{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:H2KXBHIQLCANLGDH6ZLBMX5YHQ","short_pith_number":"pith:H2KXBHIQ","canonical_record":{"source":{"id":"1403.5042","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-20T05:24:20Z","cross_cats_sorted":[],"title_canon_sha256":"cb7ab66fbdd4c08ccc2d9723b3e84a7aa9b97386b999f5ec8750d82dd7d28a87","abstract_canon_sha256":"f84849d4b3dd4a4d2c591d3cc5bcb2a2ac41b7526e725149b3f1cda9d8e1eb33"},"schema_version":"1.0"},"canonical_sha256":"3e95709d105880d59867f656165fb83c33efda02cf025275fd3dc51590f0c8cf","source":{"kind":"arxiv","id":"1403.5042","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5042","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5042v3","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5042","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"H2KXBHIQLCAN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"H2KXBHIQLCANLGDH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"H2KXBHIQ","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:H2KXBHIQLCANLGDH6ZLBMX5YHQ","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5042","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-20T05:24:20Z","cross_cats_sorted":[],"title_canon_sha256":"cb7ab66fbdd4c08ccc2d9723b3e84a7aa9b97386b999f5ec8750d82dd7d28a87","abstract_canon_sha256":"f84849d4b3dd4a4d2c591d3cc5bcb2a2ac41b7526e725149b3f1cda9d8e1eb33"},"schema_version":"1.0"},"canonical_sha256":"3e95709d105880d59867f656165fb83c33efda02cf025275fd3dc51590f0c8cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:55.627705Z","signature_b64":"XrhxVE6gW4VYOnqBgJvxhQTyuJ5L3M7/qekjByi1+Mn1vSW6anVF/BAmr28K5wJ62sjX+3OYsu8/mL/YjmnRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e95709d105880d59867f656165fb83c33efda02cf025275fd3dc51590f0c8cf","last_reissued_at":"2026-05-18T02:03:55.626913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:55.626913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5042","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TnoubSvnMm8xFlr8WEHbkdsNIAhcmnWrgoJIjwIkZVMkFaK/zf4f8QynNaW7Cw9VH7B4SrdlQLpbElSyNjiFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:59:36.510377Z"},"content_sha256":"014d3be918218527668c79f09e3e7c4539663aaf326175441a59c8cdfac3c51b","schema_version":"1.0","event_id":"sha256:014d3be918218527668c79f09e3e7c4539663aaf326175441a59c8cdfac3c51b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:H2KXBHIQLCANLGDH6ZLBMX5YHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Moser-Trudinger-Onofri inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaspard Jankowiak (CEREMADE), Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE)","submitted_at":"2014-03-20T05:24:20Z","abstract_excerpt":"This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, we state several elementary remarks. We also prove various new results. We give a proof of the inequality using mass transportation methods (in the radial case), consistently with similar results for Sobolev's inequalities. We investigate how du"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5042","kind":"arxiv","version":3},"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":"2026-05-18T02:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHiXzixusHye0A6JMUFHW9xf7YO6LqMiiVCDB4DZ2WtD8pYzbRtmhwyAyZRrOfJJaQJehNsh0+f/60KDmpjwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:59:36.510713Z"},"content_sha256":"e70b66a803b98eea6906964df2bcdafe579edd66bcdadcdbc63bd97e1ffdc5ff","schema_version":"1.0","event_id":"sha256:e70b66a803b98eea6906964df2bcdafe579edd66bcdadcdbc63bd97e1ffdc5ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H2KXBHIQLCANLGDH6ZLBMX5YHQ/bundle.json","state_url":"https://pith.science/pith/H2KXBHIQLCANLGDH6ZLBMX5YHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H2KXBHIQLCANLGDH6ZLBMX5YHQ/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":"2026-06-08T21:59:36Z","links":{"resolver":"https://pith.science/pith/H2KXBHIQLCANLGDH6ZLBMX5YHQ","bundle":"https://pith.science/pith/H2KXBHIQLCANLGDH6ZLBMX5YHQ/bundle.json","state":"https://pith.science/pith/H2KXBHIQLCANLGDH6ZLBMX5YHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H2KXBHIQLCANLGDH6ZLBMX5YHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:H2KXBHIQLCANLGDH6ZLBMX5YHQ","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":"f84849d4b3dd4a4d2c591d3cc5bcb2a2ac41b7526e725149b3f1cda9d8e1eb33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-20T05:24:20Z","title_canon_sha256":"cb7ab66fbdd4c08ccc2d9723b3e84a7aa9b97386b999f5ec8750d82dd7d28a87"},"schema_version":"1.0","source":{"id":"1403.5042","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5042","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5042v3","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5042","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"H2KXBHIQLCAN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"H2KXBHIQLCANLGDH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"H2KXBHIQ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:e70b66a803b98eea6906964df2bcdafe579edd66bcdadcdbc63bd97e1ffdc5ff","target":"graph","created_at":"2026-05-18T02:03:55Z","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 results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, we state several elementary remarks. We also prove various new results. We give a proof of the inequality using mass transportation methods (in the radial case), consistently with similar results for Sobolev's inequalities. We investigate how du","authors_text":"Gaspard Jankowiak (CEREMADE), 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":"2014-03-20T05:24:20Z","title":"The Moser-Trudinger-Onofri inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5042","kind":"arxiv","version":3},"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":"sha256:014d3be918218527668c79f09e3e7c4539663aaf326175441a59c8cdfac3c51b","target":"record","created_at":"2026-05-18T02:03:55Z","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":"f84849d4b3dd4a4d2c591d3cc5bcb2a2ac41b7526e725149b3f1cda9d8e1eb33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-20T05:24:20Z","title_canon_sha256":"cb7ab66fbdd4c08ccc2d9723b3e84a7aa9b97386b999f5ec8750d82dd7d28a87"},"schema_version":"1.0","source":{"id":"1403.5042","kind":"arxiv","version":3}},"canonical_sha256":"3e95709d105880d59867f656165fb83c33efda02cf025275fd3dc51590f0c8cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e95709d105880d59867f656165fb83c33efda02cf025275fd3dc51590f0c8cf","first_computed_at":"2026-05-18T02:03:55.626913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:55.626913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XrhxVE6gW4VYOnqBgJvxhQTyuJ5L3M7/qekjByi1+Mn1vSW6anVF/BAmr28K5wJ62sjX+3OYsu8/mL/YjmnRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:55.627705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5042","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:014d3be918218527668c79f09e3e7c4539663aaf326175441a59c8cdfac3c51b","sha256:e70b66a803b98eea6906964df2bcdafe579edd66bcdadcdbc63bd97e1ffdc5ff"],"state_sha256":"e415ff72d47ba1394baee5f6eef1cf08730859236ef457a70f41d680676a7ef7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Njb0wmkX2DFMAPpzMmhFsxxPD+xS3iELCd0MJgFviWJdoZ1CkBdg7eBmqrE2ZPZZrNhl64/uSi5iFbp385/QBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:59:36.512529Z","bundle_sha256":"0dc9d1aa05eed8dc31253272df669e8c3c5029bec73ee2a1eb9fd0a3cb0467e7"}}