{"as_of":"2026-08-18T13:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ad17178fb053fea3d12b29e3bb9f60bae2d7abe5921457fb2716118b902f21b3","coverage":[{"denominator":113,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T01:09:59.165198Z","state":"measured"},{"denominator":102,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":102,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T10:13:05.830219Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-05T18:09:22.081474Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.02136","snapshot_observed_at":"2026-08-16T10:13:05.830219Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.19060","last_updated":"2025-05-11T14:55:00Z","snapshot_observed_at":"2026-08-16T10:00:10.210272Z","submitted_at":"2025-04-27T00:35:35Z","title":"Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calder\\'{o}n--Zygmund Operators","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T10:13:05.830219Z"},"links":{"cited_paper":"/paper/2505.02136","citing_paper":"/paper/2504.19060"},"observation_digest":"sha256:2ed25bd5960695e4085c153c6106c06ac07d230776911d7d3746b71d814cb12e","observation_id":"6f956e6f-f367-43d3-8ffd-ee138f275a46","resolution":{"observed_at":"2026-08-16T10:13:05.830219Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"cited_work":{"arxiv_id":"2505.02136","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.02136","snapshot_observed_at":"2026-08-05T18:09:22.081474Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","venue":"math.FA","work_id":"67da706a-1b99-4b2d-97fd-8fe5b01bdf52","year":2025},"citing_paper":{"arxiv_id":"2508.15195","last_updated":"2025-08-21T03:08:04Z","snapshot_observed_at":"2026-08-11T13:36:13.482968Z","submitted_at":"2025-08-21T03:08:04Z","title":"Matrix-Weighted Campanato Spaces: Duality and Calder\\'on--Zygmund Operators","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T18:09:11.143094Z"},"links":{"cited_paper":"/paper/2505.02136","citing_paper":"/paper/2508.15195"},"observation_digest":"sha256:07fdd1603546f29316f662ddc1baf84edae16c7125ac108d7679da0343553669","observation_id":"a18f2ecf-f094-479f-b42c-886171839330","resolution":{"observed_at":"2026-08-05T18:09:22.188544Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.02136/citation-record","integrity":"/paper/2505.02136/integrity","json":"/paper/2505.02136/citation-record.json","paper":"/paper/2505.02136"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.597009Z","title":"Bai and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.597009Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:82b433921de4d318f9945f074a052b88e76758d24da9bac61210c5a6c9e29470","observation_id":"f1fe4d84-0489-44ef-9499-df0aeb20757b","resolution":{"observed_at":"2026-08-16T01:09:58.597009Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.602574Z","title":"Bai and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.602574Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:d2e9e0685f1e39af40d7ab92df63c44aa5c6d11050e7d8c86ff1c1260a815e41","observation_id":"e7440d0d-1f99-42fc-9539-08d1076e9053","resolution":{"observed_at":"2026-08-16T01:09:58.602574Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.607947Z","title":"Bai and J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.607947Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:e8d4845e7b61c2c1184b2abf99a04838db922725bf0acb5e4be269695d9a36ba","observation_id":"2c7c9b80-e05c-47ce-ab14-4f8453bed23c","resolution":{"observed_at":"2026-08-16T01:09:58.607947Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.613059Z","title":null,"venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.613059Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:ff196edea6de2db252585911abd7a2b086c6e1e9bed2b02ec0a876cd4f6a036a","observation_id":"eae0a578-95ec-4cea-9aef-c0a0be6b84ed","resolution":{"observed_at":"2026-08-16T01:09:58.613059Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.617669Z","title":null,"venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.617669Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:bcf8cfd646538784b16c9d80499f8b48253eba754c5258f1477fb18625fcf895","observation_id":"217cfaaf-1cdf-4529-9ee1-58911647084c","resolution":{"observed_at":"2026-08-16T01:09:58.617669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.622960Z","title":"Bownik, Atomic and molecular decompositions of aniso tropic Besov spaces, Math","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.622960Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:95990e51916ac81d39711f0f6e427a1af09cc060479b9bac2074bb65e0f2866d","observation_id":"a5f1ebc4-a203-40bf-8c3c-980e60a3e023","resolution":{"observed_at":"2026-08-16T01:09:58.622960Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.627417Z","title":"Bownik, Anisotropic Triebel–Lizorkin spaces with do ubling measures, J","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.627417Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:054e503518c4c158403e9488d63ec73f2a3aedb770df091f6109426ecee05a7d","observation_id":"5293d4e9-d62f-4317-bf8f-58b344697c4b","resolution":{"observed_at":"2026-08-16T01:09:58.627417Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.765765Z","title":"Bownik, Duality and interpolation of anisotropic Tri ebel–Lizorkin spaces, Math","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.765765Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:4381191119bc38354151516813c2d3653bd5b01d6a8456658c378881fed190ae","observation_id":"1ecda296-4f8e-4406-8220-a69b9ebc5783","resolution":{"observed_at":"2026-08-16T01:09:58.765765Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.770394Z","title":"Bownik and K.