{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2UJV44A7N6I437KBOISDKOETAB","short_pith_number":"pith:2UJV44A7","schema_version":"1.0","canonical_sha256":"d5135e701f6f91cdfd41722435389300631e7d055c8d28435392c340bfe43337","source":{"kind":"arxiv","id":"1112.4935","version":4},"attestation_state":"computed","paper":{"title":"Hardy spaces, commutators of singular integral operators related to Schr\\\"odinger operators and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Luong Dang Ky (MAPMO)","submitted_at":"2011-12-21T07:34:40Z","abstract_excerpt":"This paper has been withdrawn by the author due to crucial sign error in Lemma 8.1."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.4935","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-21T07:34:40Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"dec5aa0866a0f450b38ccf347141037fe202c39dc662b7df7fdfe8c3398a370f","abstract_canon_sha256":"4bc5d0e99e2c24013bcc6190c71f8fd2f179e2053ab5c434deaf70cd300eadec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:26.150469Z","signature_b64":"UACUn4jSQvIps4nfl+PMeVyeTngwese8pb/auQYegZcus7D9GiMs7qlz76Rd69Ojj20VKZM1U3xtomrV1mGwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5135e701f6f91cdfd41722435389300631e7d055c8d28435392c340bfe43337","last_reissued_at":"2026-05-18T03:58:26.149674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:26.149674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hardy spaces, commutators of singular integral operators related to Schr\\\"odinger operators and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Luong Dang Ky (MAPMO)","submitted_at":"2011-12-21T07:34:40Z","abstract_excerpt":"This paper has been withdrawn by the author due to crucial sign error in Lemma 8.1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4935","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.4935","created_at":"2026-05-18T03:58:26.149801+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.4935v4","created_at":"2026-05-18T03:58:26.149801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4935","created_at":"2026-05-18T03:58:26.149801+00:00"},{"alias_kind":"pith_short_12","alias_value":"2UJV44A7N6I4","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2UJV44A7N6I437KB","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2UJV44A7","created_at":"2026-05-18T12:26:18.847500+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB","json":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB.json","graph_json":"https://pith.science/api/pith-number/2UJV44A7N6I437KBOISDKOETAB/graph.json","events_json":"https://pith.science/api/pith-number/2UJV44A7N6I437KBOISDKOETAB/events.json","paper":"https://pith.science/paper/2UJV44A7"},"agent_actions":{"view_html":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB","download_json":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB.json","view_paper":"https://pith.science/paper/2UJV44A7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.4935&json=true","fetch_graph":"https://pith.science/api/pith-number/2UJV44A7N6I437KBOISDKOETAB/graph.json","fetch_events":"https://pith.science/api/pith-number/2UJV44A7N6I437KBOISDKOETAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB/action/storage_attestation","attest_author":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB/action/author_attestation","sign_citation":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB/action/citation_signature","submit_replication":"https://pith.science/pith/2UJV44A7N6I437KBOISDKOETAB/action/replication_record"}},"created_at":"2026-05-18T03:58:26.149801+00:00","updated_at":"2026-05-18T03:58:26.149801+00:00"}