{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GKU55VQM5SF5SKRBIRR4XRFY5Q","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":"38a5d67f9599b1f7071a9d726704aded219e7b7d17548481a24780f88cca9870","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-08-30T16:10:37Z","title_canon_sha256":"d0796ca1a95912d2cc2b94c04be7f4d8d1b82a6c3e68e2c1bf7caad3a55f49c6"},"schema_version":"1.0","source":{"id":"2308.16214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.16214","created_at":"2026-07-05T06:46:24Z"},{"alias_kind":"arxiv_version","alias_value":"2308.16214v1","created_at":"2026-07-05T06:46:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.16214","created_at":"2026-07-05T06:46:24Z"},{"alias_kind":"pith_short_12","alias_value":"GKU55VQM5SF5","created_at":"2026-07-05T06:46:24Z"},{"alias_kind":"pith_short_16","alias_value":"GKU55VQM5SF5SKRB","created_at":"2026-07-05T06:46:24Z"},{"alias_kind":"pith_short_8","alias_value":"GKU55VQM","created_at":"2026-07-05T06:46:24Z"}],"graph_snapshots":[{"event_id":"sha256:b65752d80c86449fb4596e349d141dcbc83ac100a4b005a2543817fbff6b8801","target":"graph","created_at":"2026-07-05T06:46:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.16214/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is to establish some characterizations of mixed central Campanato space $\\mathfrak{C}^{\\vec{p},\\lambda}(\\mathbb{R}^{n})$, via the boundedness of the commutator operators of Hardy type. Unlike the case $\\lambda\\geq0$, there are some technical difficulties caused by $\\lambda<0$ to be overcome. In addition, an extra assumption called as the mixed version of the reverse H\\\"{o}lder class be required in the proof of the converse characterization. Moreover, some further interesting conclusions for the Hardy type operators on mixed $\\lambda$-central Morrey space $\\mathcal{B}^","authors_text":"Jiang Zhou, Wenna Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-08-30T16:10:37Z","title":"Characterizations of the mixed central Campanato spaces via the commutator operators of Hardy type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.16214","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":"sha256:217d6db6bdd89ca5899cba6fd7fb8790dcb0951f88363b2840cda31fd120e69f","target":"record","created_at":"2026-07-05T06:46:24Z","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":"38a5d67f9599b1f7071a9d726704aded219e7b7d17548481a24780f88cca9870","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-08-30T16:10:37Z","title_canon_sha256":"d0796ca1a95912d2cc2b94c04be7f4d8d1b82a6c3e68e2c1bf7caad3a55f49c6"},"schema_version":"1.0","source":{"id":"2308.16214","kind":"arxiv","version":1}},"canonical_sha256":"32a9ded60cec8bd92a214463cbc4b8ec18c4325adaea4b701cec924887baa8d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a9ded60cec8bd92a214463cbc4b8ec18c4325adaea4b701cec924887baa8d1","first_computed_at":"2026-07-05T06:46:24.138672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:46:24.138672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vxwaVGCrdasoyDlhyoSF+Jn9ZtUHejohFbYeRW7tJ11wVZ1GbnizeL1ohbTS8QV8CHJtjJ3VQctgTBpYcd9/DA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:46:24.139070Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.16214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:217d6db6bdd89ca5899cba6fd7fb8790dcb0951f88363b2840cda31fd120e69f","sha256:b65752d80c86449fb4596e349d141dcbc83ac100a4b005a2543817fbff6b8801"],"state_sha256":"7e9a197932457c79f98e9777448556822cadc75633ee48e893609ceb4ea676df"}