{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4LJ3W326RJXZOYOMC57RLBVJWX","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":"c0497fc271029b37432108d36407cc123e18cae4f49cc93d92a8d2e8933ce99b","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-06-06T11:25:13Z","title_canon_sha256":"881da00bae321f662ccdccb975a7360335cc0c94401185a721d4933fab0d1c05"},"schema_version":"1.0","source":{"id":"2506.05993","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05993","created_at":"2026-07-05T11:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05993v2","created_at":"2026-07-05T11:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05993","created_at":"2026-07-05T11:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"4LJ3W326RJXZ","created_at":"2026-07-05T11:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"4LJ3W326RJXZOYOM","created_at":"2026-07-05T11:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"4LJ3W326","created_at":"2026-07-05T11:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:0275ed27f93cbe35432004b863e61a063741f96f523d2fd5efb5210d2fd257fe","target":"graph","created_at":"2026-07-05T11:20:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.05993/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We precisely characterize the relationships between the reverse H\\\"older inequality, the Fujii-Wilson condition, the B\\'ekoll\\'e-Bonami $\\mathrm{B}_p$ condition, the $\\mathrm{B}_\\infty$ condition, and the reverse Jensen inequality, for arbitrary weights in the unit disc. This is achieved by introducing new side conditions that turn out to be necessary and sufficient. The side conditions are simple and testable, and can be interpreted as integral versions of the much stronger condition of bounded hyperbolic oscillation, which has been considered earlier in the literature.","authors_text":"Carlos Mudarra, Karl-Mikael Perfekt","cross_cats":["math.CV","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-06-06T11:25:13Z","title":"Characterizations for arbitrary B\\'ekoll\\'e-Bonami weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05993","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:d23cf4e96fa2349e41ea97f60e1759061a6db7f5ed4198b3031e0727b7886f10","target":"record","created_at":"2026-07-05T11:20:13Z","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":"c0497fc271029b37432108d36407cc123e18cae4f49cc93d92a8d2e8933ce99b","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-06-06T11:25:13Z","title_canon_sha256":"881da00bae321f662ccdccb975a7360335cc0c94401185a721d4933fab0d1c05"},"schema_version":"1.0","source":{"id":"2506.05993","kind":"arxiv","version":2}},"canonical_sha256":"e2d3bb6f5e8a6f9761cc177f1586a9b5c2e5b7ef600a6ac43921527909ec805c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2d3bb6f5e8a6f9761cc177f1586a9b5c2e5b7ef600a6ac43921527909ec805c","first_computed_at":"2026-07-05T11:20:13.307340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:13.307340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xUJ0dpTgMkDkhl5eZeCzyxi1doXy5qDpPR6mL59hX5C8U4UMffcRS5kYVjzczdjFvRPoS/hQtfz2XY/AwPUwCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:13.307851Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05993","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d23cf4e96fa2349e41ea97f60e1759061a6db7f5ed4198b3031e0727b7886f10","sha256:0275ed27f93cbe35432004b863e61a063741f96f523d2fd5efb5210d2fd257fe"],"state_sha256":"79de259b42f806edce7b1c5caf3e077f6f3025a2bd8a018b1b80e634a5bccdf8"}