-P","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.770394Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:28a895f5739ec9fa4165823fff848e1c35f923c8f9c73c7dfbbb12cf32bd9abe","observation_id":"58278c13-5b2a-4d95-8dd5-aab46537b14c","resolution":{"observed_at":"2026-08-16T01:09:58.770394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.775420Z","title":"Bownik and D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.775420Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:96a5191fb2e593967ab104b25dd4c7d78ad3b5eeb0a529192cf1e7c4128a9ee9","observation_id":"889e9b03-0012-4550-9448-f7dfb8fe0260","resolution":{"observed_at":"2026-08-16T01:09:58.775420Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.18800","last_updated":"2025-01-30T23:37:29Z","snapshot_observed_at":"2026-08-12T18:25:22.382856Z","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","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.18800","snapshot_observed_at":"2026-08-16T01:09:58.779823Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.779823Z"},"links":{"cited_paper":"/paper/2501.18800","citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:79f2cefcc7d63b887705a985d526248f59a2746fc43d32a71fbbb43819f83caf","observation_id":"df429c7f-e8ff-4a64-85f5-0cccf70694b0","resolution":{"observed_at":"2026-08-16T01:09:58.779823Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.785555Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.785555Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:b938278ffd49bc758acc7941e17d06aa7f6e7d48303d70cd993f1e0f9a9df3d1","observation_id":"47eb29df-0484-4aa0-bcc6-07cfa9e0a666","resolution":{"observed_at":"2026-08-16T01:09:58.785555Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.790317Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.790317Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:c235957b4445abe3c3fea51804bf297f8b0bb00b21ecde33fed3bbe71fa9fab4","observation_id":"2c050bc2-5ef5-425d-bf76-9791cf7d0fbc","resolution":{"observed_at":"2026-08-16T01:09:58.790317Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.794741Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.794741Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:a5c85dcaea7721cf7fde09621a0d67836a2eb865b3e08c037897f38ff2c36a84","observation_id":"4aed3105-b7cb-4b17-9993-515349d9c00a","resolution":{"observed_at":"2026-08-16T01:09:58.794741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.05974","last_updated":"2023-11-10T10:14:22Z","snapshot_observed_at":"2026-08-16T14:44:24.376839Z","submitted_at":"2023-11-10T10:14:22Z","title":"New Characterizations and Properties of Matrix $A_\\infty$ Weights","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.05974","snapshot_observed_at":"2026-08-16T01:09:58.799346Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.799346Z"},"links":{"cited_paper":"/paper/2311.05974","citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:63c477a2e4945eee3423b616f8f27b101411c691d0ad41439008b4aae1a69ade","observation_id":"05d70f52-5d6f-4895-8c8a-3e5349bd5092","resolution":{"observed_at":"2026-08-16T01:09:58.799346Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.804025Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.804025Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:139ff1a7df51ac6cfa803bf05cad50cd0db054f27acb136a6c3682f989ffaa7e","observation_id":"820a1526-82d7-4fec-a756-af4b73354498","resolution":{"observed_at":"2026-08-16T01:09:58.804025Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.809146Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.809146Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:2a8e72718768ebfa60ff2e32536195a2e490d34105a15fec8b4a58bef7d19955","observation_id":"c1efb982-f1d5-4bc5-9b18-6e6a109f00db","resolution":{"observed_at":"2026-08-16T01:09:58.809146Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.813070Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.813070Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:c77c7b4b3352fdbfb3ecc204078eeba51f3a746e24b87d009ecaa4dcde30443d","observation_id":"50a2a236-a9f0-4344-8b4c-373674a6ea8c","resolution":{"observed_at":"2026-08-16T01:09:58.813070Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.817295Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.817295Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:0eea60dc3c28229ea49e9dc08d8b42e982614e1ef496a35bda5065b2152166f4","observation_id":"1361eed1-12de-4a2b-b93f-13c8a1c802ac","resolution":{"observed_at":"2026-08-16T01:09:58.817295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.821340Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.821340Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:221361a4bd068538028b6b98153fe41e984fcf987d9fe5ca52ade4817a9bd112","observation_id":"7200b2f3-6d91-461f-9403-e683f8ba46e6","resolution":{"observed_at":"2026-08-16T01:09:58.821340Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.825681Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.825681Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:298d7d81b3a9ef049ca502bf0997852cc5c1d1edb68708d4f8e7c2da40fa7f36","observation_id":"f4d1e9a3-cdaa-44a0-8820-3d15e6f1914c","resolution":{"observed_at":"2026-08-16T01:09:58.825681Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.829781Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.829781Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f6a02eaf841f2104cdfcb40dac79b6861c15637d3abe0ab5f9c1eb33a68b3769","observation_id":"473b5606-57ce-4aae-a5f1-6dc163f26918","resolution":{"observed_at":"2026-08-16T01:09:58.829781Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.834715Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.834715Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:72eb6ecd69f6d30e300dd65fc74b03e99242dc4d40861f7a63a08c85375674ad","observation_id":"9ddd98c4-1445-4542-9831-d94b6c5f2b32","resolution":{"observed_at":"2026-08-16T01:09:58.834715Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.839054Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.839054Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:632adea69c6cbd3809d4c7e5e85188978162aeb61a88d458607c9fbe93edbd6a","observation_id":"aad8dda9-105c-4e62-bdd0-f037cc17bf6a","resolution":{"observed_at":"2026-08-16T01:09:58.839054Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.843159Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.843159Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:b73c675af6160528cccb2a934187ba681aae2fca836b8713d0b9695783406d59","observation_id":"72905ace-5ed4-41b6-8f5b-1e3593f7d2fd","resolution":{"observed_at":"2026-08-16T01:09:58.843159Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.848457Z","title":"Bui, Weighted