{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5B663XIB2CPKYVK4R55WWEO3ZI","short_pith_number":"pith:5B663XIB","canonical_record":{"source":{"id":"2206.06551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-06-14T01:58:08Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"82276423a8e9b7d0ee7c956fddddf7574cfe73d06d0b33ee61c98b73a8d5059a","abstract_canon_sha256":"7fb800973824bc7106faf61f6501ddb31005c832f40523a66185fcc1cb08f2ea"},"schema_version":"1.0"},"canonical_sha256":"e87deddd01d09eac555c8f7b6b11dbca144c2ae7db0aa0c0bca919788e59f3a5","source":{"kind":"arxiv","id":"2206.06551","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.06551","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2206.06551v1","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.06551","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"5B663XIB2CPK","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"5B663XIB2CPKYVK4","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"5B663XIB","created_at":"2026-07-05T04:32:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5B663XIB2CPKYVK4R55WWEO3ZI","target":"record","payload":{"canonical_record":{"source":{"id":"2206.06551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-06-14T01:58:08Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"82276423a8e9b7d0ee7c956fddddf7574cfe73d06d0b33ee61c98b73a8d5059a","abstract_canon_sha256":"7fb800973824bc7106faf61f6501ddb31005c832f40523a66185fcc1cb08f2ea"},"schema_version":"1.0"},"canonical_sha256":"e87deddd01d09eac555c8f7b6b11dbca144c2ae7db0aa0c0bca919788e59f3a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:41.024068Z","signature_b64":"wvAJr6hfPF6JWByd3VRssdj1lAp2PRcnpvNBYs8AP/H6fdSHelKVUCom1d917UeCnPkxOg1HAo/2QzdiH0iuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e87deddd01d09eac555c8f7b6b11dbca144c2ae7db0aa0c0bca919788e59f3a5","last_reissued_at":"2026-07-05T04:32:41.023490Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:41.023490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.06551","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":"2026-07-05T04:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4KhpE+D1C697Tzop/MZ6nXcjd3hoS5Px2fCNjMbS9A8tVYo+882fzzfitUAYIlt7n3j6aeN9PbOSdpxCs/fECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:14:18.605726Z"},"content_sha256":"9483d185a33fb6d237111ae97a866775c54adf854d48a6d17ee06b48238b2426","schema_version":"1.0","event_id":"sha256:9483d185a33fb6d237111ae97a866775c54adf854d48a6d17ee06b48238b2426"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5B663XIB2CPKYVK4R55WWEO3ZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Dachun Yang, Hongchao Jia, Yiqun Chen","submitted_at":"2022-06-14T01:58:08Z","abstract_excerpt":"Let $X$ be a ball quasi-Banach function space on ${\\mathbb R}^n$ satisfying some mild assumptions and let $\\alpha\\in(0,n)$ and $\\beta\\in(1,\\infty)$. In this article, when $\\alpha\\in(0,1)$, the authors first find a reasonable version $\\widetilde{I}_{\\alpha}$ of the fractional integral $I_{\\alpha}$ on the ball Campanato-type function space $\\mathcal{L}_{X,q,s,d}(\\mathbb{R}^n)$ with $q\\in[1,\\infty)$, $s\\in\\mathbb{Z}_+^n$, and $d\\in(0,\\infty)$. Then the authors prove that $\\widetilde{I}_{\\alpha}$ is bounded from $\\mathcal{L}_{X^{\\beta},q,s,d}(\\mathbb{R}^n)$ to $\\mathcal{L}_{X,q,s,d}(\\mathbb{R}^n)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.06551","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/2206.06551/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":"2026-07-05T04:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mbAPMOClz/SCX5kmd2hFZPRVrLwIFIgkqlmqlc0jifV95G7Dj4O/VYj+rDc1+pvlT7vEz71tQi3aUqN0ICFwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:14:18.606289Z"},"content_sha256":"1edb5404f363e4d6121368489517e9021155b774a786417eff97f93977b79a63","schema_version":"1.0","event_id":"sha256:1edb5404f363e4d6121368489517e9021155b774a786417eff97f93977b79a63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5B663XIB2CPKYVK4R55WWEO3ZI/bundle.json","state_url":"https://pith.science/pith/5B663XIB2CPKYVK4R