{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DC6D5ZDIKEY7AXUOJRY5BHUMJ6","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":"b9525981cca9a4a52e16a0e094aa20de8caf0b7c476ae11d1a6ba2a5508ab1e1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-28T16:12:24Z","title_canon_sha256":"0ddcd8d286ce6951c5d219ce14e9e2e6e480cf04ff9e9fdecc1e930cac1401ec"},"schema_version":"1.0","source":{"id":"1009.5619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5619","created_at":"2026-05-18T00:37:05Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5619v1","created_at":"2026-05-18T00:37:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5619","created_at":"2026-05-18T00:37:05Z"},{"alias_kind":"pith_short_12","alias_value":"DC6D5ZDIKEY7","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DC6D5ZDIKEY7AXUO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DC6D5ZDI","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:b02308d384d2fe74fdf6caad0e2e7aa3a160e310f6789be961eb349c2f16ca17","target":"graph","created_at":"2026-05-18T00:37:05Z","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":"This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities. These results have been obtained in a series of papers in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas and are presented from a new viewpoint.","authors_text":"Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-28T16:12:24Z","title":"Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5619","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":"sha256:16b0de9dad403c6b55e5a819811db71a9ba5b7ccc62b5dbc65345d5fb2326d03","target":"record","created_at":"2026-05-18T00:37:05Z","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":"b9525981cca9a4a52e16a0e094aa20de8caf0b7c476ae11d1a6ba2a5508ab1e1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-28T16:12:24Z","title_canon_sha256":"0ddcd8d286ce6951c5d219ce14e9e2e6e480cf04ff9e9fdecc1e930cac1401ec"},"schema_version":"1.0","source":{"id":"1009.5619","kind":"arxiv","version":1}},"canonical_sha256":"18bc3ee4685131f05e8e4c71d09e8c4f9626272754c3dc0754fc2a4454501b2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18bc3ee4685131f05e8e4c71d09e8c4f9626272754c3dc0754fc2a4454501b2d","first_computed_at":"2026-05-18T00:37:05.253610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:05.253610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3QekrjRuJAjAHF8yN61Dr7Cznv21XMU1nTEQMs+fmgNO/yDz+dNJYM3SiXet/h20pJPaOYc6EI4pJbmC0JNYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:05.254584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16b0de9dad403c6b55e5a819811db71a9ba5b7ccc62b5dbc65345d5fb2326d03","sha256:b02308d384d2fe74fdf6caad0e2e7aa3a160e310f6789be961eb349c2f16ca17"],"state_sha256":"6ec3f58f464d19d1e93666019fc26ffd1764c5ad21c39c5542ed652617349507"}