{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HZYV5CUIUGAGHQNX64KK6X7AJS","short_pith_number":"pith:HZYV5CUI","schema_version":"1.0","canonical_sha256":"3e715e8a88a18063c1b7f714af5fe04cb70d924e3b8f940c499c8c444619756b","source":{"kind":"arxiv","id":"1811.11392","version":2},"attestation_state":"computed","paper":{"title":"Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Atsufumi Honda, Keisuke Teramoto, Kentaro Saji","submitted_at":"2018-11-28T05:31:39Z","abstract_excerpt":"A mixed type surface is a connected regular surface in a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced metric of a mixed type surface is a signature-changing metric, and their lightlike points may be regarded as singular points of such metrics. In this paper, we investigate the behavior of Gaussian curvature at a non-degenerate lightlike point of a mixed type surface. To characterize the boundedness of Gaussian curvature at a non-degenerate lightlike points, we introduce several fundamental invariants along non-degenerate lightlike points, such as the ligh"},"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":"1811.11392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-28T05:31:39Z","cross_cats_sorted":[],"title_canon_sha256":"5837bc202d76e046f79f86b853abc062172705ccfc803630af521d20b30e21cc","abstract_canon_sha256":"644966ecc156793271807fc041a9783a5cc834e8f2f430ac11f280357b3004c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:21:22.490090Z","signature_b64":"UpOEjM/PPiMeslCleQSA2PifigrssyaaS+LSP4j3269bcFZoLrRcchtNQ4dFuiK4gcL3lk2ggAHoCPluGUD3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e715e8a88a18063c1b7f714af5fe04cb70d924e3b8f940c499c8c444619756b","last_reissued_at":"2026-07-05T00:21:22.489697Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:21:22.489697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Atsufumi Honda, Keisuke Teramoto, Kentaro Saji","submitted_at":"2018-11-28T05:31:39Z","abstract_excerpt":"A mixed type surface is a connected regular surface in a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced metric of a mixed type surface is a signature-changing metric, and their lightlike points may be regarded as singular points of such metrics. In this paper, we investigate the behavior of Gaussian curvature at a non-degenerate lightlike point of a mixed type surface. To characterize the boundedness of Gaussian curvature at a non-degenerate lightlike points, we introduce several fundamental invariants along non-degenerate lightlike points, such as the ligh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11392","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/1811.11392/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":"1811.11392","created_at":"2026-07-05T00:21:22.489753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.11392v2","created_at":"2026-07-05T00:21:22.489753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11392","created_at":"2026-07-05T00:21:22.489753+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZYV5CUIUGAG","created_at":"2026-07-05T00:21:22.489753+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZYV5CUIUGAGHQNX","created_at":"2026-07-05T00:21:22.489753+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZYV5CUI","created_at":"2026-07-05T00:21:22.489753+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01967","citing_title":"Isometric deformations of mixed type surfaces in Lorentz-Minkowski space","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS","json":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS.json","graph_json":"https://pith.science/api/pith-number/HZYV5CUIUGAGHQNX64KK6X7AJS/graph.json","events_json":"https://pith.science/api/pith-number/HZYV5CUIUGAGHQNX64KK6X7AJS/events.json","paper":"https://pith.science/paper/HZYV5CUI"},"agent_actions":{"view_html":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS","download_json":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS.json","view_paper":"https://pith.science/paper/HZYV5CUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.11392&json=true","fetch_graph":"https://pith.science/api/pith-number/HZYV5CUIUGAGHQNX64KK6X7AJS/graph.json","fetch_events":"https://pith.science/api/pith-number/HZYV5CUIUGAGHQNX64KK6X7AJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS/action/storage_attestation","attest_author":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS/action/author_attestation","sign_citation":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS/action/citation_signature","submit_replication":"https://pith.science/pith/HZYV5CUIUGAGHQNX64KK6X7AJS/action/replication_record"}},"created_at":"2026-07-05T00:21:22.489753+00:00","updated_at":"2026-07-05T00:21:22.489753+00:00"}