{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:JXYIF5GNI4S7YQRDTC7SMITFDH","short_pith_number":"pith:JXYIF5GN","schema_version":"1.0","canonical_sha256":"4df082f4cd4725fc422398bf26226519d712e953c0e969def042f09cecfaa4d4","source":{"kind":"arxiv","id":"2011.13792","version":1},"attestation_state":"computed","paper":{"title":"A Bernstein theorem for two-valued minimal graphs in dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Fritz Hiesmayr","submitted_at":"2020-11-27T15:44:37Z","abstract_excerpt":"We prove a Bernstein-type theorem for two-valued minimal graphs in the four-dimensional Euclidean space $\\mathbf{R}^4$. This states that two-valued functions defined on the entire $\\mathbf{R}^3$, and whose graph is a minimal surface, must necessarily be linear. This is a two-valued analogue of the classical Bernstein theorem, which asserts that in dimensions up to $n+1 \\leq 8$, an entire single-valued minimal graph is linear. The main contrast with the single-valued theory is the presence of a large set of singularities in the graphs of two-valued functions. Indeed two-valued minimal graphs ar"},"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":"2011.13792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-11-27T15:44:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f43c3fe48fc72bc9bb4477d93da6a8ed0f451393f4ec81aecf0bea9d6c4091b8","abstract_canon_sha256":"1a57726de9465d760362f449358a7633f18c6f4c05b8640facf013d20a9e04fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:54:58.671522Z","signature_b64":"uV5mHz38aP2s4wmIjR1G/b9uZc6o0DXEQ2HRJdy34pWlAbh10DNy9NpJGoz/WcKHsvPFfRWyiD3LXRKNX/XsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4df082f4cd4725fc422398bf26226519d712e953c0e969def042f09cecfaa4d4","last_reissued_at":"2026-07-05T01:54:58.670887Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:54:58.670887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Bernstein theorem for two-valued minimal graphs in dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Fritz Hiesmayr","submitted_at":"2020-11-27T15:44:37Z","abstract_excerpt":"We prove a Bernstein-type theorem for two-valued minimal graphs in the four-dimensional Euclidean space $\\mathbf{R}^4$. This states that two-valued functions defined on the entire $\\mathbf{R}^3$, and whose graph is a minimal surface, must necessarily be linear. This is a two-valued analogue of the classical Bernstein theorem, which asserts that in dimensions up to $n+1 \\leq 8$, an entire single-valued minimal graph is linear. The main contrast with the single-valued theory is the presence of a large set of singularities in the graphs of two-valued functions. Indeed two-valued minimal graphs ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.13792","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.13792/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":"2011.13792","created_at":"2026-07-05T01:54:58.670960+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.13792v1","created_at":"2026-07-05T01:54:58.670960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.13792","created_at":"2026-07-05T01:54:58.670960+00:00"},{"alias_kind":"pith_short_12","alias_value":"JXYIF5GNI4S7","created_at":"2026-07-05T01:54:58.670960+00:00"},{"alias_kind":"pith_short_16","alias_value":"JXYIF5GNI4S7YQRD","created_at":"2026-07-05T01:54:58.670960+00:00"},{"alias_kind":"pith_short_8","alias_value":"JXYIF5GN","created_at":"2026-07-05T01:54:58.670960+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.01511","citing_title":"A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH","json":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH.json","graph_json":"https://pith.science/api/pith-number/JXYIF5GNI4S7YQRDTC7SMITFDH/graph.json","events_json":"https://pith.science/api/pith-number/JXYIF5GNI4S7YQRDTC7SMITFDH/events.json","paper":"https://pith.science/paper/JXYIF5GN"},"agent_actions":{"view_html":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH","download_json":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH.json","view_paper":"https://pith.science/paper/JXYIF5GN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.13792&json=true","fetch_graph":"https://pith.science/api/pith-number/JXYIF5GNI4S7YQRDTC7SMITFDH/graph.json","fetch_events":"https://pith.science/api/pith-number/JXYIF5GNI4S7YQRDTC7SMITFDH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH/action/storage_attestation","attest_author":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH/action/author_attestation","sign_citation":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH/action/citation_signature","submit_replication":"https://pith.science/pith/JXYIF5GNI4S7YQRDTC7SMITFDH/action/replication_record"}},"created_at":"2026-07-05T01:54:58.670960+00:00","updated_at":"2026-07-05T01:54:58.670960+00:00"}