{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:ZDYX7MFTLIBODNLHA5XQKH5TLT","short_pith_number":"pith:ZDYX7MFT","canonical_record":{"source":{"id":"2306.12013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-06-21T04:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"ded933edb929720273833421cdf5cce247881f246bb109a3a409f92183b84471","abstract_canon_sha256":"6439a16d6112635f751ed94b27b748a464b007b92d024c610db7865c090a3057"},"schema_version":"1.0"},"canonical_sha256":"c8f17fb0b35a02e1b567076f051fb35cf5b5662ed867ac84d6d3136d32c1b265","source":{"kind":"arxiv","id":"2306.12013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.12013","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"2306.12013v1","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.12013","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZDYX7MFTLIBO","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZDYX7MFTLIBODNLH","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZDYX7MFT","created_at":"2026-07-05T06:23:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:ZDYX7MFTLIBODNLHA5XQKH5TLT","target":"record","payload":{"canonical_record":{"source":{"id":"2306.12013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-06-21T04:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"ded933edb929720273833421cdf5cce247881f246bb109a3a409f92183b84471","abstract_canon_sha256":"6439a16d6112635f751ed94b27b748a464b007b92d024c610db7865c090a3057"},"schema_version":"1.0"},"canonical_sha256":"c8f17fb0b35a02e1b567076f051fb35cf5b5662ed867ac84d6d3136d32c1b265","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:23:09.447785Z","signature_b64":"ucnuDAr3/Un8XnmvduSZHAS8d8CWR1meIXzyKXk0qmDosSIvqlkqY8GM6xZWC2xXFMlaXFXPoxOvMC6Ua8p3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8f17fb0b35a02e1b567076f051fb35cf5b5662ed867ac84d6d3136d32c1b265","last_reissued_at":"2026-07-05T06:23:09.447454Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:23:09.447454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.12013","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":"2026-07-05T06:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kI0R55rVfjngHqdo0VgN7EcZFte+Qc1p2j3x24HWUHCnKn9Ife57eyA4r360f+QdtxsFghIEIw3OnpXr8120Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T12:31:16.836569Z"},"content_sha256":"3f5dd0e230756bf305c36218c0889178c45ef666808e4abe4e6034258ec45c5f","schema_version":"1.0","event_id":"sha256:3f5dd0e230756bf305c36218c0889178c45ef666808e4abe4e6034258ec45c5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:ZDYX7MFTLIBODNLHA5XQKH5TLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixed-norm Herz-slice Spaces and Their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jiang Zhou, Lihua Zhang","submitted_at":"2023-06-21T04:30:25Z","abstract_excerpt":"We introduce mixed-norm Herz-slice spaces unifying classical Herz spaces and mixed-norm slice spaces, establish dual spaces and the block decomposition, and prove that the boundedness of Hardy-Littlewood maximal operator on mixed-norm Herz-slice spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12013","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/2306.12013/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":"2026-07-05T06:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wiLg6053dS8cMu/quY/VbkBm18hpVZHziz1u8dhpofq+9O6tQGGxExjSkkJ9j2AyJ0K44+e+Sl1eGNgrHS9iCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T12:31:16.836946Z"},"content_sha256":"bdb37baa6c23fc1a898acf0ae6770d3aacd3fb0222aec0a531d7e79aeb970744","schema_version":"1.0","event_id":"sha256:bdb37baa6c23fc1a898acf0ae6770d3aacd3fb0222aec0a531d7e79aeb970744"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDYX7MFTLIBODNLHA5XQKH5TLT/bundle.json","state_url":"https://pith.science/pith/ZDYX7MFTLIBODNLHA5XQKH5TLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDYX7MFTLIBODNLHA5XQKH5TLT/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":"2026-07-05T12:31:16Z","links":{"resolver":"https://pith.science/pith/ZDYX7MFTLIBODNLHA5XQKH5TLT","bundle":"https://pith.science/pith/ZDYX7MFTLIBODNLHA5XQKH5TLT/bundle.json","state":"https://pith.science/pith/ZDYX7MFTLIBODNLHA5XQKH5TLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDYX7MFTLIBODNLHA5XQKH5TLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZDYX7MFTLIBODNLHA5XQKH5TLT","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":"6439a16d6112635f751ed94b27b748a464b007b92d024c610db7865c090a3057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-06-21T04:30:25Z","title_canon_sha256":"ded933edb929720273833421cdf5cce247881f246bb109a3a409f92183b84471"},"schema_version":"1.0","source":{"id":"2306.12013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.12013","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"2306.12013v1","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.12013","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZDYX7MFTLIBO","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZDYX7MFTLIBODNLH","created_at":"2026-07-05T06:23:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZDYX7MFT","created_at":"2026-07-05T06:23:09Z"}],"graph_snapshots":[{"event_id":"sha256:bdb37baa6c23fc1a898acf0ae6770d3aacd3fb0222aec0a531d7e79aeb970744","target":"graph","created_at":"2026-07-05T06:23:09Z","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/2306.12013/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce mixed-norm Herz-slice spaces unifying classical Herz spaces and mixed-norm slice spaces, establish dual spaces and the block decomposition, and prove that the boundedness of Hardy-Littlewood maximal operator on mixed-norm Herz-slice spaces.","authors_text":"Jiang Zhou, Lihua Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-06-21T04:30:25Z","title":"Mixed-norm Herz-slice Spaces and Their Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12013","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":"sha256:3f5dd0e230756bf305c36218c0889178c45ef666808e4abe4e6034258ec45c5f","target":"record","created_at":"2026-07-05T06:23:09Z","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":"6439a16d6112635f751ed94b27b748a464b007b92d024c610db7865c090a3057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-06-21T04:30:25Z","title_canon_sha256":"ded933edb929720273833421cdf5cce247881f246bb109a3a409f92183b84471"},"schema_version":"1.0","source":{"id":"2306.12013","kind":"arxiv","version":1}},"canonical_sha256":"c8f17fb0b35a02e1b567076f051fb35cf5b5662ed867ac84d6d3136d32c1b265","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8f17fb0b35a02e1b567076f051fb35cf5b5662ed867ac84d6d3136d32c1b265","first_computed_at":"2026-07-05T06:23:09.447454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:23:09.447454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucnuDAr3/Un8XnmvduSZHAS8d8CWR1meIXzyKXk0qmDosSIvqlkqY8GM6xZWC2xXFMlaXFXPoxOvMC6Ua8p3DA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:23:09.447785Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.12013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f5dd0e230756bf305c36218c0889178c45ef666808e4abe4e6034258ec45c5f","sha256:bdb37baa6c23fc1a898acf0ae6770d3aacd3fb0222aec0a531d7e79aeb970744"],"state_sha256":"8f2557ca164c2d0200ec7aa3ea987c38f07debbdfd9d98b93dfcaa1d8da6f72e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wtr+eBBwdVUrruj7wsXVlJv2GSancJabdLLIkyKeBg3oMzWxaE70y+Y4fen4XHUgWbW2+DYgx3EwnAkXwZikAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T12:31:16.838925Z","bundle_sha256":"aafd763a2a5ade0ede354c405814f8ca0e5a90ffcd84640ffabe0e264a94399b"}}