{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UZWJRHKGHUYKYFXOGQZATJDG54","short_pith_number":"pith:UZWJRHKG","schema_version":"1.0","canonical_sha256":"a66c989d463d30ac16ee343209a466ef2621aae3cc0a44f455fd4bee425d063c","source":{"kind":"arxiv","id":"1907.00739","version":1},"attestation_state":"computed","paper":{"title":"Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Yamada, Masaaki Umehara, Shintaro Akamine","submitted_at":"2019-07-01T12:56:34Z","abstract_excerpt":"Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $\\boldsymbol R^3_1$. A complete light-like line in $\\boldsymbol R^3_1$ is called an entire null line on the surface $S$ in $\\boldsymbol R^3_1$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show the existence of embedded space-like maximal graphs containing entire null lines. If such a graph is defined on a convex domain in $\\boldsymbol R^2$, then it must be a light-like plane. Our example is critical in the sense that it is defined on a certain non-convex domain."},"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":"1907.00739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-01T12:56:34Z","cross_cats_sorted":[],"title_canon_sha256":"cb4b3bf5bd8ca5623e74a51952162398d376bf86f3a0cf382b130042020cefa0","abstract_canon_sha256":"8b7a092141a50467e11872507f338baf054caa754b57dac18e4dbd880b254b27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:48.272597Z","signature_b64":"grgWqCjqTVTz5TJTg1y9HFmb18x8EBiwVlI8qy18i+oCuc/7UXVF1jjPV9UOGzg8wsgXdcagdFy6cCpro243Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a66c989d463d30ac16ee343209a466ef2621aae3cc0a44f455fd4bee425d063c","last_reissued_at":"2026-05-17T23:41:48.271837Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:48.271837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Yamada, Masaaki Umehara, Shintaro Akamine","submitted_at":"2019-07-01T12:56:34Z","abstract_excerpt":"Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $\\boldsymbol R^3_1$. A complete light-like line in $\\boldsymbol R^3_1$ is called an entire null line on the surface $S$ in $\\boldsymbol R^3_1$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show the existence of embedded space-like maximal graphs containing entire null lines. If such a graph is defined on a convex domain in $\\boldsymbol R^2$, then it must be a light-like plane. Our example is critical in the sense that it is defined on a certain non-convex domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00739","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":"1907.00739","created_at":"2026-05-17T23:41:48.271958+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.00739v1","created_at":"2026-05-17T23:41:48.271958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00739","created_at":"2026-05-17T23:41:48.271958+00:00"},{"alias_kind":"pith_short_12","alias_value":"UZWJRHKGHUYK","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UZWJRHKGHUYKYFXO","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UZWJRHKG","created_at":"2026-05-18T12:33:30.264802+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.01754","citing_title":"Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54","json":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54.json","graph_json":"https://pith.science/api/pith-number/UZWJRHKGHUYKYFXOGQZATJDG54/graph.json","events_json":"https://pith.science/api/pith-number/UZWJRHKGHUYKYFXOGQZATJDG54/events.json","paper":"https://pith.science/paper/UZWJRHKG"},"agent_actions":{"view_html":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54","download_json":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54.json","view_paper":"https://pith.science/paper/UZWJRHKG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.00739&json=true","fetch_graph":"https://pith.science/api/pith-number/UZWJRHKGHUYKYFXOGQZATJDG54/graph.json","fetch_events":"https://pith.science/api/pith-number/UZWJRHKGHUYKYFXOGQZATJDG54/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54/action/storage_attestation","attest_author":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54/action/author_attestation","sign_citation":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54/action/citation_signature","submit_replication":"https://pith.science/pith/UZWJRHKGHUYKYFXOGQZATJDG54/action/replication_record"}},"created_at":"2026-05-17T23:41:48.271958+00:00","updated_at":"2026-05-17T23:41:48.271958+00:00"}