Besov and Triebel spaces: Interpol ation by the real method, Hiroshima Math","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.848457Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:4534fcee97173db755d353b7e3b02932b03bda9415223632d523b54d4f4b3949","observation_id":"99849b0e-16bb-4efb-81ac-7333fc656b95","resolution":{"observed_at":"2026-08-16T01:09:58.848457Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.853010Z","title":"Bui and M","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.853010Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:8485f167e899cf6abeec69f8c33fef6f1297a1b7a53b65621c3659ea82559963","observation_id":"8c862904-c00e-457f-8268-ddc118a46f03","resolution":{"observed_at":"2026-08-16T01:09:58.853010Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.857425Z","title":"Cho, Continuous characterization of the Triebel –Lizorkin spaces and Fourier multi- pliers, Bull","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.857425Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:c1855cac139f99c2d5121ae518e4869fd6048daebd2ea31a8baab1e0d9e2d986","observation_id":"981442aa-f6c8-4629-b193-67fec8a9f226","resolution":{"observed_at":"2026-08-16T01:09:58.857425Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.861999Z","title":"Dafni and J","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.861999Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f678fabf7d676d3228aad149500e1cf1edb55dec78da8afad46d5ed0b778f2ed","observation_id":"f5d57b63-e12d-4123-8f91-558d9e132694","resolution":{"observed_at":"2026-08-16T01:09:58.861999Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.865822Z","title":"Daubechies, Orthonormal bases of compactly support ed wavelets, Comm","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.865822Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:1e137204a55e709f7968c831d259c915ac51ed9b0c6080b0c89596ccef654fbf","observation_id":"2708a29c-10dc-4291-9afb-0499140590c8","resolution":{"observed_at":"2026-08-16T01:09:58.865822Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.869780Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.869780Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:235ac678bff9fdb1dff0f4a6731595f5da05109cd476c632006e018fab6b4618","observation_id":"92dcac8d-d659-479c-90d3-6a44bf58604b","resolution":{"observed_at":"2026-08-16T01:09:58.869780Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.874088Z","title":"Di Plinio, T","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.874088Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f20734a5c0e6440e05d869537b00b80915a045d2748ed6a2e07b1407a40415c4","observation_id":"d3b4444f-000f-464c-a9ca-27f5d41b71e1","resolution":{"observed_at":"2026-08-16T01:09:58.874088Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.06961","last_updated":"2024-02-10T14:29:51Z","snapshot_observed_at":"2026-08-16T14:19:40.390049Z","submitted_at":"2024-02-10T14:29:51Z","title":"The matrix $A_2$ conjecture fails, i.e. $3/2>1$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.06961","snapshot_observed_at":"2026-08-16T01:09:58.878055Z","title":"Domelevo, S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.878055Z"},"links":{"cited_paper":"/paper/2402.06961","citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:d4d8c92db2bc4eeaa987d34c1a47ad560679cc47e43e6a77907bb3e3dd551840","observation_id":"0fae450a-3d47-4479-a492-9028482366e0","resolution":{"observed_at":"2026-08-16T01:09:58.878055Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.882576Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.882576Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:ead39989f3c377c03d2c87820848fdf23aa1749c22d6b120f4c0723b6a9d3f20","observation_id":"1c3c0a68-e357-4fec-b9e7-c64c477ccaed","resolution":{"observed_at":"2026-08-16T01:09:58.882576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.886916Z","title":"Fe fferman and E","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.886916Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:8a9cfd765f11a5fba469c2b6582cad4f15e36c67573841eec39dcf98b5885889","observation_id":"63024f5f-d454-431e-9014-ea38bf32eb98","resolution":{"observed_at":"2026-08-16T01:09:58.886916Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.891379Z","title":"Fe fferman and E","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.891379Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:7d7627a1903909ecdbeb496e8927d8453e0507b6c6b7f5b5d86d38658747c144","observation_id":"4f579cc7-e63f-46d0-aa62-68bcd3be2798","resolution":{"observed_at":"2026-08-16T01:09:58.891379Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.895719Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.895719Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:2c3c7bfaad7cbe17cfc30df5b5c2d73c3e1822a39c4e74ef6705c50e74b3cb2c","observation_id":"fb94263b-fbfb-416d-8d37-211983ae51ca","resolution":{"observed_at":"2026-08-16T01:09:58.895719Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.899726Z","title":"Frazier