{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CB7USSU2XNS7FIZBSJ7XU4B5TD","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":"7b6a0f6ddb7e48e8f92abae8d171dc645ca2909f0417bbd157efdaeaf4a8650e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-13T14:34:48Z","title_canon_sha256":"2e71f5ce9d7b9dc6baa84f2633cf225d97f1e60729efb04228e124b9f9908937"},"schema_version":"1.0","source":{"id":"1908.04665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04665","created_at":"2026-07-04T23:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04665v1","created_at":"2026-07-04T23:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04665","created_at":"2026-07-04T23:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"CB7USSU2XNS7","created_at":"2026-07-04T23:55:15Z"},{"alias_kind":"pith_short_16","alias_value":"CB7USSU2XNS7FIZB","created_at":"2026-07-04T23:55:15Z"},{"alias_kind":"pith_short_8","alias_value":"CB7USSU2","created_at":"2026-07-04T23:55:15Z"}],"graph_snapshots":[{"event_id":"sha256:b0948a4fcdaca84cfea93e1dbe829df3370156710f77815f95af5b3ebea74f1e","target":"graph","created_at":"2026-07-04T23:55:15Z","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/1908.04665/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, several papers have considered a nonlinear analogue of Fourier series in signal analysis, referred to as either nonlinear phase unwinding or adaptive Fourier decomposition. In these processes, a signal is represented as the real component of a complex function $F: \\partial\\mathbb{D}\\to \\mathbb{C}$, and by performing an iterative method to obtain a sequence of Blaschke decompositions, the signal can be approximated using only a few terms. To better understand the convergence of these methods, the study of Blaschke decompositions on weighted Hardy spaces was studied by Coifman and Stei","authors_text":"Stephen D. Farnham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-13T14:34:48Z","title":"Blaschke Decompositions on Weighted Hardy Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04665","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9e8fbf725827205684f1b479ecd801bacf9ad36e17bbc263e26f6e1b780da3e9","target":"record","created_at":"2026-07-04T23:55:15Z","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":"7b6a0f6ddb7e48e8f92abae8d171dc645ca2909f0417bbd157efdaeaf4a8650e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-13T14:34:48Z","title_canon_sha256":"2e71f5ce9d7b9dc6baa84f2633cf225d97f1e60729efb04228e124b9f9908937"},"schema_version":"1.0","source":{"id":"1908.04665","kind":"arxiv","version":1}},"canonical_sha256":"107f494a9abb65f2a321927f7a703d98f1ddaba8759b493613b58169f4d0adf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"107f494a9abb65f2a321927f7a703d98f1ddaba8759b493613b58169f4d0adf0","first_computed_at":"2026-07-04T23:55:15.397700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:15.397700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mV1HoVCtUFw7bi5kdyNk612ZAj580Y7pHZLIhJ86LOGL+67+ZB9W0ka9+1F9GILz4rcq1NHuHSyNicD1+gtbCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:15.398037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e8fbf725827205684f1b479ecd801bacf9ad36e17bbc263e26f6e1b780da3e9","sha256:b0948a4fcdaca84cfea93e1dbe829df3370156710f77815f95af5b3ebea74f1e"],"state_sha256":"aa8c7959b401a60ab22025583423141e9b4bc963d1bb5e38d39dc368fbea5ece"}