55WWEO3ZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5B663XIB2CPKYVK4R55WWEO3ZI/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":"2026-08-05T17:14:18Z","links":{"resolver":"https://pith.science/pith/5B663XIB2CPKYVK4R55WWEO3ZI","bundle":"https://pith.science/pith/5B663XIB2CPKYVK4R55WWEO3ZI/bundle.json","state":"https://pith.science/pith/5B663XIB2CPKYVK4R55WWEO3ZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5B663XIB2CPKYVK4R55WWEO3ZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5B663XIB2CPKYVK4R55WWEO3ZI","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":"7fb800973824bc7106faf61f6501ddb31005c832f40523a66185fcc1cb08f2ea","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-06-14T01:58:08Z","title_canon_sha256":"82276423a8e9b7d0ee7c956fddddf7574cfe73d06d0b33ee61c98b73a8d5059a"},"schema_version":"1.0","source":{"id":"2206.06551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.06551","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2206.06551v1","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.06551","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"5B663XIB2CPK","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"5B663XIB2CPKYVK4","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"5B663XIB","created_at":"2026-07-05T04:32:41Z"}],"graph_snapshots":[{"event_id":"sha256:1edb5404f363e4d6121368489517e9021155b774a786417eff97f93977b79a63","target":"graph","created_at":"2026-07-05T04:32:41Z","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/2206.06551/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a ball quasi-Banach function space on ${\\mathbb R}^n$ satisfying some mild assumptions and let $\\alpha\\in(0,n)$ and $\\beta\\in(1,\\infty)$. In this article, when $\\alpha\\in(0,1)$, the authors first find a reasonable version $\\widetilde{I}_{\\alpha}$ of the fractional integral $I_{\\alpha}$ on the ball Campanato-type function space $\\mathcal{L}_{X,q,s,d}(\\mathbb{R}^n)$ with $q\\in[1,\\infty)$, $s\\in\\mathbb{Z}_+^n$, and $d\\in(0,\\infty)$. Then the authors prove that $\\widetilde{I}_{\\alpha}$ is bounded from $\\mathcal{L}_{X^{\\beta},q,s,d}(\\mathbb{R}^n)$ to $\\mathcal{L}_{X,q,s,d}(\\mathbb{R}^n)$","authors_text":"Dachun Yang, Hongchao Jia, Yiqun Chen","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-06-14T01:58:08Z","title":"Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.06551","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":"sha256:9483d185a33fb6d237111ae97a866775c54adf854d48a6d17ee06b48238b2426","target":"record","created_at":"2026-07-05T04:32:41Z","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":"7fb800973824bc7106faf61f6501ddb31005c832f40523a66185fcc1cb08f2ea","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-06-14T01:58:08Z","title_canon_sha256":"82276423a8e9b7d0ee7c956fddddf7574cfe73d06d0b33ee61c98b73a8d5059a"},"schema_version":"1.0","source":{"id":"2206.06551","kind":"arxiv","version":1}},"canonical_sha256":"e87deddd01d09eac555c8f7b6b11dbca144c2ae7db0aa0c0bca919788e59f3a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e87deddd01d09eac555c8f7b6b11dbca144c2ae7db0aa0c0bca919788e59f3a5","first_computed_at":"2026-07-05T04:32:41.023490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:32:41.023490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wvAJr6hfPF6JWByd3VRssdj1lAp2PRcnpvNBYs8AP/H6fdSHelKVUCom1d917UeCnPkxOg1HAo/2QzdiH0iuDg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:32:41.024068Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.06551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9483d185a33fb6d237111ae97a866775c54adf854d48a6d17ee06b48238b2426","sha256:1edb5404f363e4d6121368489517e9021155b774a786417eff97f93977b79a63"],"state_sha256":"bf4298338c83c233d3bea88357c4ec9bb71ff622b07de83defdd572cd5681508"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mlJDX2Rj34gWw+dwT/YcAZdkt8nHbr2V8GgAdOSNoAJXUr9KEh/juni5P/pg2h5q4Dse4Ao8TXZNjkZXd8ljBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T17:14:18.611733Z","bundle_sha256":"a6e61288e8e0e3cb2a9adfff32bde5cae715cd219dcb4944e15f97ee0f33dde0"}}