{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:S4WIFWKD62YTN2BXTDRXHQWVSW","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":"70dc9a46248053447dada4fc889045b191a60962c5ea3b9c771c06edb03aba38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T23:10:49Z","title_canon_sha256":"ffc618c96d8d450161b56fd255222a07e1b9836615c6551d6b98082634e3a644"},"schema_version":"1.0","source":{"id":"1205.6516","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6516","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6516v3","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6516","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"S4WIFWKD62YT","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"S4WIFWKD62YTN2BX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"S4WIFWKD","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:abe52af960a1ed3ce1ea9bf98006753904f956cf84c4655d833d0d0031b2d00f","target":"graph","created_at":"2026-05-18T02:51:57Z","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":"We prove that Calder\\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.","authors_text":"Justin Feuto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T23:10:49Z","title":"Norm inequalities in generalized Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6516","kind":"arxiv","version":3},"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:cde0c3dabcf531732bb5d8e0fde59c3b478ddcfc34789ebaf9009913e7001ce7","target":"record","created_at":"2026-05-18T02:51:57Z","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":"70dc9a46248053447dada4fc889045b191a60962c5ea3b9c771c06edb03aba38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-29T23:10:49Z","title_canon_sha256":"ffc618c96d8d450161b56fd255222a07e1b9836615c6551d6b98082634e3a644"},"schema_version":"1.0","source":{"id":"1205.6516","kind":"arxiv","version":3}},"canonical_sha256":"972c82d943f6b136e83798e373c2d595b512d64fbe0bad04f509a87773c7297a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"972c82d943f6b136e83798e373c2d595b512d64fbe0bad04f509a87773c7297a","first_computed_at":"2026-05-18T02:51:57.274933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:57.274933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49lv3vltAqKXRcioyfuAc59XrjbO91zDHeN/5ulQnJ1CRUddJ1SVO8rPFfEyE7h75dz/bGK0UO9ZdHGu36rwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:57.275383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6516","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cde0c3dabcf531732bb5d8e0fde59c3b478ddcfc34789ebaf9009913e7001ce7","sha256:abe52af960a1ed3ce1ea9bf98006753904f956cf84c4655d833d0d0031b2d00f"],"state_sha256":"2efff21bd8f9ea6192c3ba24675d89497436e8dc55b174b8a51e068b356c6317"}