{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6LIKJHRICRU4C3VC34JAK2NVJ5","short_pith_number":"pith:6LIKJHRI","canonical_record":{"source":{"id":"1309.1302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T10:26:24Z","cross_cats_sorted":[],"title_canon_sha256":"e20de66a68a394dd557ffb39ca13819c8bef4afe179e399c619ce8cf798c6253","abstract_canon_sha256":"d4140327946b129117c776ebdc66d9f45299bee65d147cdc5c744d01931de706"},"schema_version":"1.0"},"canonical_sha256":"f2d0a49e281469c16ea2df120569b54f5cf85ddcbf90d990b998835d6f648ff8","source":{"kind":"arxiv","id":"1309.1302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1302","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1302v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1302","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"6LIKJHRICRU4","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6LIKJHRICRU4C3VC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6LIKJHRI","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6LIKJHRICRU4C3VC34JAK2NVJ5","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T10:26:24Z","cross_cats_sorted":[],"title_canon_sha256":"e20de66a68a394dd557ffb39ca13819c8bef4afe179e399c619ce8cf798c6253","abstract_canon_sha256":"d4140327946b129117c776ebdc66d9f45299bee65d147cdc5c744d01931de706"},"schema_version":"1.0"},"canonical_sha256":"f2d0a49e281469c16ea2df120569b54f5cf85ddcbf90d990b998835d6f648ff8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:07.681562Z","signature_b64":"rQKFDf4rfzIsiiVCGU5Yao13+iC4Ny+PODq51nEHJfeq7SRp5if2uTqbosHIEbr4E2NByTugVV44/9oJRPUDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2d0a49e281469c16ea2df120569b54f5cf85ddcbf90d990b998835d6f648ff8","last_reissued_at":"2026-05-18T03:14:07.681156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:07.681156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1302","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"quSD9KyfcS5hM6bTkV8UmelYGALWqFQ2Cl9cQVnXwBukbaSs/4gCuAyc2IX/P0+Z1pavVS9HRRn5z0E2ElqDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:49:58.222152Z"},"content_sha256":"8096ec6337846da463048b8e7ad6412fc184168edf15a711a9f07503aa59edc7","schema_version":"1.0","event_id":"sha256:8096ec6337846da463048b8e7ad6412fc184168edf15a711a9f07503aa59edc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6LIKJHRICRU4C3VC34JAK2NVJ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Calderon-Zygmund and Rellich inequalities in L^p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Spina, G. Metafune, M. Sobajima","submitted_at":"2013-09-05T10:26:24Z","abstract_excerpt":"We find necessary and sufficient conditions for the validity of weighted Rellich and Calderon-Zygmund inequalities in L^p, 1 \\leq p \\leq \\infty, in the whole space and in the half-space with Dirichlet boundary conditions. General operators like L=\\Delta+c\\frac{x}{|x|^2}\\cdot\\nabla-\\frac{b}{|x|^2} are considered. We compute best constants in some situations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1302","kind":"arxiv","version":1},"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":"2026-05-18T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pp4QURYxJDJkk3s8wpQHm+4NRO9mBR5525lGqhAkTlywywygzCummaxJLc8Fib6Xa0VSLfo9e97z2KS3e7apCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:49:58.222856Z"},"content_sha256":"619b27f266238fe0b8e8601b992bb01b26f3fbe4727022ce0358e4c1b2e391b2","schema_version":"1.0","event_id":"sha256:619b27f266238fe0b8e8601b992bb01b26f3fbe4727022ce0358e4c1b2e391b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LIKJHRICRU4C3VC34JAK2NVJ5/bundle.json","state_url":"https://pith.science/pith/6LIKJHRICRU4C3VC34JAK2NVJ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LIKJHRICRU4C3VC34JAK2NVJ5/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":"2026-06-11T22:49:58Z","links":{"resolver":"https://pith.science/pith/6LIKJHRICRU4C3VC34JAK2NVJ5","bundle":"https://pith.science/pith/6LIKJHRICRU4C3VC34JAK2NVJ5/bundle.json","state":"https://pith.science/pith/6LIKJHRICRU4C3VC34JAK2NVJ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LIKJHRICRU4C3VC34JAK2NVJ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6LIKJHRICRU4C3VC34JAK2NVJ5","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":"d4140327946b129117c776ebdc66d9f45299bee65d147cdc5c744d01931de706","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T10:26:24Z","title_canon_sha256":"e20de66a68a394dd557ffb39ca13819c8bef4afe179e399c619ce8cf798c6253"},"schema_version":"1.0","source":{"id":"1309.1302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1302","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1302v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1302","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"6LIKJHRICRU4","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6LIKJHRICRU4C3VC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6LIKJHRI","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:619b27f266238fe0b8e8601b992bb01b26f3fbe4727022ce0358e4c1b2e391b2","target":"graph","created_at":"2026-05-18T03:14:07Z","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":"We find necessary and sufficient conditions for the validity of weighted Rellich and Calderon-Zygmund inequalities in L^p, 1 \\leq p \\leq \\infty, in the whole space and in the half-space with Dirichlet boundary conditions. General operators like L=\\Delta+c\\frac{x}{|x|^2}\\cdot\\nabla-\\frac{b}{|x|^2} are considered. We compute best constants in some situations.","authors_text":"C. Spina, G. Metafune, M. Sobajima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T10:26:24Z","title":"Weighted Calderon-Zygmund and Rellich inequalities in L^p"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1302","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":"sha256:8096ec6337846da463048b8e7ad6412fc184168edf15a711a9f07503aa59edc7","target":"record","created_at":"2026-05-18T03:14:07Z","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":"d4140327946b129117c776ebdc66d9f45299bee65d147cdc5c744d01931de706","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-05T10:26:24Z","title_canon_sha256":"e20de66a68a394dd557ffb39ca13819c8bef4afe179e399c619ce8cf798c6253"},"schema_version":"1.0","source":{"id":"1309.1302","kind":"arxiv","version":1}},"canonical_sha256":"f2d0a49e281469c16ea2df120569b54f5cf85ddcbf90d990b998835d6f648ff8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2d0a49e281469c16ea2df120569b54f5cf85ddcbf90d990b998835d6f648ff8","first_computed_at":"2026-05-18T03:14:07.681156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:07.681156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rQKFDf4rfzIsiiVCGU5Yao13+iC4Ny+PODq51nEHJfeq7SRp5if2uTqbosHIEbr4E2NByTugVV44/9oJRPUDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:07.681562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8096ec6337846da463048b8e7ad6412fc184168edf15a711a9f07503aa59edc7","sha256:619b27f266238fe0b8e8601b992bb01b26f3fbe4727022ce0358e4c1b2e391b2"],"state_sha256":"3d07e9eb52b053d3650af59f29df3a0ef365454fc91f2c603da83c782dae080d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WlHgMbUTmvJ1YOE/JwWPuwUTBL+hF/NLKpjbYgzUVLI7+oB3VvDX0qIjAAh7N9r1c7xLfMOUZIf4ig97E5OVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:49:58.227020Z","bundle_sha256":"5ff7dd6412e53a19ee275d8d6ab97d6fd9b2e97a0f8b644067f4eea33de4fa14"}}