{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RUL3IDZREFDN6EF5QCZNQ7UPG2","short_pith_number":"pith:RUL3IDZR","canonical_record":{"source":{"id":"1404.7338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-29T12:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"b452d88da0d9730db0c7a2bba44c42372bf462943fca6b43f5d9751fa70f2a1d","abstract_canon_sha256":"ff51f696e5affe080d1bf7917640b5189797778a5942adbec0b238aab514eaa7"},"schema_version":"1.0"},"canonical_sha256":"8d17b40f312146df10bd80b2d87e8f36ab19404b1566ae473c7984b896cca261","source":{"kind":"arxiv","id":"1404.7338","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7338","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7338v2","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7338","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"RUL3IDZREFDN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RUL3IDZREFDN6EF5","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RUL3IDZR","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RUL3IDZREFDN6EF5QCZNQ7UPG2","target":"record","payload":{"canonical_record":{"source":{"id":"1404.7338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-29T12:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"b452d88da0d9730db0c7a2bba44c42372bf462943fca6b43f5d9751fa70f2a1d","abstract_canon_sha256":"ff51f696e5affe080d1bf7917640b5189797778a5942adbec0b238aab514eaa7"},"schema_version":"1.0"},"canonical_sha256":"8d17b40f312146df10bd80b2d87e8f36ab19404b1566ae473c7984b896cca261","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:38.229762Z","signature_b64":"o0WWbgMcq30pblu8pmOcEfoe8AQJFjvJnXJmYRylS4NEnutkhTLUjHxDiWd7r/zTxW1pnyb8qoI0nwyvOYM7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d17b40f312146df10bd80b2d87e8f36ab19404b1566ae473c7984b896cca261","last_reissued_at":"2026-05-18T01:12:38.229420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:38.229420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.7338","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lf4rJJykf2+g3qhJq33oAqiyvPUkwhPDbuEbMjVSlifgOeWzxlO464k/9y7ruVo7x8yseP+4OTdIjNl09IaMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:41:04.572031Z"},"content_sha256":"2d37c1a3aaa51b4399aea53550664c0cbe41c7e67baea293e0e5d4d43792c151","schema_version":"1.0","event_id":"sha256:2d37c1a3aaa51b4399aea53550664c0cbe41c7e67baea293e0e5d4d43792c151"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RUL3IDZREFDN6EF5QCZNQ7UPG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Onofri inequalities and rigidity results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaspard Jankowiak (RICAM), Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE)","submitted_at":"2014-04-29T12:33:36Z","abstract_excerpt":"This paper is devoted to the Moser-Trudinger-Onofri inequality on smooth compact connected Riemannian manifolds. We establish a rigidity result for the Euler-Lagrange equation and deduce an estimate of the optimal constant in the inequality on two-dimensional closed Riemannian manifolds. Compared to existing results, we provide a non-local criterion which is well adapted to variational methods, introduce a nonlinear flow along which the evolution of a functional related with the inequality is monotone and get an integral remainder term which allows us to discuss optimality issues. As an import"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7338","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AmkTV7I7ZTvkRk23Tkx2bcMkl9DQiMVe/Qn+I4GuVS5aaUJZz+tK2Ms8ZKRCkDvYElvvcUbcy1+xbmuDwxJaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:41:04.572752Z"},"content_sha256":"f06275d1b83ca5cd85b3eefc4faa87cfc35bb5f012bf914e3748e4d8cc60b4de","schema_version":"1.0","event_id":"sha256:f06275d1b83ca5cd85b3eefc4faa87cfc35bb5f012bf914e3748e4d8cc60b4de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUL3IDZREFDN6EF5QCZNQ7UPG2/bundle.json","state_url":"https://pith.science/pith/RUL3IDZREFDN6EF5QCZNQ7UPG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUL3IDZREFDN6EF5QCZNQ7UPG2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T20:41:04Z","links":{"resolver":"https://pith.science/pith/RUL3IDZREFDN6EF5QCZNQ7UPG2","bundle":"https://pith.science/pith/RUL3IDZREFDN6EF5QCZNQ7UPG2/bundle.json","state":"https://pith.science/pith/RUL3IDZREFDN6EF5QCZNQ7UPG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUL3IDZREFDN6EF5QCZNQ7UPG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RUL3IDZREFDN6EF5QCZNQ7UPG2","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":"ff51f696e5affe080d1bf7917640b5189797778a5942adbec0b238aab514eaa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-29T12:33:36Z","title_canon_sha256":"b452d88da0d9730db0c7a2bba44c42372bf462943fca6b43f5d9751fa70f2a1d"},"schema_version":"1.0","source":{"id":"1404.7338","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7338","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7338v2","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7338","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"RUL3IDZREFDN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RUL3IDZREFDN6EF5","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RUL3IDZR","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f06275d1b83ca5cd85b3eefc4faa87cfc35bb5f012bf914e3748e4d8cc60b4de","target":"graph","created_at":"2026-05-18T01:12:38Z","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 paper is devoted to the Moser-Trudinger-Onofri inequality on smooth compact connected Riemannian manifolds. We establish a rigidity result for the Euler-Lagrange equation and deduce an estimate of the optimal constant in the inequality on two-dimensional closed Riemannian manifolds. Compared to existing results, we provide a non-local criterion which is well adapted to variational methods, introduce a nonlinear flow along which the evolution of a functional related with the inequality is monotone and get an integral remainder term which allows us to discuss optimality issues. As an import","authors_text":"Gaspard Jankowiak (RICAM), Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-29T12:33:36Z","title":"Onofri inequalities and rigidity results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7338","kind":"arxiv","version":2},"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":"sha256:2d37c1a3aaa51b4399aea53550664c0cbe41c7e67baea293e0e5d4d43792c151","target":"record","created_at":"2026-05-18T01:12:38Z","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":"ff51f696e5affe080d1bf7917640b5189797778a5942adbec0b238aab514eaa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-29T12:33:36Z","title_canon_sha256":"b452d88da0d9730db0c7a2bba44c42372bf462943fca6b43f5d9751fa70f2a1d"},"schema_version":"1.0","source":{"id":"1404.7338","kind":"arxiv","version":2}},"canonical_sha256":"8d17b40f312146df10bd80b2d87e8f36ab19404b1566ae473c7984b896cca261","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d17b40f312146df10bd80b2d87e8f36ab19404b1566ae473c7984b896cca261","first_computed_at":"2026-05-18T01:12:38.229420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:38.229420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o0WWbgMcq30pblu8pmOcEfoe8AQJFjvJnXJmYRylS4NEnutkhTLUjHxDiWd7r/zTxW1pnyb8qoI0nwyvOYM7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:38.229762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7338","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d37c1a3aaa51b4399aea53550664c0cbe41c7e67baea293e0e5d4d43792c151","sha256:f06275d1b83ca5cd85b3eefc4faa87cfc35bb5f012bf914e3748e4d8cc60b4de"],"state_sha256":"aa62bdc22b919bfc8c502f1d3c31587b53285efe5ab6c0056361108df1461d10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7biUbtwg/vGsmvHMSBNj4xN28SA8c4nOmixZ1FsegclyYmClHWG39s8FMXxY4EtykyjjAhyeM0EHVknjRhb7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:41:04.576205Z","bundle_sha256":"9626caaa0896c0a6a1d9dd0e851aa54d041dafdd9f13174a534bd83c2061cf64"}}