{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2ZU26MXEL5Z25RVYCET5Y7DXEB","short_pith_number":"pith:2ZU26MXE","schema_version":"1.0","canonical_sha256":"d669af32e45f73aec6b81127dc7c77204b192425313307e50ca4313dce5cc8b5","source":{"kind":"arxiv","id":"1208.4578","version":2},"attestation_state":"computed","paper":{"title":"Signal Analysis based on Complex Wavelet Signs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Laurent Demaret, Martin Storath, Peter Massopust","submitted_at":"2012-08-22T19:05:28Z","abstract_excerpt":"We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show that the signature equals zero at sufficiently regular points of a signal whereas at salient features, such as jumps or cusps, it is non-zero. At such feature points, the orientation of the signature in the complex plane can be interpreted as an indicator of local symmetry and antisymmetry. We establish that the signature rotates in the complex plane under "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.4578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-22T19:05:28Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e7b7a74cb78a0f057f2e3bdb50912479223892611c35aba262bd8d354e399e28","abstract_canon_sha256":"5874e6c8a15881466759312cdeb9f2f184cdf5a67951b1ab9edbc9697dcdc261"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.363428Z","signature_b64":"K264lZldOFmgdk1cf7vY8RvLXUceuLr4uZUrkU9B0QHyyWcqUMWuZkUdXa+/oyhV0safn1eW+9YSJXyTI8B0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d669af32e45f73aec6b81127dc7c77204b192425313307e50ca4313dce5cc8b5","last_reissued_at":"2026-05-18T01:35:05.362935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.362935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Signal Analysis based on Complex Wavelet Signs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Laurent Demaret, Martin Storath, Peter Massopust","submitted_at":"2012-08-22T19:05:28Z","abstract_excerpt":"We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show that the signature equals zero at sufficiently regular points of a signal whereas at salient features, such as jumps or cusps, it is non-zero. At such feature points, the orientation of the signature in the complex plane can be interpreted as an indicator of local symmetry and antisymmetry. We establish that the signature rotates in the complex plane under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4578","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.4578","created_at":"2026-05-18T01:35:05.363009+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4578v2","created_at":"2026-05-18T01:35:05.363009+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4578","created_at":"2026-05-18T01:35:05.363009+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ZU26MXEL5Z2","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ZU26MXEL5Z25RVY","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ZU26MXE","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB","json":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB.json","graph_json":"https://pith.science/api/pith-number/2ZU26MXEL5Z25RVYCET5Y7DXEB/graph.json","events_json":"https://pith.science/api/pith-number/2ZU26MXEL5Z25RVYCET5Y7DXEB/events.json","paper":"https://pith.science/paper/2ZU26MXE"},"agent_actions":{"view_html":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB","download_json":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB.json","view_paper":"https://pith.science/paper/2ZU26MXE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4578&json=true","fetch_graph":"https://pith.science/api/pith-number/2ZU26MXEL5Z25RVYCET5Y7DXEB/graph.json","fetch_events":"https://pith.science/api/pith-number/2ZU26MXEL5Z25RVYCET5Y7DXEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB/action/storage_attestation","attest_author":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB/action/author_attestation","sign_citation":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB/action/citation_signature","submit_replication":"https://pith.science/pith/2ZU26MXEL5Z25RVYCET5Y7DXEB/action/replication_record"}},"created_at":"2026-05-18T01:35:05.363009+00:00","updated_at":"2026-05-18T01:35:05.363009+00:00"}