and B","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.899726Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:137782fcb40899b640f631f9bccb62c8efa609ca8f01d44463fa67bc4c971287","observation_id":"af0ef30f-f503-461e-92eb-cf204c80ea52","resolution":{"observed_at":"2026-08-16T01:09:58.899726Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.903860Z","title":"Frazier, B","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.903860Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:ea90718c15d3bf6a65533620ea9033db394b7a0da9a019c47ccf34d7e8c0d103","observation_id":"36d84b13-b037-42fd-b7d1-a4b47a808fb1","resolution":{"observed_at":"2026-08-16T01:09:58.903860Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.908154Z","title":"Frazier and S","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.908154Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:23f0ef33bb173d3751ab721061c7ebee9a06098fec4fddadae5d1d43c38789af","observation_id":"3be0585f-3663-440a-969b-2e8d1de7e921","resolution":{"observed_at":"2026-08-16T01:09:58.908154Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.912144Z","title":"Frazier and S","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.912144Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:90f8affd85d61d48730b908ca5479142aa9d80b44745388e7e3771b62ae027a0","observation_id":"d47f8eb2-e26a-4a65-b0bc-32f17d4a9666","resolution":{"observed_at":"2026-08-16T01:09:58.912144Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.725895Z","title":null,"venue":null,"work_id":"875d11f5-e996-439e-895f-0669f77d7fb7","year":2019},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.916215Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:ab69c43c7055cb43c883387b42f2b4b5efeeb32138e2b6535043bb597fee8f2b","observation_id":"253ca4ff-e9fc-4647-a302-34d9f7a53333","resolution":{"observed_at":"2026-08-16T01:10:00.731314Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.920568Z","title":"Goldberg, Matrix Ap weights via maximal functions, Pacific J","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.920568Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f1274f9fdbde53207cbea1c231edb07c8dce3f6b08df71e955385bd9ea37feba","observation_id":"6c545f7a-129a-4fbf-907c-222002cb62df","resolution":{"observed_at":"2026-08-16T01:09:58.920568Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.699272Z","title":null,"venue":null,"work_id":"7d727964-d375-4e0f-92bb-ecc3afbd4262","year":2021},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.925436Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:d8b912ccc536a1e473986a48dfe084ff08c619b5e5ffb9f765e1cd9d6e6350e2","observation_id":"baa12e7a-1ae6-4e9b-9faf-e75b2caa1d38","resolution":{"observed_at":"2026-08-16T01:10:00.704131Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.683647Z","title":null,"venue":null,"work_id":"2be52107-e4a6-467c-bb2e-392b8620db3f","year":2023},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.929556Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:51d1b2bb72387ddb48bc6952b0c3c83955f582a294a215d051d52783d9b39d5b","observation_id":"cba36d13-5240-4cf2-b9b2-daf4a27b9482","resolution":{"observed_at":"2026-08-16T01:10:00.689101Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.933843Z","title":"Grafakos, Classical Fourier Analysis, Third editio n, Graduate Texts in Mathematics 249, Springer, New Y ork, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.933843Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:2c72a132bcd46137e3fda12fe7be31ee79a4edbcdafdff63e6a149ac7764ce8d","observation_id":"9a0a3622-1ad9-4b78-bd06-ac97e80dcfa5","resolution":{"observed_at":"2026-08-16T01:09:58.933843Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.937817Z","title":"Grafakos, Modern Fourier Analysis, Third edition, G raduate Texts in Mathematics 250, Springer, New Y ork, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.937817Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:a30c1ef23f0b2a1266415ccf6e14ea0526bd572ed2792d609d7eac871e4b99d5","observation_id":"2beef7e9-a73e-4a4c-a18a-a1d8c4450b08","resolution":{"observed_at":"2026-08-16T01:09:58.937817Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.646931Z","title":null,"venue":null,"work_id":"6e147bce-ac46-44cd-b160-9f684eaf32ba","year":2021},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.941753Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:ba18cb78ea0a59ad537352299a4c5ee9f6dd3e0c42a27ce87c41d86715e24302","observation_id":"68f89a51-c047-4432-be4e-e34c8cbfd3b5","resolution":{"observed_at":"2026-08-16T01:10:00.652975Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.945576Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.945576Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:dd95f72603563b51d0d3ae6f44217c415fd785fb0baff38a96870594a55a769f","observation_id":"91ceec00-e889-4ea3-9797-f8efa7631cbc","resolution":{"observed_at":"2026-08-16T01:09:58.945576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.620953Z","title":null,"venue":null,"work_id":"9a3b4543-7785-42cb-a5b5-9ed6153386ac","year":2025},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.949271Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f155c78b35cbfcf9832ff5f2fb84db53b7dfae9cd4175d8bc6e7fc3f92e783f5","observation_id":"a6474651-8580-46f8-b8a5-c0dac71a9588","resolution":{"observed_at":"2026-08-16T01:10:00.625911Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.604990Z","title":null,"venue":null,"work_id":"74e53e0b-5aa5-46d4-a142-96b47a0bf50c","year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.953373Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:c9b5760a13cd96e281948c32d01cad