{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:L5MOXMVA4EQR7P7YORPLNSPFXJ","short_pith_number":"pith:L5MOXMVA","canonical_record":{"source":{"id":"2409.14387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-09-22T10:11:46Z","cross_cats_sorted":[],"title_canon_sha256":"f5ca5182bed5c867c484df3f4fd46e6630ec5dc4511d514d02123751394bf760","abstract_canon_sha256":"9765e218bbfdc0e037598a6a4bba298e4dc9aaa0e71ed716088582bc4c4bf679"},"schema_version":"1.0"},"canonical_sha256":"5f58ebb2a0e1211fbff8745eb6c9e5ba7996d3965ea28dad84d36a62aea231a0","source":{"kind":"arxiv","id":"2409.14387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.14387","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"2409.14387v1","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.14387","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"L5MOXMVA4EQR","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"pith_short_16","alias_value":"L5MOXMVA4EQR7P7Y","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"pith_short_8","alias_value":"L5MOXMVA","created_at":"2026-07-05T09:10:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:L5MOXMVA4EQR7P7YORPLNSPFXJ","target":"record","payload":{"canonical_record":{"source":{"id":"2409.14387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-09-22T10:11:46Z","cross_cats_sorted":[],"title_canon_sha256":"f5ca5182bed5c867c484df3f4fd46e6630ec5dc4511d514d02123751394bf760","abstract_canon_sha256":"9765e218bbfdc0e037598a6a4bba298e4dc9aaa0e71ed716088582bc4c4bf679"},"schema_version":"1.0"},"canonical_sha256":"5f58ebb2a0e1211fbff8745eb6c9e5ba7996d3965ea28dad84d36a62aea231a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:10:16.017797Z","signature_b64":"t+r8TW91DaAWFELs6WSNgN4alTg2x/UtNJJc6D1UE6+WITnh2K1dbOTxM168ra1EI56Fd3ECgF3yGdzUQWCTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f58ebb2a0e1211fbff8745eb6c9e5ba7996d3965ea28dad84d36a62aea231a0","last_reissued_at":"2026-07-05T09:10:16.017323Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:10:16.017323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.14387","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":"2026-07-05T09:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"noGbEhWkHof3jw9WvCaMV7KyEnEqt0Efy33qL0h49ZwAVEV7sd4XN744Sb/B3pwEXvVxts5Oq5war+b95tnAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:04:47.298324Z"},"content_sha256":"f3a592e4d2a35245a06225a2184c899fe22e8ac41757e269bd51d30428a603d2","schema_version":"1.0","event_id":"sha256:f3a592e4d2a35245a06225a2184c899fe22e8ac41757e269bd51d30428a603d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:L5MOXMVA4EQR7P7YORPLNSPFXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of BMO spaces via commutators of some maximal operators on the slice spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J. Wu, Y. Chang, Y. Sun","submitted_at":"2024-09-22T10:11:46Z","abstract_excerpt":"In this paper, the main aim is to demonstrate the boundedness for commutators of (fractional) maximal function and sharp maximal function in the slice spaces, where the symbols of the commutators belong to the BMO space, whereby some new characterizations for BMO spaces are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14387","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.14387/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJkRYfNFGPEPmaDP+x6UViYvW0IAkjGndnkSPBdnt8N35cySbuMdApCfQepPXvD7wSiayKn4dn9apZjxEFQsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:04:47.299110Z"},"content_sha256":"764c22b11418212c17a7318a0dd406d26ff8dc3bbbe0ef29d284287c95edf573","schema_version":"1.0","event_id":"sha256:764c22b11418212c17a7318a0dd406d26ff8dc3bbbe0ef29d284287c95edf573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5MOXMVA4EQR7P7YORPLNSPFXJ/bundle.json","state_url":"https://pith.science/pith/L5MOXMVA4EQR7P7YORPLNSPFXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5MOXMVA4EQR7P7YORPLNSPFXJ/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":"2026-08-07T08:04:47Z","links":{"resolver":"https://pith.science/pith/L5MOXMVA4EQR7P7YORPLNSPFXJ","bundle":"https://pith.science/pith/L5MOXMVA4EQR7P7YORPLNSPFXJ/bundle.json","state":"https://pith.science/pith/L5MOXMVA4EQR7P7YORPLNSPFXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5MOXMVA4EQR7P7YORPLNSPFXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:L5MOXMVA4EQR7P7YORPLNSPFXJ","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":"9765e218bbfdc0e037598a6a4bba298e4dc9aaa0e71ed716088582bc4c4bf679","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-09-22T10:11:46Z","title_canon_sha256":"f5ca5182bed5c867c484df3f4fd46e6630ec5dc4511d514d02123751394bf760"},"schema_version":"1.0","source":{"id":"2409.14387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.14387","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"2409.14387v1","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.14387","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"L5MOXMVA4EQR","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"pith_short_16","alias_value":"L5MOXMVA4EQR7P7Y","created_at":"2026-07-05T09:10:16Z"},{"alias_kind":"pith_short_8","alias_value":"L5MOXMVA","created_at":"2026-07-05T09:10:16Z"}],"graph_snapshots":[{"event_id":"sha256:764c22b11418212c17a7318a0dd406d26ff8dc3bbbe0ef29d284287c95edf573","target":"graph","created_at":"2026-07-05T09:10:16Z","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/2409.14387/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, the main aim is to demonstrate the boundedness for commutators of (fractional) maximal function and sharp maximal function in the slice spaces, where the symbols of the commutators belong to the BMO space, whereby some new characterizations for BMO spaces are given.","authors_text":"J. Wu, Y. Chang, Y. Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-09-22T10:11:46Z","title":"Characterization of BMO spaces via commutators of some maximal operators on the slice spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14387","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:f3a592e4d2a35245a06225a2184c899fe22e8ac41757e269bd51d30428a603d2","target":"record","created_at":"2026-07-05T09:10:16Z","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":"9765e218bbfdc0e037598a6a4bba298e4dc9aaa0e71ed716088582bc4c4bf679","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-09-22T10:11:46Z","title_canon_sha256":"f5ca5182bed5c867c484df3f4fd46e6630ec5dc4511d514d02123751394bf760"},"schema_version":"1.0","source":{"id":"2409.14387","kind":"arxiv","version":1}},"canonical_sha256":"5f58ebb2a0e1211fbff8745eb6c9e5ba7996d3965ea28dad84d36a62aea231a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f58ebb2a0e1211fbff8745eb6c9e5ba7996d3965ea28dad84d36a62aea231a0","first_computed_at":"2026-07-05T09:10:16.017323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:10:16.017323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+r8TW91DaAWFELs6WSNgN4alTg2x/UtNJJc6D1UE6+WITnh2K1dbOTxM168ra1EI56Fd3ECgF3yGdzUQWCTCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:10:16.017797Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.14387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a592e4d2a35245a06225a2184c899fe22e8ac41757e269bd51d30428a603d2","sha256:764c22b11418212c17a7318a0dd406d26ff8dc3bbbe0ef29d284287c95edf573"],"state_sha256":"0fd48343189d77b738dd072907fc60ce10e703b43c1772de0842ad2348d730ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"27VJWbufPxkl76f6RZkkZYt0hZgjJqn+gXYuynrOU+FM+z+3e2Lbi8YKt5RNhe3WGROWYVHJRV18U+6RWJwHCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T08:04:47.304929Z","bundle_sha256":"e48d9abf7afe1b0fa0f4f8bf3a9e0c6e91e0562e4b9a789e270500b4d762a1ed"}}