{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FFICCWLSASGECHU2OCMOWMDYAP","short_pith_number":"pith:FFICCWLS","schema_version":"1.0","canonical_sha256":"2950215972048c411e9a7098eb307803ff52d96d312580708cb3ce0c3c23a63f","source":{"kind":"arxiv","id":"2412.18501","version":3},"attestation_state":"computed","paper":{"title":"Hilbert Transform on Graphs: Let There Be Phase","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Alexandre Cionca, Chun Hei Michael Chan, Dimitri Van De Ville","submitted_at":"2024-12-24T15:40:06Z","abstract_excerpt":"In the past years, many signal processing operations have been successfully adapted to the graph setting. One elegant and effective approach is to exploit the eigendecomposition of a graph shift operator (GSO), such as the adjacency or Laplacian operator, to define a graph Fourier transform when projecting graph signals on the corresponding basis. However, the extension of this scheme to directed graphs is challenging since the associated GSO is non-symmetric and, in general, not diagonalizable. Here, we build upon a recent framework that adds a minimal number of edges to allow diagonalization"},"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":"2412.18501","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SP","submitted_at":"2024-12-24T15:40:06Z","cross_cats_sorted":[],"title_canon_sha256":"279e2af8de224eb84bd3f74b9ae8573c215fed252b62eb25fdaba686bff3aa5e","abstract_canon_sha256":"3fdd7d2c5a2da8dc9523e0408caa4cfc87aa521e5b8a9c1f8afcce7ac87bff4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:46:40.201052Z","signature_b64":"cMuJRGI1VEEf3f61AVAvUqYcNNcYq/hfOOw4TQdHE+TUtmcWNZqdBEjB/nJ5wjPlJRa4KW8TMMpzl790tzBTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2950215972048c411e9a7098eb307803ff52d96d312580708cb3ce0c3c23a63f","last_reissued_at":"2026-07-05T10:46:40.200565Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:46:40.200565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert Transform on Graphs: Let There Be Phase","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Alexandre Cionca, Chun Hei Michael Chan, Dimitri Van De Ville","submitted_at":"2024-12-24T15:40:06Z","abstract_excerpt":"In the past years, many signal processing operations have been successfully adapted to the graph setting. One elegant and effective approach is to exploit the eigendecomposition of a graph shift operator (GSO), such as the adjacency or Laplacian operator, to define a graph Fourier transform when projecting graph signals on the corresponding basis. However, the extension of this scheme to directed graphs is challenging since the associated GSO is non-symmetric and, in general, not diagonalizable. Here, we build upon a recent framework that adds a minimal number of edges to allow diagonalization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18501","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.18501/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.18501","created_at":"2026-07-05T10:46:40.200625+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.18501v3","created_at":"2026-07-05T10:46:40.200625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18501","created_at":"2026-07-05T10:46:40.200625+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFICCWLSASGE","created_at":"2026-07-05T10:46:40.200625+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFICCWLSASGECHU2","created_at":"2026-07-05T10:46:40.200625+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFICCWLS","created_at":"2026-07-05T10:46:40.200625+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/FFICCWLSASGECHU2OCMOWMDYAP","json":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP.json","graph_json":"https://pith.science/api/pith-number/FFICCWLSASGECHU2OCMOWMDYAP/graph.json","events_json":"https://pith.science/api/pith-number/FFICCWLSASGECHU2OCMOWMDYAP/events.json","paper":"https://pith.science/paper/FFICCWLS"},"agent_actions":{"view_html":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP","download_json":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP.json","view_paper":"https://pith.science/paper/FFICCWLS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.18501&json=true","fetch_graph":"https://pith.science/api/pith-number/FFICCWLSASGECHU2OCMOWMDYAP/graph.json","fetch_events":"https://pith.science/api/pith-number/FFICCWLSASGECHU2OCMOWMDYAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP/action/storage_attestation","attest_author":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP/action/author_attestation","sign_citation":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP/action/citation_signature","submit_replication":"https://pith.science/pith/FFICCWLSASGECHU2OCMOWMDYAP/action/replication_record"}},"created_at":"2026-07-05T10:46:40.200625+00:00","updated_at":"2026-07-05T10:46:40.200625+00:00"}