6ce2bdf169375a7380c5dcc413b2ece3fe","observation_id":"61b4e8ba-77d4-47b4-bf59-f82e5db13898","resolution":{"observed_at":"2026-08-16T01:10:00.610329Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.958142Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.958142Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:cc7aca4c8c77008dfff6c45128d1553b587cffc6b5e9789e32cd49df856e2d02","observation_id":"0fed2756-3573-4323-851f-b992f0d23687","resolution":{"observed_at":"2026-08-16T01:09:58.958142Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.576534Z","title":null,"venue":null,"work_id":"a088250e-9227-4a6a-9c1f-6a23ba1a6d73","year":2012},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.962360Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:114e403aba66f05b62b72d72f0437717be17d1e4c7cfc2fc6abd3aefbe70e796","observation_id":"b544fd34-5ba7-411a-ac88-cf41a0b9c311","resolution":{"observed_at":"2026-08-16T01:10:00.582675Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.560389Z","title":null,"venue":null,"work_id":"f4fe36ad-e82c-4083-9340-610d03577276","year":2013},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.966389Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:4d87b628095242c7cb306fc045968a3de22cafc8ba9bed7d09e031da4de4ca1a","observation_id":"58d6aaee-6214-45c5-ae1d-1526889f56ca","resolution":{"observed_at":"2026-08-16T01:10:00.564799Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.970551Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.970551Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:902403aafdd21f8639d0c8bf54d2937e776b5ded0cefa9f60bd4d5733333f792","observation_id":"1652dd86-a60f-41e4-8b5a-e63ba675f572","resolution":{"observed_at":"2026-08-16T01:09:58.970551Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.535648Z","title":"Ho, Singular integral operators, John–Nirenber g inequalities and Triebel–Lizorkin type spaces on weighted Lebesgue spaces with variable exponents, Rev","venue":null,"work_id":"1210173f-504b-4070-bf5e-486316795447","year":2016},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.974748Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:7276a54fda446636e3a220701b12b915643a3078be400759a06816f812dce52b","observation_id":"5697e00a-2c9d-42a5-9685-64b2ce224e31","resolution":{"observed_at":"2026-08-16T01:10:00.540550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.520992Z","title":"Ho, V ector-valued operators with singular kerne l and Triebel–Lizorkin block spaces with variable exponents, Kyoto J","venue":null,"work_id":"1d54940a-5ff0-4626-a6ff-b50d523bb2ec","year":2016},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.978901Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:9aba9acb818a81a95d351a9d9bdc73a4947e11de01fa5df1faad21cfd9117787","observation_id":"97091da4-3859-4e33-9026-42bc0a2807c3","resolution":{"observed_at":"2026-08-16T01:10:00.525817Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.982833Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.982833Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:6a928106c6c3189691538411fe39a0b6c53077db634f7077d96506258f472d73","observation_id":"7cd71823-f1b2-448a-9593-be383fd07150","resolution":{"observed_at":"2026-08-16T01:09:58.982833Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.987170Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.987170Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:4bed761a8c28578741754d4ec50fb7b9f4d124395b1eaa1a49c3eafefe504495","observation_id":"d4590b7d-748f-46d0-95f9-e24eb0f5a633","resolution":{"observed_at":"2026-08-16T01:09:58.987170Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.483820Z","title":"Kozono and M","venue":null,"work_id":"7cbce075-75c0-4692-8e5a-6ccfc165bfb6","year":1994},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.991577Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:5eea3d01e9bb5ec6bd585d9c72a96f0d3fac9c374f7f8261cdae333b8662121a","observation_id":"cbc4ec29-6023-4142-a023-98620666f047","resolution":{"observed_at":"2026-08-16T01:10:00.488733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:58.995719Z","title":"Kakaroumpas and O","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.995719Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:d3874e7a32362aba38e2610aa1bb31acc479be6a8476c12550415666af049f8a","observation_id":"cb1d22e0-a950-4385-851e-e17b5ad7d6eb","resolution":{"observed_at":"2026-08-16T01:09:58.995719Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.466917Z","title":"Lerner, K","venue":null,"work_id":"85012603-691e-4587-a34b-436ee11b960f","year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:58.999952Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:0fdd60d5bce4e6adac019c410cfcb58f58b09a8ba2a0dc989f711436fd4277d8","observation_id":"172e6853-1629-4a33-93b7-6a933c8128e8","resolution":{"observed_at":"2026-08-16T01:10:00.472912Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.003996Z","title":"Lerner, K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.003996Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:548cc2aaa31774c64ae29fba46c51e51b1c00ec5e914e5ac322760d2d82c4f2b","observation_id":"ee863ebb-cd22-406c-8992-52096110319f","resolution":{"observed_at":"2026-08-16T01:09:59.003996Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.449851Z","title":null,"venue":null,"work_id":"04050428-e5cd-4239-8388-58c4e110e8f9","year":2012},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.008166Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:2373d73ed30aae5cac86c4ad673423940ee70d3cdf0a9f76546b1170a59f27c5","observation_id":"3fd935fc-1765-48ab-95f5-f0e407e68b1e","resolution":{"observed_at":"2026-08-16T01:10:00.455443Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.432280Z","title":null,"venue":null,"work_id":"c29489eb-0d67-4ffa-9151-6c2db3e40f34","year":2014},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.012174Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:33d0d272039830cf74ae9bbea38dacb849bcb3de8da0e5d99329b9654e60e604","observation_id":"18930660-0b6a-48c2-86cc-01aa227ad9d9","resolution":{"observed_at":"2026-08-16T01:10:00.437877Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.416540Z","title":"Li