{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YCP25I76Q6SCR3XLLYN24JB6S7","short_pith_number":"pith:YCP25I76","schema_version":"1.0","canonical_sha256":"c09faea3fe87a428eeeb5e1bae243e97d96745f1bb49c0b7c94c30398d1afbef","source":{"kind":"arxiv","id":"1509.08584","version":2},"attestation_state":"computed","paper":{"title":"Isometric Immersion of Surface with Negative Gauss Curvature and the Lax-Friedrichs Scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dehua Wang, Feimin Huang, Wentao Cao","submitted_at":"2015-09-29T04:05:05Z","abstract_excerpt":"The isometric immersion of two-dimensional Riemannian manifold with negative Gauss curvature into the three-dimensional Euclidean space is considered through the Gauss-Codazzi equations for the first and second fundamental forms. The large $L^\\infty$ solution is obtained which leads to a $C^{1,1}$ isometric immersion. The approximate solutions are constructed by the the Lax-Friedrichs finite-difference scheme with the fractional step. The uniform estimate is established by studying the equations satisfied by the Riemann invariants and using the sign of the nonlinear part. The $H^{-1}$ compactn"},"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":"1509.08584","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T04:05:05Z","cross_cats_sorted":[],"title_canon_sha256":"504ff4fcc2186f85de6caae735e5712308a5a1df3548f68cd9351d8067ed8bed","abstract_canon_sha256":"e246eafe8c4dc9e463d4db13f6c55a38271efa315e650a1a10eab561b3dd327f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:05.106942Z","signature_b64":"nF3Q/d7lFV3qXEnh5DEmYbmFxmUb5ci0XKM1MmB/oP20KcMKwTw2ArNawveBBfFElGcX8ntrRKIFJSBB47OsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c09faea3fe87a428eeeb5e1bae243e97d96745f1bb49c0b7c94c30398d1afbef","last_reissued_at":"2026-05-18T01:24:05.106198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:05.106198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometric Immersion of Surface with Negative Gauss Curvature and the Lax-Friedrichs Scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dehua Wang, Feimin Huang, Wentao Cao","submitted_at":"2015-09-29T04:05:05Z","abstract_excerpt":"The isometric immersion of two-dimensional Riemannian manifold with negative Gauss curvature into the three-dimensional Euclidean space is considered through the Gauss-Codazzi equations for the first and second fundamental forms. The large $L^\\infty$ solution is obtained which leads to a $C^{1,1}$ isometric immersion. The approximate solutions are constructed by the the Lax-Friedrichs finite-difference scheme with the fractional step. The uniform estimate is established by studying the equations satisfied by the Riemann invariants and using the sign of the nonlinear part. The $H^{-1}$ compactn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08584","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":""},"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":"1509.08584","created_at":"2026-05-18T01:24:05.106330+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08584v2","created_at":"2026-05-18T01:24:05.106330+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08584","created_at":"2026-05-18T01:24:05.106330+00:00"},{"alias_kind":"pith_short_12","alias_value":"YCP25I76Q6SC","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YCP25I76Q6SCR3XL","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YCP25I76","created_at":"2026-05-18T12:29:50.041715+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/YCP25I76Q6SCR3XLLYN24JB6S7","json":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7.json","graph_json":"https://pith.science/api/pith-number/YCP25I76Q6SCR3XLLYN24JB6S7/graph.json","events_json":"https://pith.science/api/pith-number/YCP25I76Q6SCR3XLLYN24JB6S7/events.json","paper":"https://pith.science/paper/YCP25I76"},"agent_actions":{"view_html":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7","download_json":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7.json","view_paper":"https://pith.science/paper/YCP25I76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08584&json=true","fetch_graph":"https://pith.science/api/pith-number/YCP25I76Q6SCR3XLLYN24JB6S7/graph.json","fetch_events":"https://pith.science/api/pith-number/YCP25I76Q6SCR3XLLYN24JB6S7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7/action/storage_attestation","attest_author":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7/action/author_attestation","sign_citation":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7/action/citation_signature","submit_replication":"https://pith.science/pith/YCP25I76Q6SCR3XLLYN24JB6S7/action/replication_record"}},"created_at":"2026-05-18T01:24:05.106330+00:00","updated_at":"2026-05-18T01:24:05.106330+00:00"}