{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TRTMZX2E6ODDLAF4M4O2SLYDVF","short_pith_number":"pith:TRTMZX2E","schema_version":"1.0","canonical_sha256":"9c66ccdf44f3863580bc671da92f03a96522b7258eda9395955e33dc77eb84c9","source":{"kind":"arxiv","id":"1201.5007","version":1},"attestation_state":"computed","paper":{"title":"On the Interplay of Regularity and Decay in Case of Radial Functions I. Inhomogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jan Vybiral, Leszek Skrzypczak, Winfried Sickel","submitted_at":"2012-01-24T15:15:44Z","abstract_excerpt":"We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination with trace theorems."},"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":"1201.5007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-24T15:15:44Z","cross_cats_sorted":[],"title_canon_sha256":"feb624302f1b6002cbd825a17da21d4a4c10d0ddcc2b6ab45f99a5b192053102","abstract_canon_sha256":"3af7dfb7836bba7a62353de6821f3f840e1f799550229cf60a7243d3b31b4048"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:55.555765Z","signature_b64":"pdtzr4Cn0sRGzW5gINgbRTTsk8DJXUsLkg+kp6oTGjpYdtWAbKIWKMTsKKqlsefSe51yLcfuZVnA86n9WaPnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c66ccdf44f3863580bc671da92f03a96522b7258eda9395955e33dc77eb84c9","last_reissued_at":"2026-05-18T04:03:55.555180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:55.555180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Interplay of Regularity and Decay in Case of Radial Functions I. Inhomogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jan Vybiral, Leszek Skrzypczak, Winfried Sickel","submitted_at":"2012-01-24T15:15:44Z","abstract_excerpt":"We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination with trace theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5007","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":"1201.5007","created_at":"2026-05-18T04:03:55.555274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5007v1","created_at":"2026-05-18T04:03:55.555274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5007","created_at":"2026-05-18T04:03:55.555274+00:00"},{"alias_kind":"pith_short_12","alias_value":"TRTMZX2E6ODD","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TRTMZX2E6ODDLAF4","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TRTMZX2E","created_at":"2026-05-18T12:27:23.164592+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/TRTMZX2E6ODDLAF4M4O2SLYDVF","json":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF.json","graph_json":"https://pith.science/api/pith-number/TRTMZX2E6ODDLAF4M4O2SLYDVF/graph.json","events_json":"https://pith.science/api/pith-number/TRTMZX2E6ODDLAF4M4O2SLYDVF/events.json","paper":"https://pith.science/paper/TRTMZX2E"},"agent_actions":{"view_html":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF","download_json":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF.json","view_paper":"https://pith.science/paper/TRTMZX2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5007&json=true","fetch_graph":"https://pith.science/api/pith-number/TRTMZX2E6ODDLAF4M4O2SLYDVF/graph.json","fetch_events":"https://pith.science/api/pith-number/TRTMZX2E6ODDLAF4M4O2SLYDVF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF/action/storage_attestation","attest_author":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF/action/author_attestation","sign_citation":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF/action/citation_signature","submit_replication":"https://pith.science/pith/TRTMZX2E6ODDLAF4M4O2SLYDVF/action/replication_record"}},"created_at":"2026-05-18T04:03:55.555274+00:00","updated_at":"2026-05-18T04:03:55.555274+00:00"}