{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TK4REFT6DAJ3Y5ACPV6G4EZN4D","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":"dc282bfbe5a281a67f3a57fd17c40b8b9eaf77c1e2771022c969a7a3eeb76dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-10T20:19:34Z","title_canon_sha256":"2fdef30adbef6d463458433894b9677420fa2420af0fc2821c60eeb4dc5e07c7"},"schema_version":"1.0","source":{"id":"1201.2162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2162","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2162v1","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2162","created_at":"2026-05-18T03:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"TK4REFT6DAJ3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TK4REFT6DAJ3Y5AC","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TK4REFT6","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:9c74c19ec2af3d747b0db52f224bfb62cb07761173abe722ff3eadfb554353f3","target":"graph","created_at":"2026-05-18T03:39:06Z","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":"The classical Onofri inequality in the two-dimensional sphere assumes a natural form in the plane when transformed via stereographic projection. We establish an optimal version of a generalization of this inequality in the d-dimensional Euclidean space for any d\\geq2, by considering the endpoint of a family of optimal Gagliardo-Nirenberg interpolation inequalities. Unlike the two-dimensional case, this extension involves a rather unexpected Sobolev-Orlicz norm, as well as a probability measure no longer related to stereographic projection.","authors_text":"Jean Dolbeault (CEREMADE), Manuel Del Pino (DIM)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-10T20:19:34Z","title":"The Euclidean Onofri inequality in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2162","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":"sha256:51e9e7d6d72fb60bb4f6e628aea9089cc1ea12a16a4be256d81bb93784ac8aa1","target":"record","created_at":"2026-05-18T03:39:06Z","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":"dc282bfbe5a281a67f3a57fd17c40b8b9eaf77c1e2771022c969a7a3eeb76dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-10T20:19:34Z","title_canon_sha256":"2fdef30adbef6d463458433894b9677420fa2420af0fc2821c60eeb4dc5e07c7"},"schema_version":"1.0","source":{"id":"1201.2162","kind":"arxiv","version":1}},"canonical_sha256":"9ab912167e1813bc74027d7c6e132de0db242059cd3e9aef82a13f837bddafba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ab912167e1813bc74027d7c6e132de0db242059cd3e9aef82a13f837bddafba","first_computed_at":"2026-05-18T03:39:06.419215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:06.419215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NNhTnNCL4x8I7N7BtEUjkgpSX/J/298u+UI9ay1aUY4iRCcPnRYLFk3a23AgkBYJgtjhYUm0X0iRDjNxA9okAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:06.420027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51e9e7d6d72fb60bb4f6e628aea9089cc1ea12a16a4be256d81bb93784ac8aa1","sha256:9c74c19ec2af3d747b0db52f224bfb62cb07761173abe722ff3eadfb554353f3"],"state_sha256":"f116e123ed419d4e476ffcf2b688dfe7345638e43f6a1f25f77e7b4bf862ea1f"}