{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7GDTQQR43HCMKQ65FTQGUY7OQY","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":"86b260f54f2d4bb82d36b02942dde836a75992e5bbe46dfbf0f6c312dce3a542","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-02-04T18:35:07Z","title_canon_sha256":"bf33d94633d5b21869df873842af18d8a6cc7d7d864a92f5b15459e97125b728"},"schema_version":"1.0","source":{"id":"2602.04844","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.04844","created_at":"2026-06-19T16:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"2602.04844v2","created_at":"2026-06-19T16:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04844","created_at":"2026-06-19T16:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"7GDTQQR43HCM","created_at":"2026-06-19T16:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"7GDTQQR43HCMKQ65","created_at":"2026-06-19T16:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"7GDTQQR4","created_at":"2026-06-19T16:09:54Z"}],"graph_snapshots":[{"event_id":"sha256:b1f668b1eef88faed2c714f48a45b1089bce3ef645e6ffbe17494099a1c67205","target":"graph","created_at":"2026-06-19T16:09:54Z","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/2602.04844/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The action of the finite Hilbert transform defined on $L^\\infty(-1,1)$ and taking its values in the Zygmund space $L_{\\textnormal{exp}}(-1,1)$ is studied in detail. This is a reciprocal situation to the investigation recently undertaken in [11] of the finite Hilbert transform defined on the Zygumd space $L\\textnormal{log} L(-1,1)$ and taking its values in $L^1(-1,1)$. The fact that both $L^\\infty(-1,1)$ and $L_{\\textnormal{exp}}(-1,1)$ fail to be separable generates new features not present in[11].","authors_text":"Guillermo P. Curbera, Susumu Okada, Werner J. Ricker","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-02-04T18:35:07Z","title":"The finite Hilbert transform acting on $L^\\infty$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04844","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":"sha256:047afc803150e11a344dc6ddb19ec4e6b3810057d01f0143084af2f67ba62397","target":"record","created_at":"2026-06-19T16:09:54Z","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":"86b260f54f2d4bb82d36b02942dde836a75992e5bbe46dfbf0f6c312dce3a542","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-02-04T18:35:07Z","title_canon_sha256":"bf33d94633d5b21869df873842af18d8a6cc7d7d864a92f5b15459e97125b728"},"schema_version":"1.0","source":{"id":"2602.04844","kind":"arxiv","version":2}},"canonical_sha256":"f98738423cd9c4c543dd2ce06a63ee862deaa1281609a5c64cb1d0f26b0b943d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f98738423cd9c4c543dd2ce06a63ee862deaa1281609a5c64cb1d0f26b0b943d","first_computed_at":"2026-06-19T16:09:54.444683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:09:54.444683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cHYjQTF9p2fPAsrWGCpui5pVO5W18rCUHYVvi3+RKUztNFgBbTZan01j9CW7Ojb38viinG/L+oth018l09J1Cw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:09:54.445243Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.04844","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:047afc803150e11a344dc6ddb19ec4e6b3810057d01f0143084af2f67ba62397","sha256:b1f668b1eef88faed2c714f48a45b1089bce3ef645e6ffbe17494099a1c67205"],"state_sha256":"f6b837bbba83298e0e353057c021a21b9eaff277f799f10490577d0c2d914989"}