{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3WVV2JYHLANHTTI6DWYK572IE2","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":"91f78e9239214cf110c0dc68a1992d935c5ed6b0c1d014db9d030156a3407b32","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-01-30T23:37:29Z","title_canon_sha256":"a811bbd7a3a5e698dac133ea81be3a50318b05e71ac0e674190f6dbb9ed75082"},"schema_version":"1.0","source":{"id":"2501.18800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18800","created_at":"2026-07-05T10:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18800v1","created_at":"2026-07-05T10:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18800","created_at":"2026-07-05T10:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"3WVV2JYHLANH","created_at":"2026-07-05T10:07:51Z"},{"alias_kind":"pith_short_16","alias_value":"3WVV2JYHLANHTTI6","created_at":"2026-07-05T10:07:51Z"},{"alias_kind":"pith_short_8","alias_value":"3WVV2JYH","created_at":"2026-07-05T10:07:51Z"}],"graph_snapshots":[{"event_id":"sha256:2d4e1b86cc9ec629b0f99486f2d43ae28c1fb3d3d009630b10b5a9f234735b65","target":"graph","created_at":"2026-07-05T10:07:51Z","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/2501.18800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $p\\in(0,1]$ and $W$ be an $A_p$-matrix weight, which in scalar case is exactly a Muckenhoupt $A_1$ weight. In this article, we introduce matrix-weighted Hardy spaces $H^p_W$ via the matrix-weighted grand non-tangential maximal function and characterize them, respectively, in terms of various other maximal functions and atoms, both of which are closely related to matrix weights under consideration and their corresponding reducing operators. As applications, we first establish the finite atomic characterization of $H^p_W$, then using it we give a criterion on the boundedness of sublinear ope","authors_text":"Dachun Yang, Fan Bu, Wen Yuan, Yiqun Chen","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-01-30T23:37:29Z","title":"Maximal Function and Atomic Characterizations of Matrix-Weighted Hardy Spaces with Their Applications to Boundedness of Calder\\'on--Zygmund Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18800","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":"sha256:82f8616af9a487784bdba358224b2734fd6e2b00e02d820c401ecdc251765bb4","target":"record","created_at":"2026-07-05T10:07:51Z","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":"91f78e9239214cf110c0dc68a1992d935c5ed6b0c1d014db9d030156a3407b32","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-01-30T23:37:29Z","title_canon_sha256":"a811bbd7a3a5e698dac133ea81be3a50318b05e71ac0e674190f6dbb9ed75082"},"schema_version":"1.0","source":{"id":"2501.18800","kind":"arxiv","version":1}},"canonical_sha256":"ddab5d2707581a79cd1e1db0aeff4826b936083f3e647d1a6cc32134756bb96c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddab5d2707581a79cd1e1db0aeff4826b936083f3e647d1a6cc32134756bb96c","first_computed_at":"2026-07-05T10:07:51.776024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:51.776024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xwr5icgm6aJUMD/uF5Y1x/aKfQwDEvOBkrSNWhjAy6KYSLNNEMVA51+3YfVHfB7UVCe7akiVUxcR4FT9bBYYBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:51.776533Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.18800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82f8616af9a487784bdba358224b2734fd6e2b00e02d820c401ecdc251765bb4","sha256:2d4e1b86cc9ec629b0f99486f2d43ae28c1fb3d3d009630b10b5a9f234735b65"],"state_sha256":"2c3839a1ad216711d7097ef47f4fd334a1515c3e93cbbe273dba2724b25654ff"}