{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JHCNN7NY7CPZIHWWUJHNUCAMO4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a8703eac53f01f4764e4241501d690e6326ffeefdd3cf03db28502342c850403","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-03T17:17:38Z","title_canon_sha256":"087c3474f66367c26b3a3bfeb78076f34c45221754c86a0001b384a771363e3e"},"schema_version":"1.0","source":{"id":"1304.1015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1015","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1015v2","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1015","created_at":"2026-05-18T01:33:16Z"},{"alias_kind":"pith_short_12","alias_value":"JHCNN7NY7CPZ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHCNN7NY7CPZIHWW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHCNN7NY","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:f85f6fc65dc8807156cd0000c1fff275046b261f8b52d8e781eb3f2eeed7364a","target":"graph","created_at":"2026-05-18T01:33:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We give an alternative characterization of the class of Muckenhoupt weights $A_{\\infty, \\mathfrak B}$ for homothecy invariant Muckenhoupt bases $\\mathfrak B$ consisting of convex sets. In particular we show that $w\\in A_{\\infty, \\mathfrak B}$ if and only if there exists a constant $c>0$ such that for all measurable sets $E\\subset \\mathbb R^n$ we have $$ w({x\\in \\mathbb R^n: M_{\\mathfrak B} (\\mathbf {1}_E)(x)>1/2}) < c w(E).$$ This applies for example to the collection $\\mathfrak R$ of rectangles with sides parallel to the coordinate axes, giving a new characterization of strong (multiparameter","authors_text":"Ioannis Parissis, Paul A. Hagelstein, Teresa Luque","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-03T17:17:38Z","title":"Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1015","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:69a48fc06a6907f34d8b3cf264b77ed3e4d6f03b49342efac100b0696b3c8d09","target":"record","created_at":"2026-05-18T01:33:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a8703eac53f01f4764e4241501d690e6326ffeefdd3cf03db28502342c850403","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-03T17:17:38Z","title_canon_sha256":"087c3474f66367c26b3a3bfeb78076f34c45221754c86a0001b384a771363e3e"},"schema_version":"1.0","source":{"id":"1304.1015","kind":"arxiv","version":2}},"canonical_sha256":"49c4d6fdb8f89f941ed6a24eda080c77258b1d76fdbe2c7ed452d648afee5166","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49c4d6fdb8f89f941ed6a24eda080c77258b1d76fdbe2c7ed452d648afee5166","first_computed_at":"2026-05-18T01:33:16.966728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:16.966728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oVNd/zYMfxlg5J8upGMJ6b26ECRcXL3A3iFGvxyp0z3eMQxlPU4oW74g8DisTMXknRcyVTVH6yeJk2H4yWvRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:16.967395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69a48fc06a6907f34d8b3cf264b77ed3e4d6f03b49342efac100b0696b3c8d09","sha256:f85f6fc65dc8807156cd0000c1fff275046b261f8b52d8e781eb3f2eeed7364a"],"state_sha256":"85a3c566918f776a452dc6067ba41d9799a00b9a84d7e90f44c5ceb71e66201c"}