and Q","venue":null,"work_id":"dda58f84-23ff-48d9-8bb4-e44d670ac22a","year":2013},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.016808Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:5ea11eed42a72549e785e24ad03ccf79b84342051014fb9497f86476925ebfe1","observation_id":"0632c027-cbb5-4b20-abf6-9697a8505ab0","resolution":{"observed_at":"2026-08-16T01:10:00.421463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.021063Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.021063Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:2e6bd64603db6afc8cb055978a853e75e264bf997ab3b25e97abb2b19e606b84","observation_id":"44f4ad8b-55f1-46cc-9168-1958a353978f","resolution":{"observed_at":"2026-08-16T01:09:59.021063Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.025409Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.025409Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:b4e613030274077804b284f9b52e20c714b514c17b7b09db16976fac1b635d95","observation_id":"c8d8c30d-4670-4379-b3b1-7a8d33966937","resolution":{"observed_at":"2026-08-16T01:09:59.025409Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.377811Z","title":null,"venue":null,"work_id":"36cdc473-15c7-40e2-83ac-4d909cadc7ea","year":1972},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.029616Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:fae01ed4c0cb79c4f87fda9515e19023a223d57f42c03eac3953b5e4b19cc308","observation_id":"5734f6c2-26ea-4af1-8a25-dffbe7ce8a0e","resolution":{"observed_at":"2026-08-16T01:10:00.382629Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.363906Z","title":null,"venue":null,"work_id":"14bbb3be-c33b-4914-8c59-f1abc4b4427b","year":1974},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.033840Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:1c9ebe8d4e12507264453d6066d7092adfd70b8b336e6be96e8f7122e7d934bc","observation_id":"1ccb09d9-9ba9-43c3-bb06-ec45c052d1dc","resolution":{"observed_at":"2026-08-16T01:10:00.367907Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.350100Z","title":null,"venue":null,"work_id":"bdb6d440-37f0-491a-bc4f-9111f692d92e","year":2003},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.038197Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:83b8a20d2c0115d69398a531fa1ad943962e616aec331266c14dd0b19d0b7887","observation_id":"093e4f38-75bb-4ae2-97e0-eb27f71c8768","resolution":{"observed_at":"2026-08-16T01:10:00.354458Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.335292Z","title":"Meyer, Wavelets and Operators, Translated from the 1 990 French original by D","venue":null,"work_id":"65962e17-2596-405a-90d0-79e65caa6e9f","year":1992},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.042552Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f3ae8daf9975385f82e042822c6effb392facdf5fee8cf1f25305332ec994b12","observation_id":"a6378e9f-27ee-464c-8111-b8d50baf1c42","resolution":{"observed_at":"2026-08-16T01:10:00.339907Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.320367Z","title":"Nakamura, T","venue":null,"work_id":"5144777c-24f7-4ad7-9077-f2bc1039ebce","year":2016},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.047017Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:1765e58862baefd8a01876681c331b5b5f5906089c0e1842f8ec54feebd9dd53","observation_id":"b335ef5d-2ab7-4d5f-9029-b82c02cd07e3","resolution":{"observed_at":"2026-08-16T01:10:00.325066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.051400Z","title":"Nazarov, S","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.051400Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:580589c64ae7f4b712c1fcfa55248aa428141bdb625a744a1e5ed615d2062a82","observation_id":"1c3491be-9498-4bae-ac5c-500686c32b2d","resolution":{"observed_at":"2026-08-16T01:09:59.051400Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.294630Z","title":null,"venue":null,"work_id":"d4d18d15-4ccb-400b-9f43-6e29dd264c57","year":1996},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.055875Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:5ddf46054758ddeb67a3417e5bfef8d9e06934c3fc2664d30f80e04c4af62d51","observation_id":"d2a70cd1-aee4-49cf-b6bf-e574f3e6c815","resolution":{"observed_at":"2026-08-16T01:10:00.299318Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.277724Z","title":"Nielsen, Bandlimited multipliers on matrix-weight ed Lp-spaces, J","venue":null,"work_id":"02f11f47-ac08-4450-9c74-3c775339098d","year":2025},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.060216Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:3c15ba659377744cf695af337a11d63b1a1801a02a2601e9fc462afed0254d59","observation_id":"b4bf8a17-4565-4c64-8045-d648e53d7bb7","resolution":{"observed_at":"2026-08-16T01:10:00.283457Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.260627Z","title":null,"venue":null,"work_id":"fef5f81f-2250-4bd5-86ff-dce2bcdf9574","year":1951},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.065008Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:1ba133324ecac6bb7a4afce4cce36e05bb59c014d7491d3606f450b5afe233b7","observation_id":"71484f49-294c-49ea-af4a-4dd376a0e4b9","resolution":{"observed_at":"2026-08-16T01:10:00.266631Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.245060Z","title":"Ron and