{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ALXAEM5KBBASIOSMX4JXX3LWJW","short_pith_number":"pith:ALXAEM5K","schema_version":"1.0","canonical_sha256":"02ee0233aa0841243a4cbf137bed764d9ed0a4f62d269b6d2e6b9cf1537fc5a9","source":{"kind":"arxiv","id":"1411.5743","version":1},"attestation_state":"computed","paper":{"title":"The Nirenberg problem and its generalizations: A unified approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Tianling Jin, Yanyan Li","submitted_at":"2014-11-21T02:27:07Z","abstract_excerpt":"Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations $P_\\sigma(v)= Kv^{\\frac{n+2\\sigma}{n-2\\sigma}}$ on the standard unit sphere $\\mathbb{S}^n$ for all $\\sigma\\in (0,n/2)$, where $P_\\sigma$ is the intertwining operator of order $2\\sigma$. Finding positive solutions of these equations is equivalent to seeking metrics in the conformal class of the standard metric on spheres with prescribed certain curvatures. When $\\sigma=1$, it is the prescribing scalar curvatur"},"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":"1411.5743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-21T02:27:07Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c5f62da70ad8b1b7d8c9c609d9e14bd1659dc375fbdb7cf20760ba03f0cee37d","abstract_canon_sha256":"265026b74957abc0bd5e2ff0fd003a8c2e08395fb9db66f8eb56cad9ab49502e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:07.191681Z","signature_b64":"JKoQkj54LZoK00clhKD0mNjYMq6GB5/jKLYOlc5mMgP6HhO4HXH0DAMrjbuv7cJjRDeyws/2v+lhOM8I+u/1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ee0233aa0841243a4cbf137bed764d9ed0a4f62d269b6d2e6b9cf1537fc5a9","last_reissued_at":"2026-05-18T02:33:07.191107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:07.191107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Nirenberg problem and its generalizations: A unified approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Tianling Jin, Yanyan Li","submitted_at":"2014-11-21T02:27:07Z","abstract_excerpt":"Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations $P_\\sigma(v)= Kv^{\\frac{n+2\\sigma}{n-2\\sigma}}$ on the standard unit sphere $\\mathbb{S}^n$ for all $\\sigma\\in (0,n/2)$, where $P_\\sigma$ is the intertwining operator of order $2\\sigma$. Finding positive solutions of these equations is equivalent to seeking metrics in the conformal class of the standard metric on spheres with prescribed certain curvatures. When $\\sigma=1$, it is the prescribing scalar curvatur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5743","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":"1411.5743","created_at":"2026-05-18T02:33:07.191190+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.5743v1","created_at":"2026-05-18T02:33:07.191190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5743","created_at":"2026-05-18T02:33:07.191190+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALXAEM5KBBAS","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALXAEM5KBBASIOSM","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALXAEM5K","created_at":"2026-05-18T12:28:19.803747+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/ALXAEM5KBBASIOSMX4JXX3LWJW","json":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW.json","graph_json":"https://pith.science/api/pith-number/ALXAEM5KBBASIOSMX4JXX3LWJW/graph.json","events_json":"https://pith.science/api/pith-number/ALXAEM5KBBASIOSMX4JXX3LWJW/events.json","paper":"https://pith.science/paper/ALXAEM5K"},"agent_actions":{"view_html":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW","download_json":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW.json","view_paper":"https://pith.science/paper/ALXAEM5K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.5743&json=true","fetch_graph":"https://pith.science/api/pith-number/ALXAEM5KBBASIOSMX4JXX3LWJW/graph.json","fetch_events":"https://pith.science/api/pith-number/ALXAEM5KBBASIOSMX4JXX3LWJW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW/action/storage_attestation","attest_author":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW/action/author_attestation","sign_citation":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW/action/citation_signature","submit_replication":"https://pith.science/pith/ALXAEM5KBBASIOSMX4JXX3LWJW/action/replication_record"}},"created_at":"2026-05-18T02:33:07.191190+00:00","updated_at":"2026-05-18T02:33:07.191190+00:00"}