{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V5YQ4H6AYL6HRQ6RDJT4ZPKK33","short_pith_number":"pith:V5YQ4H6A","schema_version":"1.0","canonical_sha256":"af710e1fc0c2fc78c3d11a67ccbd4adee51bf3fc4db8eb24602d6d190bc81cf3","source":{"kind":"arxiv","id":"1806.06189","version":1},"attestation_state":"computed","paper":{"title":"Isometric embedding with nonnegative Gauss curvature under the graph setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xumin Jiang","submitted_at":"2018-06-16T05:30:34Z","abstract_excerpt":"We study the regularity of the isometric embedding X: (B(O,r),g) -> (R3, gcan) of a 2-ball with nonnegatively curved C4 metric into R3. Under the assumption that X can be expressed in the graph form, we show X is C2,1 near P, which is optimal by Iaia's example."},"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":"1806.06189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-16T05:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"f481cfe326862502281fab332aae8991a0dfbd27200cce7059ebb6407690dfc6","abstract_canon_sha256":"f64a0df28359bec672b35ace49023bb28106a00b73ff4aeb6d06c5f0ff81a84c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:03.358420Z","signature_b64":"NAXcsSTaYoAuFjgBY++zF7UJOvPELB9Ppif2xSglWXDK4EjcTCCxkPSU+tsc+n1MAJO1m+k140CIQajroJfhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af710e1fc0c2fc78c3d11a67ccbd4adee51bf3fc4db8eb24602d6d190bc81cf3","last_reissued_at":"2026-05-18T00:13:03.357763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:03.357763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometric embedding with nonnegative Gauss curvature under the graph setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xumin Jiang","submitted_at":"2018-06-16T05:30:34Z","abstract_excerpt":"We study the regularity of the isometric embedding X: (B(O,r),g) -> (R3, gcan) of a 2-ball with nonnegatively curved C4 metric into R3. Under the assumption that X can be expressed in the graph form, we show X is C2,1 near P, which is optimal by Iaia's example."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06189","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":"1806.06189","created_at":"2026-05-18T00:13:03.357840+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.06189v1","created_at":"2026-05-18T00:13:03.357840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06189","created_at":"2026-05-18T00:13:03.357840+00:00"},{"alias_kind":"pith_short_12","alias_value":"V5YQ4H6AYL6H","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"V5YQ4H6AYL6HRQ6R","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"V5YQ4H6A","created_at":"2026-05-18T12:32:59.047623+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/V5YQ4H6AYL6HRQ6RDJT4ZPKK33","json":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33.json","graph_json":"https://pith.science/api/pith-number/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/graph.json","events_json":"https://pith.science/api/pith-number/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/events.json","paper":"https://pith.science/paper/V5YQ4H6A"},"agent_actions":{"view_html":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33","download_json":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33.json","view_paper":"https://pith.science/paper/V5YQ4H6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.06189&json=true","fetch_graph":"https://pith.science/api/pith-number/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/graph.json","fetch_events":"https://pith.science/api/pith-number/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/action/storage_attestation","attest_author":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/action/author_attestation","sign_citation":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/action/citation_signature","submit_replication":"https://pith.science/pith/V5YQ4H6AYL6HRQ6RDJT4ZPKK33/action/replication_record"}},"created_at":"2026-05-18T00:13:03.357840+00:00","updated_at":"2026-05-18T00:13:03.357840+00:00"}