{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:O7QLCRQ4AC55K4VPSOUHMXBH3B","short_pith_number":"pith:O7QLCRQ4","canonical_record":{"source":{"id":"1705.00030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-28T18:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"6286fad867de031b2536da6d216e002660aa583e93a3dae54fe14eaeae8ef470","abstract_canon_sha256":"082737d0219e2a9958f5e37f7661765680e13c5b5aeba63a8f32ee1a289ec33e"},"schema_version":"1.0"},"canonical_sha256":"77e0b1461c00bbd572af93a8765c27d8521f385bdc0f0afbac01eed57063cfd9","source":{"kind":"arxiv","id":"1705.00030","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00030","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00030v2","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00030","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"O7QLCRQ4AC55","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7QLCRQ4AC55K4VP","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7QLCRQ4","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:O7QLCRQ4AC55K4VPSOUHMXBH3B","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-28T18:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"6286fad867de031b2536da6d216e002660aa583e93a3dae54fe14eaeae8ef470","abstract_canon_sha256":"082737d0219e2a9958f5e37f7661765680e13c5b5aeba63a8f32ee1a289ec33e"},"schema_version":"1.0"},"canonical_sha256":"77e0b1461c00bbd572af93a8765c27d8521f385bdc0f0afbac01eed57063cfd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:28.977679Z","signature_b64":"sVr7dHeYazDbs72o/9jOwt3MlancAabX5eczMMlhkM4dnrOQDkm15yWmarPLDKWzbqO9aKtuA8jy4yswtt32BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77e0b1461c00bbd572af93a8765c27d8521f385bdc0f0afbac01eed57063cfd9","last_reissued_at":"2026-05-18T00:14:28.976972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:28.976972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00030","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":"2026-05-18T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+eP66Rv7dsl51WCI4kkEcbBUFg5KvgrygZ6dGH8sF2+9E8TXSo58PmUVaxsM+oQLp36ztXj4IMPyikT5KNuHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:34:27.344371Z"},"content_sha256":"8e024f97980cdbd2b8c1f5e0da7083069d80bbf94e4afbc95cbd0e8ea689fb3a","schema_version":"1.0","event_id":"sha256:8e024f97980cdbd2b8c1f5e0da7083069d80bbf94e4afbc95cbd0e8ea689fb3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:O7QLCRQ4AC55K4VPSOUHMXBH3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Inequalities for the Fractional Laplacian and the Existence of Extremals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel Salort, Irene Drelichman, Pablo De N\\'apoli","submitted_at":"2017-04-28T18:38:07Z","abstract_excerpt":"In this article we obtain improved versions of Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein-Weiss inequality in certain cases, some of which are not contained in the celebrated theorem of E. Lieb."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00030","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":"2026-05-18T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WkWNMxqZt1nJ3gwBCNkdcC0zk2jb0AtS5lFLEZsa+T+TgIbbhuaXlF4bBQ9XsS9+H/m0/foGkqH4K2XfXc0NAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:34:27.344788Z"},"content_sha256":"84c7e782068ab91c23ffe63bd50c1244e1ecb3d46f0b7ccd45d4dc5e6f081bfd","schema_version":"1.0","event_id":"sha256:84c7e782068ab91c23ffe63bd50c1244e1ecb3d46f0b7ccd45d4dc5e6f081bfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7QLCRQ4AC55K4VPSOUHMXBH3B/bundle.json","state_url":"https://pith.science/pith/O7QLCRQ4AC55K4VPSOUHMXBH3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7QLCRQ4AC55K4VPSOUHMXBH3B/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":"2026-06-03T16:34:27Z","links":{"resolver":"https://pith.science/pith/O7QLCRQ4AC55K4VPSOUHMXBH3B","bundle":"https://pith.science/pith/O7QLCRQ4AC55K4VPSOUHMXBH3B/bundle.json","state":"https://pith.science/pith/O7QLCRQ4AC55K4VPSOUHMXBH3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7QLCRQ4AC55K4VPSOUHMXBH3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O7QLCRQ4AC55K4VPSOUHMXBH3B","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":"082737d0219e2a9958f5e37f7661765680e13c5b5aeba63a8f32ee1a289ec33e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-28T18:38:07Z","title_canon_sha256":"6286fad867de031b2536da6d216e002660aa583e93a3dae54fe14eaeae8ef470"},"schema_version":"1.0","source":{"id":"1705.00030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00030","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00030v2","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00030","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"O7QLCRQ4AC55","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7QLCRQ4AC55K4VP","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7QLCRQ4","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:84c7e782068ab91c23ffe63bd50c1244e1ecb3d46f0b7ccd45d4dc5e6f081bfd","target":"graph","created_at":"2026-05-18T00:14:28Z","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":"In this article we obtain improved versions of Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein-Weiss inequality in certain cases, some of which are not contained in the celebrated theorem of E. Lieb.","authors_text":"Ariel Salort, Irene Drelichman, Pablo De N\\'apoli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-28T18:38:07Z","title":"Weighted Inequalities for the Fractional Laplacian and the Existence of Extremals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00030","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":"sha256:8e024f97980cdbd2b8c1f5e0da7083069d80bbf94e4afbc95cbd0e8ea689fb3a","target":"record","created_at":"2026-05-18T00:14:28Z","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":"082737d0219e2a9958f5e37f7661765680e13c5b5aeba63a8f32ee1a289ec33e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-28T18:38:07Z","title_canon_sha256":"6286fad867de031b2536da6d216e002660aa583e93a3dae54fe14eaeae8ef470"},"schema_version":"1.0","source":{"id":"1705.00030","kind":"arxiv","version":2}},"canonical_sha256":"77e0b1461c00bbd572af93a8765c27d8521f385bdc0f0afbac01eed57063cfd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77e0b1461c00bbd572af93a8765c27d8521f385bdc0f0afbac01eed57063cfd9","first_computed_at":"2026-05-18T00:14:28.976972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:28.976972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sVr7dHeYazDbs72o/9jOwt3MlancAabX5eczMMlhkM4dnrOQDkm15yWmarPLDKWzbqO9aKtuA8jy4yswtt32BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:28.977679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e024f97980cdbd2b8c1f5e0da7083069d80bbf94e4afbc95cbd0e8ea689fb3a","sha256:84c7e782068ab91c23ffe63bd50c1244e1ecb3d46f0b7ccd45d4dc5e6f081bfd"],"state_sha256":"cbe93d2d97fb488803eeaaa224e95d401954275e652ca56ccbcad5387e116d10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vp5BJx1PobXmw9CLLmVI5vmWQipH3hI3lm474cnxbSXRe6i0Jz5oXmBcC4wT22pcdk+iJlGqzxZtjEKSCV6YCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:34:27.347021Z","bundle_sha256":"7d0c4e78036dc4b66028ad84ee006961738244f7a93ff302fce6064cb46ad9d1"}}