Z","venue":null,"work_id":"4ef68b5b-06b2-4c30-9fb0-4bad00589c85","year":1995},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.069673Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:0675167e628ee355f3b439c6dd43d7c6010589f9c1d32e8f855bf7542ae4121f","observation_id":"456c65dd-5d1f-44a3-a3c3-52dee553bb41","resolution":{"observed_at":"2026-08-16T01:10:00.249880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.074106Z","title":"Roudenko, Matrix-weighted Besov spaces, Trans","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.074106Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:db8b2f975b20976cbae2c144b10841fa14c4c607df493973ec797f36fc7002c1","observation_id":"63b7c710-49c0-4bc3-a73f-207bdc49ce3f","resolution":{"observed_at":"2026-08-16T01:09:59.074106Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.078712Z","title":"Roudenko, Duality of matrix-weighted Besov spaces, Studia Math","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.078712Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:e605fd4fdf338ac182321eee293294dd305db5af1e4fac7f9e142beb1b627abd","observation_id":"70464a7f-3ced-4918-8c85-03ad8e8bee4b","resolution":{"observed_at":"2026-08-16T01:09:59.078712Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.208762Z","title":"Salo ff-Coste, Aspects of Sobolev-Type Inequalities, London Math ematical Society Lec- ture Note Series, 289","venue":null,"work_id":"bd3ca115-f5c3-4ffb-85e5-fc4e427ff578","year":2002},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.083072Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:1d30c7d1978507a565ccecc5475158b15ab962644c0a0c4881142dca16a76d6a","observation_id":"f1bac697-4b7a-43ae-9f6b-2568793ee55e","resolution":{"observed_at":"2026-08-16T01:10:00.213833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.194825Z","title":"Sawano, Wavelet characterization of Besov–Morrey a nd Triebel–Lizorkin–Morrey spaces, Funct","venue":null,"work_id":"e023de3c-096f-4790-80fc-fccda913b9f9","year":2008},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.087151Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:a45f57940d234082482c2ac74bbf619b94aa1423ca8bd2f1d19bd3bbeda2ba48","observation_id":"f580b3a6-f5ea-40de-8eac-82b5b5c15066","resolution":{"observed_at":"2026-08-16T01:10:00.199105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.178290Z","title":"Sawano, A note on Besov–Morrey spaces and Triebel–Li zorkin–Morrey spaces, Acta Math","venue":null,"work_id":"dffcf554-94dc-43a3-adaf-f873e5436f90","year":2009},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.091344Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:6e5bcd7149d44d5480e138e961fb02987129f60e71d85fbe75af1a3536e10c0a","observation_id":"a04ef91e-96e3-488b-a230-e8c835b1b2c1","resolution":{"observed_at":"2026-08-16T01:10:00.184037Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.160984Z","title":"Sawano, Br´ ezis–Gallou¨ et–Wainger type inequalit y for Besov–Morrey spaces, Studia Math","venue":null,"work_id":"d202425a-6a39-46d7-b3e2-b0f5e620d25b","year":2010},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.095425Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:3bcef36cc3bd484198b08f38941a616fa498912c0f5c83cbb45f0ab088e2bbee","observation_id":"4c24107d-c884-4c66-a107-58fe31ee6711","resolution":{"observed_at":"2026-08-16T01:10:00.166692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.143126Z","title":"Sawano, Besov–Morrey spaces and Triebel–Lizorkin– Morrey spaces on domains, Math","venue":null,"work_id":"15b6d9a6-4ac9-4c7e-81a3-3dda7f9d2ce9","year":2010},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.099502Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:a9ac4431738fd36b27b6ce170f2ba874835ffc6507c0577f7f59757d24bb299a","observation_id":"06ff07bc-7660-4fe5-83b0-c3b465f99454","resolution":{"observed_at":"2026-08-16T01:10:00.148729Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.128097Z","title":"Sawano, G","venue":null,"work_id":"61ddaa9b-94ba-4e6e-8268-e0ff0792bf4b","year":2020},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.103493Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:afdf1c97dd792487f2dd970c1ee37daa8c26a7d88bf3664cc058568de7b196b9","observation_id":"4871c01f-637b-493f-8eaf-78c750fc8343","resolution":{"observed_at":"2026-08-16T01:10:00.132460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.112894Z","title":"Sawano and H","venue":null,"work_id":"84d0b6b9-3c80-4391-b4e7-1ec345d4cfd0","year":2007},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.108065Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:bdc5af2f682f37844ca699faf9ef98597d25fdada4d9d18f52e77c0750c64754","observation_id":"a4b5e62c-cdce-4a07-b740-46132eca7d43","resolution":{"observed_at":"2026-08-16T01:10:00.117768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.098022Z","title":"Sawano and H","venue":null,"work_id":"9a11b436-ef39-4d1d-b6d3-c0a9982daf72","year":2009},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.112936Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:22beae59c05e4619b9fb440b2c7a8e0b982523f9c55d66de66efac1fd0881727","observation_id":"59666b32-2ec4-4163-aa28-1c8ecb2a3876","resolution":{"observed_at":"2026-08-16T01:10:00.102260Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.083676Z","title":null,"venue":null,"work_id":"ba83725b-e89c-4649-8309-38cf6fd4918c","year":2024},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.117014Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:838b22ca8a455f66d1d311729e2d998e1e7e053877d57b6b8ada0bcbf7f6b46c","observation_id":"9fb0363e-4539-4fa3-85d6-d2039bed0265","resolution":{"observed_at":"2026-08-16T01:10:00.087991Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.121662Z","title":"Tang, A note on weighted Besov-type and Triebel–Lizo rkin-type