_sha256":"b85a031350b3798f09c3dcfdc9952e4cef3c29d46f34856c48f9cefc608900e6","source":{"kind":"arxiv","id":"1809.04586","version":1},"attestation_state":"computed","paper":{"title":"The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francesco Serra Cassano, Sebastiano Nicolussi","submitted_at":"2018-09-12T17:50:26Z","abstract_excerpt":"We prove that, in the first Heisenberg group $\\mathbb{H}$, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of $\\mathbb{H}$. Moreover two examples are given for stressing result's sharpness."},"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":"1809.04586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-12T17:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"889a465b5b7b8181564f9f0a4d58e2e4fb2da7c3e1f154ccc1a704bf006312a0","abstract_canon_sha256":"7c2dd405b01c9e563e09f4180179575a85f3eec7e1a3db87c7081db2ed74033a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:51.831665Z","signature_b64":"dq7KhC7xvWB5C/d6O82F7X4cuKMV+AOsMoAzJ3EeWtX/juqARRUqnCNpHM7sbrHRFAcyNONNyVU8HoNQZsgPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b85a031350b3798f09c3dcfdc9952e4cef3c29d46f34856c48f9cefc608900e6","last_reissued_at":"2026-05-18T00:05:51.830968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:51.830968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francesco Serra Cassano, Sebastiano Nicolussi","submitted_at":"2018-09-12T17:50:26Z","abstract_excerpt":"We prove that, in the first Heisenberg group $\\mathbb{H}$, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of $\\mathbb{H}$. Moreover two examples are given for stressing result's sharpness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04586","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":"1809.04586","created_at":"2026-05-18T00:05:51.831070+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.04586v1","created_at":"2026-05-18T00:05:51.831070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04586","created_at":"2026-05-18T00:05:51.831070+00:00"},{"alias_kind":"pith_short_12","alias_value":"XBNAGE2QWN4Y","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XBNAGE2QWN4Y6COD","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XBNAGE2Q","created_at":"2026-05-18T12:33:01.666342+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/XBNAGE2QWN4Y6COD3T64TFJOJT","json":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT.json","graph_json":"https://pith.science/api/pith-number/XBNAGE2QWN4Y6COD3T64TFJOJT/graph.json","events_json":"https://pith.science/api/pith-number/XBNAGE2QWN4Y6COD3T64TFJOJT/events.json","paper":"https://pith.science/paper/XBNAGE2Q"},"agent_actions":{"view_html":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT","download_json":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT.json","view_paper":"https://pith.science/paper/XBNAGE2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.04586&json=true","fetch_graph":"https://pith.science/api/pith-number/XBNAGE2QWN4Y6COD3T64TFJOJT/graph.json","fetch_events":"https://pith.science/api/pith-number/XBNAGE2QWN4Y6COD3T64TFJOJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT/action/storage_attestation","attest_author":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT/action/author_attestation","sign_citation":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT/action/citation_signature","submit_replication":"https://pith.science/pith/XBNAGE2QWN4Y6COD3T64TFJOJT/action/replication_record"}},"created_at":"2026-05-18T00:05:51.831070+00:00","updated_at":"2026-05-18T00:05:51.831070+00:00"}