{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:34I2DCSOU4QSUD4SLKTFLHDMXG","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":"980e0de3ad975b2f16b325b7ae23caf3f21299a806c5502166fa18f54f9e2493","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SP","submitted_at":"2024-10-24T21:19:58Z","title_canon_sha256":"ee61c295084b987015b91c307e7a4db1e7df4205a3fbf337dcca282bb0f7627d"},"schema_version":"1.0","source":{"id":"2410.19167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19167","created_at":"2026-07-05T09:25:52Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19167v1","created_at":"2026-07-05T09:25:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19167","created_at":"2026-07-05T09:25:52Z"},{"alias_kind":"pith_short_12","alias_value":"34I2DCSOU4QS","created_at":"2026-07-05T09:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"34I2DCSOU4QSUD4S","created_at":"2026-07-05T09:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"34I2DCSO","created_at":"2026-07-05T09:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a2dbb1b7e3c99b0204bff8319061f2f7b05bae9d48ec6865edc51a8e55bd7f32","target":"graph","created_at":"2026-07-05T09:25:52Z","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/2410.19167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a well-suited formalism and then investigate some general properties of empirical wavelet systems. In particular, we provide some sufficient conditions to the existence of a reconstruction formula. In the second part of the paper, we propose the construction of empirical wavelet systems based on some classic mother wavelets.","authors_text":"Jerome Gilles","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SP","submitted_at":"2024-10-24T21:19:58Z","title":"Continuous empirical wavelets systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19167","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":"sha256:57fe8411ccc5c85e5c57c46ba5db25b42ee76a7ff55c90196b4eae3fcc09e9b0","target":"record","created_at":"2026-07-05T09:25:52Z","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":"980e0de3ad975b2f16b325b7ae23caf3f21299a806c5502166fa18f54f9e2493","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SP","submitted_at":"2024-10-24T21:19:58Z","title_canon_sha256":"ee61c295084b987015b91c307e7a4db1e7df4205a3fbf337dcca282bb0f7627d"},"schema_version":"1.0","source":{"id":"2410.19167","kind":"arxiv","version":1}},"canonical_sha256":"df11a18a4ea7212a0f925aa6559c6cb9b453e628c64bf8c582d794f63228a257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df11a18a4ea7212a0f925aa6559c6cb9b453e628c64bf8c582d794f63228a257","first_computed_at":"2026-07-05T09:25:52.532966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:25:52.532966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kGtlutw57LFZKjZbAbNVS+eq/rn4eu9hXXfLHEp4G4GD3Bfj/+cGGugZfKO+s4JAYoIgHYEXKU4JeGLvPSDXBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:25:52.533437Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.19167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57fe8411ccc5c85e5c57c46ba5db25b42ee76a7ff55c90196b4eae3fcc09e9b0","sha256:a2dbb1b7e3c99b0204bff8319061f2f7b05bae9d48ec6865edc51a8e55bd7f32"],"state_sha256":"9f7d6e4319622896472bc708bf3c97c832246677dadbff4a8221cb1d78f41eef"}