spaces, J","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.121662Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:c59185989d8eb39356da43e0e63e76150d3b994975ba31dc1baf8f12b08b4437","observation_id":"f8d113fb-b2af-46ee-90a8-2e01c0cc8386","resolution":{"observed_at":"2026-08-16T01:09:59.121662Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.058359Z","title":"Tang and J","venue":null,"work_id":"18e0b179-b1e6-45c4-bb52-749167735d55","year":2005},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.126164Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f790a440b2f368d3bb2dba80bd6972fa8fbbfa3e9ee11beabc85f0fe22089dbd","observation_id":"8973d60c-011d-48df-aa57-31a95b1bd290","resolution":{"observed_at":"2026-08-16T01:10:00.062711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.043850Z","title":"Treil and A","venue":null,"work_id":"5ce9c90b-8aec-4d16-a82d-034822c385b4","year":1997},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.131522Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:f661ff2251750c5aa37cc09c80c4e694b0fe9e1baa9d61c410835985a0ea1a21","observation_id":"3174e3dc-0012-4248-99b6-0266d39cd9a5","resolution":{"observed_at":"2026-08-16T01:10:00.048225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.027311Z","title":"Triebel, Spaces of distributions of Besov type on Euc lidean n-space, duality, interpola- tion, Ark","venue":null,"work_id":"001cc3d4-24d0-44bb-98c2-c545f9ad88a5","year":1973},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.135597Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:4351da74a893af243c7984366c8fd85eaf5b5e4f68acc77b7cb57ca73a4676a3","observation_id":"e4263b0f-2e95-4b76-bc8c-d89f92d1ebe1","resolution":{"observed_at":"2026-08-16T01:10:00.032977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:10:00.010486Z","title":"Triebel, Theory of Function Spaces, Monographs in Ma thematics 78, Birkh¨ auser, Basel, 1983","venue":null,"work_id":"bc87f33a-3cdf-4905-a0a3-3d71cc1035bb","year":1983},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.139522Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:e308f7b5020ac0b42e5f34b6d75c0b87bd8c1ff4b1f9de1db29e7bad02a4d193","observation_id":"3853793a-67d1-478c-834a-7e7ee6a241e3","resolution":{"observed_at":"2026-08-16T01:10:00.015454Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.993859Z","title":"Triebel, Theory of function spaces","venue":null,"work_id":"49544397-7dc2-40e2-810e-ad5ecb9d52d9","year":1992},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.143862Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:bda1277567da2111edac8a305c115b7a28e23b4f332fb67d4cef751949db93fb","observation_id":"d1682d92-4750-41e7-92e2-a42ff40d2e59","resolution":{"observed_at":"2026-08-16T01:09:59.999464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.978960Z","title":"Triebel, Theory of Function Spaces","venue":null,"work_id":"3195f337-5c53-4a17-aead-d282cdf5ab09","year":2006},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.147863Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:453df763f640165262c8dd5d0dfcc9c17b23a17bff700c38df9efb13ca2505bd","observation_id":"9e8bf3aa-a952-4d0e-82b3-a0fc5b85dee3","resolution":{"observed_at":"2026-08-16T01:09:59.983285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.964872Z","title":"Triebel, Local Function Spaces, Heat and Navier–Sto kes Equations, EMS Tracts in Mathematics 20, European Mathematical Society (EMS), Z¨ urich, 2013","venue":null,"work_id":"e2534871-64ea-4c41-a648-0e1c20224802","year":2013},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.152049Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:ccb9e3fe7bab0ea8c1971fdebb79bc78468d5a04db4df79dbef42a741bdbd705","observation_id":"f3c824fa-6331-4f61-8d64-f6d1c933bf4d","resolution":{"observed_at":"2026-08-16T01:09:59.969185Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.950336Z","title":"Triebel, Hybrid Function Spaces, Heat and Navier–St okes Equations, EMS Tracts in Mathematics 24, European Mathematical Society (EMS), Z¨ urich, 2014","venue":null,"work_id":"a4166d0a-3779-4a85-8f1f-90e23f014085","year":2014},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.156157Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:8f5e05dae95f29f8899417f6861144655fb6ee49726e307c2103f07a10db3578","observation_id":"e422f823-7cc1-43ee-a256-50479218d6ea","resolution":{"observed_at":"2026-08-16T01:09:59.954672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.160824Z","title":"V olberg, Matrix Ap weights via S -functions, J","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.160824Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:834f1446ca8ec6c8ed244a089f227d6c637aa7793053822afdba751b05737944","observation_id":"bc75488a-6fad-4ce4-a922-d4b53e583d5a","resolution":{"observed_at":"2026-08-16T01:09:59.160824Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T01:09:59.926006Z","title":null,"venue":null,"work_id":"e8b43eb8-a5e4-45f7-bd15-e165431ffba2","year":2025},"citing_paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-16T01:09:59.165198Z"},"links":{"citing_paper":"/paper/2505.02136"},"observation_digest":"sha256:92b1e817a7661e42bef0efd3e6eaf8c1952c8bf7aa63e8fe691623d7e646809d","observation_id":"f2228ae4-93a1-49ed-9935-a31f9f2f76c7","resolution":{"observed_at":"2026-08-16T01:09:59.930167Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.02136","last_updated":"2025-05-04T14:53:33Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-18T12:27:58.877659Z","submitted_at":"2025-05-04T14:53:33Z","title":"Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":74,"verified_exact":0,"verified_fuzzy":25},"total_outbound_references":113},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 100 of 113 outbound references and 2 inbound Pith citation observations for arXiv:2505.02136."}