{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RDDJACCBPIJTPXN7FXVX64IETZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"62b67096f89099c271ac7ad902a630878e13b81b44e60d321bd001dc0b83a436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-05T18:38:59Z","title_canon_sha256":"e667df7b0fb8a178004bc65b0aca020d592a4150b9445b9d821d2fca19de0526"},"schema_version":"1.0","source":{"id":"1203.1003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1003","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1003v1","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1003","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"RDDJACCBPIJT","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RDDJACCBPIJTPXN7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RDDJACCB","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:c77639d1bc8a6c094fe9b4c82ecb0a289c911a70284dce87e2a161a66941f3a6","target":"graph","created_at":"2026-05-18T03:39:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We establish some sharp weighted trace inequalities $W^{1,2}(\\rho^{1-2\\sigma}, M)\\hookrightarrow L^{\\frac{2n}{n-2\\sigma}}(\\pa M)$ on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\\rho$ is a defining function of $M$ and $\\sigma\\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.","authors_text":"Jingang Xiong, Tianling Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-05T18:38:59Z","title":"Sharp constants in weighted trace inequalities on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1003","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b60baa7bed6e8512f7f2b7970b99a9633bc50816ebe0619631db7119ad37bfa7","target":"record","created_at":"2026-05-18T03:39:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"62b67096f89099c271ac7ad902a630878e13b81b44e60d321bd001dc0b83a436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-05T18:38:59Z","title_canon_sha256":"e667df7b0fb8a178004bc65b0aca020d592a4150b9445b9d821d2fca19de0526"},"schema_version":"1.0","source":{"id":"1203.1003","kind":"arxiv","version":1}},"canonical_sha256":"88c69008417a1337ddbf2deb7f71049e75e367677639ec30d03eb8b4f363d483","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88c69008417a1337ddbf2deb7f71049e75e367677639ec30d03eb8b4f363d483","first_computed_at":"2026-05-18T03:39:53.040311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:53.040311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i8Sc9ZmNEKSpdPE7z1RCnot4eMBxCsI2767HI9zoU9/T7sRoAl4kUiL66a94AWXkWnTgPehLeEACE1NwpX2qBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:53.040809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b60baa7bed6e8512f7f2b7970b99a9633bc50816ebe0619631db7119ad37bfa7","sha256:c77639d1bc8a6c094fe9b4c82ecb0a289c911a70284dce87e2a161a66941f3a6"],"state_sha256":"6c39bbe0feb27847a6555b48e5cd4779fd602391ee917492f42e525b068ea99c"}