{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XILBLHZOGUNF47FBERKGMILTWC","short_pith_number":"pith:XILBLHZO","schema_version":"1.0","canonical_sha256":"ba16159f2e351a5e7ca12454662173b09dcf48ff21c2f028b9ec4b5bfccd1b31","source":{"kind":"arxiv","id":"1101.5561","version":1},"attestation_state":"computed","paper":{"title":"Local real analysis in locally homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Maochun Zhu, Marco Bramanti","submitted_at":"2011-01-28T16:06:52Z","abstract_excerpt":"We introduce the concept of locally homogeneous space, and prove in this context L^p and Holder estimates for singular and fractional integrals, as well as L^p estimates on the commutator of a singular or fractional integral with a BMO or VMO function. These results are motivated by local a-priori estimates for subelliptic equations."},"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":"1101.5561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-28T16:06:52Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"77a43c0a84d5dc4797e8d9ef257706727b8aa37d9eb865c3335a5b1e89bd2aea","abstract_canon_sha256":"cf6303b260e09ab13740181b114c27335d71f9bafee6fc726e32a3e9874d131b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:34.748745Z","signature_b64":"8z4TmP3xMW52y+CJPKnth6U45yDTuMrpgk4lDEmpyOT2JCAchrGTFUQiZkflZM4OVmV2Q4MRLJ/KbLK9tQNUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba16159f2e351a5e7ca12454662173b09dcf48ff21c2f028b9ec4b5bfccd1b31","last_reissued_at":"2026-05-18T04:30:34.748301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:34.748301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local real analysis in locally homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Maochun Zhu, Marco Bramanti","submitted_at":"2011-01-28T16:06:52Z","abstract_excerpt":"We introduce the concept of locally homogeneous space, and prove in this context L^p and Holder estimates for singular and fractional integrals, as well as L^p estimates on the commutator of a singular or fractional integral with a BMO or VMO function. These results are motivated by local a-priori estimates for subelliptic equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5561","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.5561","created_at":"2026-05-18T04:30:34.748383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.5561v1","created_at":"2026-05-18T04:30:34.748383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5561","created_at":"2026-05-18T04:30:34.748383+00:00"},{"alias_kind":"pith_short_12","alias_value":"XILBLHZOGUNF","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"XILBLHZOGUNF47FB","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"XILBLHZO","created_at":"2026-05-18T12:26:44.992195+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/XILBLHZOGUNF47FBERKGMILTWC","json":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC.json","graph_json":"https://pith.science/api/pith-number/XILBLHZOGUNF47FBERKGMILTWC/graph.json","events_json":"https://pith.science/api/pith-number/XILBLHZOGUNF47FBERKGMILTWC/events.json","paper":"https://pith.science/paper/XILBLHZO"},"agent_actions":{"view_html":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC","download_json":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC.json","view_paper":"https://pith.science/paper/XILBLHZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.5561&json=true","fetch_graph":"https://pith.science/api/pith-number/XILBLHZOGUNF47FBERKGMILTWC/graph.json","fetch_events":"https://pith.science/api/pith-number/XILBLHZOGUNF47FBERKGMILTWC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC/action/storage_attestation","attest_author":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC/action/author_attestation","sign_citation":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC/action/citation_signature","submit_replication":"https://pith.science/pith/XILBLHZOGUNF47FBERKGMILTWC/action/replication_record"}},"created_at":"2026-05-18T04:30:34.748383+00:00","updated_at":"2026-05-18T04:30:34.748383+00:00"}