{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:SEBP7Z4RUR6DH7A3JZNQSHZ3WI","short_pith_number":"pith:SEBP7Z4R","canonical_record":{"source":{"id":"2308.04111","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-08T07:53:21Z","cross_cats_sorted":[],"title_canon_sha256":"3686a4550e54c464cefc09b6d13263aeabcca56aec0d066a314adbb979fd9912","abstract_canon_sha256":"08e8be8b7699003c79e729014c477296698e6606c85bb60ae2943ed603220ff3"},"schema_version":"1.0"},"canonical_sha256":"9102ffe791a47c33fc1b4e5b091f3bb218ea0d76db5f830422bdef5eaf7ad50b","source":{"kind":"arxiv","id":"2308.04111","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04111","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04111v4","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04111","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"SEBP7Z4RUR6D","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"pith_short_16","alias_value":"SEBP7Z4RUR6DH7A3","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"pith_short_8","alias_value":"SEBP7Z4R","created_at":"2026-07-05T09:54:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:SEBP7Z4RUR6DH7A3JZNQSHZ3WI","target":"record","payload":{"canonical_record":{"source":{"id":"2308.04111","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-08T07:53:21Z","cross_cats_sorted":[],"title_canon_sha256":"3686a4550e54c464cefc09b6d13263aeabcca56aec0d066a314adbb979fd9912","abstract_canon_sha256":"08e8be8b7699003c79e729014c477296698e6606c85bb60ae2943ed603220ff3"},"schema_version":"1.0"},"canonical_sha256":"9102ffe791a47c33fc1b4e5b091f3bb218ea0d76db5f830422bdef5eaf7ad50b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:42.891274Z","signature_b64":"WBgo6FBLfdbJ7+l8Xwl83toPlIO9ETaYLr6Rr3XFKLnj9DxtV10TfA0Ed4IXFmIUaOjXOrb3HVW00S/JWe+YDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9102ffe791a47c33fc1b4e5b091f3bb218ea0d76db5f830422bdef5eaf7ad50b","last_reissued_at":"2026-07-05T09:54:42.890841Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:42.890841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.04111","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CVj5waCbjkOXZD4r7buvjHXNAiN4SUbotixzx39VZ1FGuyF4debaHAPgVdcQqs5/pJqvUhia+zbLKNRNaDsABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:18:26.895121Z"},"content_sha256":"c91181d80f70aa30451c33b8a9582650b54f003962e090d9a6b404d0bfef65ce","schema_version":"1.0","event_id":"sha256:c91181d80f70aa30451c33b8a9582650b54f003962e090d9a6b404d0bfef65ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:SEBP7Z4RUR6DH7A3JZNQSHZ3WI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the stability constant of Caffarelli-Kohn-Nirenberg inequality","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shengbing Deng, Xingliang Tian","submitted_at":"2023-08-08T07:53:21Z","abstract_excerpt":"By using a spectral analysis, we first show that the Caffarelli--Kohn--Nirenberg inequality with gradient remainder term of any order less than $4$ does not hold on the {\\em Felli-Schneider} curve $b_{\\mathrm{FS}}(a)$. Furthermore, we prove the existence of minimizers of sharp stability constant of Caffarelli--Kohn--Nirenberg inequality near the new curve $b^*_{\\mathrm{FS}}(a)(>b_{\\mathrm{FS}}(a))$, which extends the work of Wei and Wu [Math. Z., 2024] to a sightly larger region."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04111","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.04111/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jL0iZtigmtP4v3Y5spm4/tkp1dJ7l1Ny05Em0qV/GcSZ5AMtkyh+owaXoxlQflTNAWEssxHEbA3mLImb1egeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:18:26.895649Z"},"content_sha256":"af90a235b4ca93f8b5b554f3ca61625688be0f451c7061e00c0b78f908b01312","schema_version":"1.0","event_id":"sha256:af90a235b4ca93f8b5b554f3ca61625688be0f451c7061e00c0b78f908b01312"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEBP7Z4RUR6DH7A3JZNQSHZ3WI/bundle.json","state_url":"https://pith.science/pith/SEBP7Z4RUR6DH7A3JZNQSHZ3WI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEBP7Z4RUR6DH7A3JZNQSHZ3WI/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":"2026-08-21T01:18:26Z","links":{"resolver":"https://pith.science/pith/SEBP7Z4RUR6DH7A3JZNQSHZ3WI","bundle":"https://pith.science/pith/SEBP7Z4RUR6DH7A3JZNQSHZ3WI/bundle.json","state":"https://pith.science/pith/SEBP7Z4RUR6DH7A3JZNQSHZ3WI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEBP7Z4RUR6DH7A3JZNQSHZ3WI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SEBP7Z4RUR6DH7A3JZNQSHZ3WI","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":"08e8be8b7699003c79e729014c477296698e6606c85bb60ae2943ed603220ff3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-08T07:53:21Z","title_canon_sha256":"3686a4550e54c464cefc09b6d13263aeabcca56aec0d066a314adbb979fd9912"},"schema_version":"1.0","source":{"id":"2308.04111","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04111","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04111v4","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04111","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"SEBP7Z4RUR6D","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"pith_short_16","alias_value":"SEBP7Z4RUR6DH7A3","created_at":"2026-07-05T09:54:42Z"},{"alias_kind":"pith_short_8","alias_value":"SEBP7Z4R","created_at":"2026-07-05T09:54:42Z"}],"graph_snapshots":[{"event_id":"sha256:af90a235b4ca93f8b5b554f3ca61625688be0f451c7061e00c0b78f908b01312","target":"graph","created_at":"2026-07-05T09:54:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.04111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By using a spectral analysis, we first show that the Caffarelli--Kohn--Nirenberg inequality with gradient remainder term of any order less than $4$ does not hold on the {\\em Felli-Schneider} curve $b_{\\mathrm{FS}}(a)$. Furthermore, we prove the existence of minimizers of sharp stability constant of Caffarelli--Kohn--Nirenberg inequality near the new curve $b^*_{\\mathrm{FS}}(a)(>b_{\\mathrm{FS}}(a))$, which extends the work of Wei and Wu [Math. Z., 2024] to a sightly larger region.","authors_text":"Shengbing Deng, Xingliang Tian","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-08T07:53:21Z","title":"On the stability constant of Caffarelli-Kohn-Nirenberg inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04111","kind":"arxiv","version":4},"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:c91181d80f70aa30451c33b8a9582650b54f003962e090d9a6b404d0bfef65ce","target":"record","created_at":"2026-07-05T09:54:42Z","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":"08e8be8b7699003c79e729014c477296698e6606c85bb60ae2943ed603220ff3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-08T07:53:21Z","title_canon_sha256":"3686a4550e54c464cefc09b6d13263aeabcca56aec0d066a314adbb979fd9912"},"schema_version":"1.0","source":{"id":"2308.04111","kind":"arxiv","version":4}},"canonical_sha256":"9102ffe791a47c33fc1b4e5b091f3bb218ea0d76db5f830422bdef5eaf7ad50b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9102ffe791a47c33fc1b4e5b091f3bb218ea0d76db5f830422bdef5eaf7ad50b","first_computed_at":"2026-07-05T09:54:42.890841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:42.890841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WBgo6FBLfdbJ7+l8Xwl83toPlIO9ETaYLr6Rr3XFKLnj9DxtV10TfA0Ed4IXFmIUaOjXOrb3HVW00S/JWe+YDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:42.891274Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.04111","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c91181d80f70aa30451c33b8a9582650b54f003962e090d9a6b404d0bfef65ce","sha256:af90a235b4ca93f8b5b554f3ca61625688be0f451c7061e00c0b78f908b01312"],"state_sha256":"843b8128181503d17c9575a6790b3093d2e72ad6615dfcef36f0d95e9a688b78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pHtO8iTy9J27/vKFKFq3zxdNO/phpOxb42E202nSBly0pisCF03p98k8/8HzCWGBmx+3GguPWny4N6btPfJKAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T01:18:26.900604Z","bundle_sha256":"7c0a75d810d52b19c9f408a391ad8c1b1bcb78b1a862d0bc87c2a20abd56b8dc"}}