{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:XVTTWWBRRMONYSXDBLXTT5PUUL","short_pith_number":"pith:XVTTWWBR","schema_version":"1.0","canonical_sha256":"bd673b58318b1cdc4ae30aef39f5f4a2c193f16b4dcd9d19407e1f3ba1e0d3bb","source":{"kind":"arxiv","id":"cs/0512063","version":1},"attestation_state":"computed","paper":{"title":"Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability","license":"","headline":"","cross_cats":["cs.CE","cs.IR","cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Jan Eriksson, Visa Koivunen","submitted_at":"2005-12-15T14:51:36Z","abstract_excerpt":"In this paper the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA problems to complex-valued models. Relevant properties of complex random vectors are described in order to extend the Darmois-Skitovich theorem for complex-valued models. This theorem is used to construct a proof of a theorem for each of the above ICA model concepts. Both circular and noncircular complex random vectors are covered. Examples clarifying the abo"},"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":"cs/0512063","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2005-12-15T14:51:36Z","cross_cats_sorted":["cs.CE","cs.IR","cs.LG","math.IT"],"title_canon_sha256":"6d22088d9db5fc8c9824befd5105bb4a72306ba8b8888e8785afe65c351db6f9","abstract_canon_sha256":"85558acb3e0ea59a493896db7b6fb625085e1b23c070dc09f8210f560800c09c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:54.127158Z","signature_b64":"MJF/PXPEx0w3ihMt3WdRiq6GsSsbmVV2T/B5A6qsXrw5OGdaLaXmIOr5XRdpK+nILi1mmGtjrpbJumm0M5hwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd673b58318b1cdc4ae30aef39f5f4a2c193f16b4dcd9d19407e1f3ba1e0d3bb","last_reissued_at":"2026-05-18T04:08:54.126635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:54.126635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complex Random Vectors and ICA Models: Identifiability, Uniqueness and Separability","license":"","headline":"","cross_cats":["cs.CE","cs.IR","cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Jan Eriksson, Visa Koivunen","submitted_at":"2005-12-15T14:51:36Z","abstract_excerpt":"In this paper the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA problems to complex-valued models. Relevant properties of complex random vectors are described in order to extend the Darmois-Skitovich theorem for complex-valued models. This theorem is used to construct a proof of a theorem for each of the above ICA model concepts. Both circular and noncircular complex random vectors are covered. Examples clarifying the abo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0512063","kind":"arxiv","version":1},"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":"cs/0512063","created_at":"2026-05-18T04:08:54.126732+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0512063v1","created_at":"2026-05-18T04:08:54.126732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0512063","created_at":"2026-05-18T04:08:54.126732+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVTTWWBRRMON","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVTTWWBRRMONYSXD","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVTTWWBR","created_at":"2026-05-18T12:25:53.939244+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/XVTTWWBRRMONYSXDBLXTT5PUUL","json":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL.json","graph_json":"https://pith.science/api/pith-number/XVTTWWBRRMONYSXDBLXTT5PUUL/graph.json","events_json":"https://pith.science/api/pith-number/XVTTWWBRRMONYSXDBLXTT5PUUL/events.json","paper":"https://pith.science/paper/XVTTWWBR"},"agent_actions":{"view_html":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL","download_json":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL.json","view_paper":"https://pith.science/paper/XVTTWWBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0512063&json=true","fetch_graph":"https://pith.science/api/pith-number/XVTTWWBRRMONYSXDBLXTT5PUUL/graph.json","fetch_events":"https://pith.science/api/pith-number/XVTTWWBRRMONYSXDBLXTT5PUUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL/action/storage_attestation","attest_author":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL/action/author_attestation","sign_citation":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL/action/citation_signature","submit_replication":"https://pith.science/pith/XVTTWWBRRMONYSXDBLXTT5PUUL/action/replication_record"}},"created_at":"2026-05-18T04:08:54.126732+00:00","updated_at":"2026-05-18T04:08:54.126732+00:00"}