{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ADJ243VE7OVZXHMQHBCMYBXR3G","short_pith_number":"pith:ADJ243VE","canonical_record":{"source":{"id":"1312.5823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T06:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"7f9eeb3398b7c4f42af3df5b5581122132c5a33d1bed7f47b08c0d542315507a","abstract_canon_sha256":"067d71cab118083e86c099ac11f8dd5500250ac38d15bec8eb19c8820b83bd9e"},"schema_version":"1.0"},"canonical_sha256":"00d3ae6ea4fbab9b9d903844cc06f1d9b9c51ef2c60023a6df5663476eb89dee","source":{"kind":"arxiv","id":"1312.5823","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5823","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5823v1","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5823","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"ADJ243VE7OVZ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ADJ243VE7OVZXHMQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ADJ243VE","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ADJ243VE7OVZXHMQHBCMYBXR3G","target":"record","payload":{"canonical_record":{"source":{"id":"1312.5823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T06:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"7f9eeb3398b7c4f42af3df5b5581122132c5a33d1bed7f47b08c0d542315507a","abstract_canon_sha256":"067d71cab118083e86c099ac11f8dd5500250ac38d15bec8eb19c8820b83bd9e"},"schema_version":"1.0"},"canonical_sha256":"00d3ae6ea4fbab9b9d903844cc06f1d9b9c51ef2c60023a6df5663476eb89dee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:07.762503Z","signature_b64":"9R1Ww1VlwnObWmZAuwtnOqSkqG1Wg9dD/aaHguQLWoB4L0qc5mZtqGNLHh0F8R5pjsGmw3nzGt344ef1wHZyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00d3ae6ea4fbab9b9d903844cc06f1d9b9c51ef2c60023a6df5663476eb89dee","last_reissued_at":"2026-05-18T03:04:07.761930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:07.761930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.5823","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":"2026-05-18T03:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hu7wwUyD7/of2uXIcFBWIUADaafm1DHq/FvzDdTc6cE4CKSzPOYKgI75ANnqsadMQ80a1kzCRxZBqHKPwN7oBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:45:52.445025Z"},"content_sha256":"c1511c4310e60079810de1779d200899526d84b861c335572d319b8a4faee744","schema_version":"1.0","event_id":"sha256:c1511c4310e60079810de1779d200899526d84b861c335572d319b8a4faee744"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ADJ243VE7OVZXHMQHBCMYBXR3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lorentz space estimates for vector fields with divergence and curl in Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Xingfei Xiang, Yoshikazu Giga","submitted_at":"2013-12-20T06:47:06Z","abstract_excerpt":"In this note, we establish the estimate on the Lorentz space $L(3/2,1)$ for vector fields in bounded domains under the assumption that the normal or the tangential component of the vector fields on the boundary vanishing. We prove that the $L(3/2,1)$ norm of the vector field can be controlled by the norms of its divergence and curl in the atomic Hardy spaces and the $L^1$ norm of the vector field itself."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5823","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":"2026-05-18T03:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZNJctaUT6LAGhoJ1N7BBtjrXF3OoJZcQu0nXBywFwPaKFljazXGq3I/2U1MHwCExG4rKrn6MMWg2DcGU+oTSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:45:52.445375Z"},"content_sha256":"39929ed665099a69424704169f4b479e18b511528e22325d101380c9c82b4157","schema_version":"1.0","event_id":"sha256:39929ed665099a69424704169f4b479e18b511528e22325d101380c9c82b4157"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ADJ243VE7OVZXHMQHBCMYBXR3G/bundle.json","state_url":"https://pith.science/pith/ADJ243VE7OVZXHMQHBCMYBXR3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ADJ243VE7OVZXHMQHBCMYBXR3G/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":"2026-06-22T12:45:52Z","links":{"resolver":"https://pith.science/pith/ADJ243VE7OVZXHMQHBCMYBXR3G","bundle":"https://pith.science/pith/ADJ243VE7OVZXHMQHBCMYBXR3G/bundle.json","state":"https://pith.science/pith/ADJ243VE7OVZXHMQHBCMYBXR3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ADJ243VE7OVZXHMQHBCMYBXR3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ADJ243VE7OVZXHMQHBCMYBXR3G","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":"067d71cab118083e86c099ac11f8dd5500250ac38d15bec8eb19c8820b83bd9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T06:47:06Z","title_canon_sha256":"7f9eeb3398b7c4f42af3df5b5581122132c5a33d1bed7f47b08c0d542315507a"},"schema_version":"1.0","source":{"id":"1312.5823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5823","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5823v1","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5823","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"ADJ243VE7OVZ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ADJ243VE7OVZXHMQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ADJ243VE","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:39929ed665099a69424704169f4b479e18b511528e22325d101380c9c82b4157","target":"graph","created_at":"2026-05-18T03:04:07Z","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":"In this note, we establish the estimate on the Lorentz space $L(3/2,1)$ for vector fields in bounded domains under the assumption that the normal or the tangential component of the vector fields on the boundary vanishing. We prove that the $L(3/2,1)$ norm of the vector field can be controlled by the norms of its divergence and curl in the atomic Hardy spaces and the $L^1$ norm of the vector field itself.","authors_text":"Xingfei Xiang, Yoshikazu Giga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T06:47:06Z","title":"Lorentz space estimates for vector fields with divergence and curl in Hardy spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5823","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:c1511c4310e60079810de1779d200899526d84b861c335572d319b8a4faee744","target":"record","created_at":"2026-05-18T03:04:07Z","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":"067d71cab118083e86c099ac11f8dd5500250ac38d15bec8eb19c8820b83bd9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T06:47:06Z","title_canon_sha256":"7f9eeb3398b7c4f42af3df5b5581122132c5a33d1bed7f47b08c0d542315507a"},"schema_version":"1.0","source":{"id":"1312.5823","kind":"arxiv","version":1}},"canonical_sha256":"00d3ae6ea4fbab9b9d903844cc06f1d9b9c51ef2c60023a6df5663476eb89dee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00d3ae6ea4fbab9b9d903844cc06f1d9b9c51ef2c60023a6df5663476eb89dee","first_computed_at":"2026-05-18T03:04:07.761930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:07.761930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9R1Ww1VlwnObWmZAuwtnOqSkqG1Wg9dD/aaHguQLWoB4L0qc5mZtqGNLHh0F8R5pjsGmw3nzGt344ef1wHZyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:07.762503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1511c4310e60079810de1779d200899526d84b861c335572d319b8a4faee744","sha256:39929ed665099a69424704169f4b479e18b511528e22325d101380c9c82b4157"],"state_sha256":"da29739202cb80fd5fad899403e7f83f00ff73fa29709a351fab2ef57d01990b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TzgDE55wwmiG7UjrAV4++ep2tg9zzHpkuTMCv95zTqzo7E/hzyf2F01qtRQUdIosjPyjK0hxcYLRdgAb6eq1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:45:52.447326Z","bundle_sha256":"73b5ab447f24df273d3a7e1bfb3e2a2f929ec652e5af0c0ad3539ebf09f975fb"}}