{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TYJTPOURFLDYZDNFEIYYAKGTJ6","short_pith_number":"pith:TYJTPOUR","schema_version":"1.0","canonical_sha256":"9e1337ba912ac78c8da522318028d34fa0d509017d3e952e414afa4c83f6d2bd","source":{"kind":"arxiv","id":"1608.07539","version":2},"attestation_state":"computed","paper":{"title":"On Weyl's embedding problem in Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Siyuan Lu","submitted_at":"2016-08-26T17:54:32Z","abstract_excerpt":"We consider a priori estimates of Weyl's embedding problem of $(\\mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, \\bar g)$. We establish interior $C^2$ estimate under natural geometric assumption. Together with a recent work by Li and Wang, we obtain an isometric embedding of $(\\mathbb{S}^2,g)$ in Riemannian manifold. In addition, we reprove Weyl's embedding theorem in space form under the condition that $g\\in C^2$ with $D^2g$ Dini continuous."},"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":"1608.07539","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-26T17:54:32Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"419da0bca038851e0514117e0849076d1dfaad22c5b2234f2785850c8f48701b","abstract_canon_sha256":"518e3fd769c4f3ff7c08df9f1f1f32f79f12e164baae04b50139457fce904ca2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:57.365578Z","signature_b64":"99hLeH1zYzCbVq3kz8axKlwde9eqRmz16nRv48NIt0GBdlam+Rpd4ThjK3afCrwonXLXivGVCrAJ+T5JZJdPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e1337ba912ac78c8da522318028d34fa0d509017d3e952e414afa4c83f6d2bd","last_reissued_at":"2026-05-18T00:14:57.364687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:57.364687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Weyl's embedding problem in Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Siyuan Lu","submitted_at":"2016-08-26T17:54:32Z","abstract_excerpt":"We consider a priori estimates of Weyl's embedding problem of $(\\mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, \\bar g)$. We establish interior $C^2$ estimate under natural geometric assumption. Together with a recent work by Li and Wang, we obtain an isometric embedding of $(\\mathbb{S}^2,g)$ in Riemannian manifold. In addition, we reprove Weyl's embedding theorem in space form under the condition that $g\\in C^2$ with $D^2g$ Dini continuous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07539","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":"1608.07539","created_at":"2026-05-18T00:14:57.364841+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.07539v2","created_at":"2026-05-18T00:14:57.364841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07539","created_at":"2026-05-18T00:14:57.364841+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYJTPOURFLDY","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYJTPOURFLDYZDNF","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYJTPOUR","created_at":"2026-05-18T12:30:46.583412+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/TYJTPOURFLDYZDNFEIYYAKGTJ6","json":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6.json","graph_json":"https://pith.science/api/pith-number/TYJTPOURFLDYZDNFEIYYAKGTJ6/graph.json","events_json":"https://pith.science/api/pith-number/TYJTPOURFLDYZDNFEIYYAKGTJ6/events.json","paper":"https://pith.science/paper/TYJTPOUR"},"agent_actions":{"view_html":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6","download_json":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6.json","view_paper":"https://pith.science/paper/TYJTPOUR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.07539&json=true","fetch_graph":"https://pith.science/api/pith-number/TYJTPOURFLDYZDNFEIYYAKGTJ6/graph.json","fetch_events":"https://pith.science/api/pith-number/TYJTPOURFLDYZDNFEIYYAKGTJ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6/action/storage_attestation","attest_author":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6/action/author_attestation","sign_citation":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6/action/citation_signature","submit_replication":"https://pith.science/pith/TYJTPOURFLDYZDNFEIYYAKGTJ6/action/replication_record"}},"created_at":"2026-05-18T00:14:57.364841+00:00","updated_at":"2026-05-18T00:14:57.364841+00:00"}