{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MPVGPTKD2Q364I3VVPXGGGORE2","short_pith_number":"pith:MPVGPTKD","schema_version":"1.0","canonical_sha256":"63ea67cd43d437ee2375abee6319d12696e02eb7f1813916f7fa390b658edd67","source":{"kind":"arxiv","id":"1502.02097","version":1},"attestation_state":"computed","paper":{"title":"Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Meijun Zhu, Yazhou Han","submitted_at":"2015-02-07T05:33:17Z","abstract_excerpt":"In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and a new variational approach. Even for the classic Yamabe problem on locally conformally flat manifolds, our approach provides a new and relatively simpler solution."},"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":"1502.02097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-07T05:33:17Z","cross_cats_sorted":[],"title_canon_sha256":"a6b9577ae8924dcb67081bb1c6ff190af5965d1dd3afe81e23406df693a8ce09","abstract_canon_sha256":"38e4562aeb07f7e3ff0d8630422c307a365197a4c9d11f4cc4e3196d940b1746"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:32.132967Z","signature_b64":"n9pdVXvXLWFZT2GiM1+O2/uKD0T3y44TRr14Z8RI4u4sQHOmbArcYUf5IjrYy6DntOeCdpFJVWWNerP7IpiYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63ea67cd43d437ee2375abee6319d12696e02eb7f1813916f7fa390b658edd67","last_reissued_at":"2026-05-18T00:57:32.132302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:32.132302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Meijun Zhu, Yazhou Han","submitted_at":"2015-02-07T05:33:17Z","abstract_excerpt":"In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and a new variational approach. Even for the classic Yamabe problem on locally conformally flat manifolds, our approach provides a new and relatively simpler solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02097","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":"1502.02097","created_at":"2026-05-18T00:57:32.132403+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.02097v1","created_at":"2026-05-18T00:57:32.132403+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02097","created_at":"2026-05-18T00:57:32.132403+00:00"},{"alias_kind":"pith_short_12","alias_value":"MPVGPTKD2Q36","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MPVGPTKD2Q364I3V","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MPVGPTKD","created_at":"2026-05-18T12:29:32.376354+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/MPVGPTKD2Q364I3VVPXGGGORE2","json":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2.json","graph_json":"https://pith.science/api/pith-number/MPVGPTKD2Q364I3VVPXGGGORE2/graph.json","events_json":"https://pith.science/api/pith-number/MPVGPTKD2Q364I3VVPXGGGORE2/events.json","paper":"https://pith.science/paper/MPVGPTKD"},"agent_actions":{"view_html":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2","download_json":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2.json","view_paper":"https://pith.science/paper/MPVGPTKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.02097&json=true","fetch_graph":"https://pith.science/api/pith-number/MPVGPTKD2Q364I3VVPXGGGORE2/graph.json","fetch_events":"https://pith.science/api/pith-number/MPVGPTKD2Q364I3VVPXGGGORE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2/action/storage_attestation","attest_author":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2/action/author_attestation","sign_citation":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2/action/citation_signature","submit_replication":"https://pith.science/pith/MPVGPTKD2Q364I3VVPXGGGORE2/action/replication_record"}},"created_at":"2026-05-18T00:57:32.132403+00:00","updated_at":"2026-05-18T00:57:32.132403+00:00"}