{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZQIBMWR7V45Y6JWXCTYKOIHFDH","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":"e9622e483452b6e01584d0da29aa26e34c365f890867be420953d2829469ab5c","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-22T20:33:13Z","title_canon_sha256":"7d52bc4a521a7842b073f0e6821147bf00c57825744240aced2f3079286cc7f0"},"schema_version":"1.0","source":{"id":"1107.4619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4619","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4619v1","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4619","created_at":"2026-05-18T03:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZQIBMWR7V45Y","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZQIBMWR7V45Y6JWX","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZQIBMWR7","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:1880a940df9458227329cc8822ea3e46ad88cd98b8f056233f8b20e37bee11d3","target":"graph","created_at":"2026-05-18T03:17:57Z","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":"A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp estimates of the localization, vanishing moments, and smoothness of the transformed wavelet. We work in the general setting of non-compactly supported wavelets. Our main result is that, in the presence of some minimal smoothness and decay, the Hilbert transform of a wavelet is again as smooth and oscillating as the original wavelet, whereas its localization is cont","authors_text":"Kunal Narayan Chaudhury, Michael Unser","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-22T20:33:13Z","title":"On the Hilbert transform of wavelets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4619","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:fdc6f0569bab866009e9cefe1a0ab0405c0b7506dc812ab3ad3107492e9f7312","target":"record","created_at":"2026-05-18T03:17:57Z","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":"e9622e483452b6e01584d0da29aa26e34c365f890867be420953d2829469ab5c","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-22T20:33:13Z","title_canon_sha256":"7d52bc4a521a7842b073f0e6821147bf00c57825744240aced2f3079286cc7f0"},"schema_version":"1.0","source":{"id":"1107.4619","kind":"arxiv","version":1}},"canonical_sha256":"cc10165a3faf3b8f26d714f0a720e519d592ae999f20be196960202053b61eee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc10165a3faf3b8f26d714f0a720e519d592ae999f20be196960202053b61eee","first_computed_at":"2026-05-18T03:17:57.597525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:57.597525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1lYa6Md2donj9r2tH3oRjBC0AuvejlcjFJMZTtIgs6a/HDnh4lFGXUWZ8+aL57KPle1d1dor3ZnvWcumOlPaBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:57.598121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdc6f0569bab866009e9cefe1a0ab0405c0b7506dc812ab3ad3107492e9f7312","sha256:1880a940df9458227329cc8822ea3e46ad88cd98b8f056233f8b20e37bee11d3"],"state_sha256":"ecae93472664ab46c456e6543f54e765bb3d6eee28e84cfd6d2b6f70eaf3d524"}