{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7RNN62YYV23W2ALWAP2TOXZTLD","short_pith_number":"pith:7RNN62YY","canonical_record":{"source":{"id":"1803.03069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-08T12:46:52Z","cross_cats_sorted":[],"title_canon_sha256":"ff0949b51e8a184f282ece6f42c5817697a06dbee28f5eaa0bf6dae1b70b2eec","abstract_canon_sha256":"362c10f71e70e841fb2078827035c9662945756f3c19783b8e97fe66376a890d"},"schema_version":"1.0"},"canonical_sha256":"fc5adf6b18aeb76d017603f5375f3358d7041486e1523d01c6f9a8b22a9cd2df","source":{"kind":"arxiv","id":"1803.03069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03069","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03069v1","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03069","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"7RNN62YYV23W","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7RNN62YYV23W2ALW","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7RNN62YY","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7RNN62YYV23W2ALWAP2TOXZTLD","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-08T12:46:52Z","cross_cats_sorted":[],"title_canon_sha256":"ff0949b51e8a184f282ece6f42c5817697a06dbee28f5eaa0bf6dae1b70b2eec","abstract_canon_sha256":"362c10f71e70e841fb2078827035c9662945756f3c19783b8e97fe66376a890d"},"schema_version":"1.0"},"canonical_sha256":"fc5adf6b18aeb76d017603f5375f3358d7041486e1523d01c6f9a8b22a9cd2df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:44.556713Z","signature_b64":"y2ZBcuoJec1bJetG0OJXcle4HOHF2ngQGx7G4IqYr5lsnwNrufLh8ppRaSxglxudRjsfalrOS5L2WSQ9q0JTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc5adf6b18aeb76d017603f5375f3358d7041486e1523d01c6f9a8b22a9cd2df","last_reissued_at":"2026-05-18T00:21:44.556058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:44.556058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03069","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DfboN8nMNJL3HDnCPN918oZROPDIAOhtQdRq6myCI9mA7D6JFCSrlNUJUi02OQynZoRkZv+H9RGe6ZIdAVP+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:36:55.732369Z"},"content_sha256":"74e4bbd8785934ed004c9fef5ea647f6b46aacd9fb6f845d72c796d4cf5f901d","schema_version":"1.0","event_id":"sha256:74e4bbd8785934ed004c9fef5ea647f6b46aacd9fb6f845d72c796d4cf5f901d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7RNN62YYV23W2ALWAP2TOXZTLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional maximal function and its commutators on Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fatih Deringoz, Sabir G. Hasanov, Vagif S. Guliyev","submitted_at":"2018-03-08T12:46:52Z","abstract_excerpt":"In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $M_{b,\\alpha}$ and nonlinear commutator of fractional maximal operator $[b,M_{\\alpha}]$ on Orlicz spaces, when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03069","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NFR4Rr5WFKyxkFR091dCLEDehaBLcdGXNPd4FShk9OkrhLuZ4LunNZQ0x+KmF/HbNTAya1BkhiBeO/MwCge1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:36:55.732714Z"},"content_sha256":"f2ba1e6db2a8ebc22c74cb4170c9272a669d49134a68b35118744ed4bbdc0b99","schema_version":"1.0","event_id":"sha256:f2ba1e6db2a8ebc22c74cb4170c9272a669d49134a68b35118744ed4bbdc0b99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RNN62YYV23W2ALWAP2TOXZTLD/bundle.json","state_url":"https://pith.science/pith/7RNN62YYV23W2ALWAP2TOXZTLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RNN62YYV23W2ALWAP2TOXZTLD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T20:36:55Z","links":{"resolver":"https://pith.science/pith/7RNN62YYV23W2ALWAP2TOXZTLD","bundle":"https://pith.science/pith/7RNN62YYV23W2ALWAP2TOXZTLD/bundle.json","state":"https://pith.science/pith/7RNN62YYV23W2ALWAP2TOXZTLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RNN62YYV23W2ALWAP2TOXZTLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7RNN62YYV23W2ALWAP2TOXZTLD","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":"362c10f71e70e841fb2078827035c9662945756f3c19783b8e97fe66376a890d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-08T12:46:52Z","title_canon_sha256":"ff0949b51e8a184f282ece6f42c5817697a06dbee28f5eaa0bf6dae1b70b2eec"},"schema_version":"1.0","source":{"id":"1803.03069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03069","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03069v1","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03069","created_at":"2026-05-18T00:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"7RNN62YYV23W","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7RNN62YYV23W2ALW","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7RNN62YY","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:f2ba1e6db2a8ebc22c74cb4170c9272a669d49134a68b35118744ed4bbdc0b99","target":"graph","created_at":"2026-05-18T00:21:44Z","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":"In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $M_{b,\\alpha}$ and nonlinear commutator of fractional maximal operator $[b,M_{\\alpha}]$ on Orlicz spaces, when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.","authors_text":"Fatih Deringoz, Sabir G. Hasanov, Vagif S. Guliyev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-08T12:46:52Z","title":"Fractional maximal function and its commutators on Orlicz spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03069","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":"sha256:74e4bbd8785934ed004c9fef5ea647f6b46aacd9fb6f845d72c796d4cf5f901d","target":"record","created_at":"2026-05-18T00:21:44Z","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":"362c10f71e70e841fb2078827035c9662945756f3c19783b8e97fe66376a890d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-08T12:46:52Z","title_canon_sha256":"ff0949b51e8a184f282ece6f42c5817697a06dbee28f5eaa0bf6dae1b70b2eec"},"schema_version":"1.0","source":{"id":"1803.03069","kind":"arxiv","version":1}},"canonical_sha256":"fc5adf6b18aeb76d017603f5375f3358d7041486e1523d01c6f9a8b22a9cd2df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc5adf6b18aeb76d017603f5375f3358d7041486e1523d01c6f9a8b22a9cd2df","first_computed_at":"2026-05-18T00:21:44.556058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:44.556058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y2ZBcuoJec1bJetG0OJXcle4HOHF2ngQGx7G4IqYr5lsnwNrufLh8ppRaSxglxudRjsfalrOS5L2WSQ9q0JTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:44.556713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74e4bbd8785934ed004c9fef5ea647f6b46aacd9fb6f845d72c796d4cf5f901d","sha256:f2ba1e6db2a8ebc22c74cb4170c9272a669d49134a68b35118744ed4bbdc0b99"],"state_sha256":"289455a2e7196cb82312d0afca04ed9763220ac52733b1c359b3d269b8699cd7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1QJsnNJ0axbqPICve4P4ayEzUd5WW+yUC77cynVoYgCXkNH3KRttAlHBXtk0PD3utuJ2pwhVAbp2EA/8DL6MAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:36:55.734683Z","bundle_sha256":"4cc84ae79f1f78f475edd4b21ca2d273cf57a8faa29173b25312b858fbb480f6"}}