{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X7XYL6347VXRYIW3H74LXNE6CS","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":"4155988b405c9cfbb02907ce698ecc5f0ce317237c8fd6f42726e2aeda0eb102","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-01-06T14:38:23Z","title_canon_sha256":"57e30e8d7c336f6ae59d105120f522cccd9e05d8a7c01cb5c925ae6fd621b90f"},"schema_version":"1.0","source":{"id":"2501.03050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03050","created_at":"2026-07-05T09:57:29Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03050v1","created_at":"2026-07-05T09:57:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03050","created_at":"2026-07-05T09:57:29Z"},{"alias_kind":"pith_short_12","alias_value":"X7XYL6347VXR","created_at":"2026-07-05T09:57:29Z"},{"alias_kind":"pith_short_16","alias_value":"X7XYL6347VXRYIW3","created_at":"2026-07-05T09:57:29Z"},{"alias_kind":"pith_short_8","alias_value":"X7XYL634","created_at":"2026-07-05T09:57:29Z"}],"graph_snapshots":[{"event_id":"sha256:e648286d9d2c2cdf6fd3348a2a86a96bdb75946124fbd6733600d538af0b2e90","target":"graph","created_at":"2026-07-05T09:57:29Z","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/2501.03050/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Introduced by A. Volberg, matrix $A_{p,\\infty}$ weights provide a suitable generalization of Muckenhoupt $A_\\infty$ weights from the classical theory. In our previous work, we established new characterizations of these weights. Here, we use these results to study inhomogeneous Besov-type and Triebel--Lizorkin-type spaces with such weights. In particular, we characterize these spaces, in terms of the $\\varphi$-transform, molecules, and wavelets, and obtain the boundedness of almost diagonal operators, pseudo-differential operators, trace operators, pointwise multipliers, and Calder\\'on--Zygmund","authors_text":"Dachun Yang, Fan Bu, Tuomas Hyt\\\"onen, Wen Yuan","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-01-06T14:38:23Z","title":"Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_\\infty$ Weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03050","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:f32ea2b94a3a386c9cd92f37b8bd659de9ecbcede10533271fbc19f507bf9558","target":"record","created_at":"2026-07-05T09:57:29Z","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":"4155988b405c9cfbb02907ce698ecc5f0ce317237c8fd6f42726e2aeda0eb102","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-01-06T14:38:23Z","title_canon_sha256":"57e30e8d7c336f6ae59d105120f522cccd9e05d8a7c01cb5c925ae6fd621b90f"},"schema_version":"1.0","source":{"id":"2501.03050","kind":"arxiv","version":1}},"canonical_sha256":"bfef85fb7cfd6f1c22db3ff8bbb49e149c317af0a7f45061f3445cc36001f90a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfef85fb7cfd6f1c22db3ff8bbb49e149c317af0a7f45061f3445cc36001f90a","first_computed_at":"2026-07-05T09:57:29.877312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:29.877312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HV4HV3WAkv3I5uTFUMFrXqUCMunJ1VDB/Gqz9TQZvCbpgXnqeRwRvmBqBVZDkQ9ezfsnTDMNwq64SJLfV+EDAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:29.877737Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.03050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f32ea2b94a3a386c9cd92f37b8bd659de9ecbcede10533271fbc19f507bf9558","sha256:e648286d9d2c2cdf6fd3348a2a86a96bdb75946124fbd6733600d538af0b2e90"],"state_sha256":"0f447f8bb1d55d9093acc68ed092a99d912bffaf20d5526115d05d47b7fccd70"}