{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JBUVDNJEVM6Y5BP7J426DOK3QQ","short_pith_number":"pith:JBUVDNJE","canonical_record":{"source":{"id":"1306.0331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-06-03T09:00:28Z","cross_cats_sorted":[],"title_canon_sha256":"35515e46fb22edc8c97d35b3541acd2e0ffd4b13770162b5e7847c231a2b1499","abstract_canon_sha256":"132d47060180341a12ba24a8cbcb80e012f4fbd4bdf2c8cdbf68238ddb06c2c7"},"schema_version":"1.0"},"canonical_sha256":"486951b524ab3d8e85ff4f35e1b95b8407f4c583e07eab312253eb12b3c55efb","source":{"kind":"arxiv","id":"1306.0331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0331","created_at":"2026-05-18T01:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0331v1","created_at":"2026-05-18T01:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0331","created_at":"2026-05-18T01:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"JBUVDNJEVM6Y","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JBUVDNJEVM6Y5BP7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JBUVDNJE","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JBUVDNJEVM6Y5BP7J426DOK3QQ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.0331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-06-03T09:00:28Z","cross_cats_sorted":[],"title_canon_sha256":"35515e46fb22edc8c97d35b3541acd2e0ffd4b13770162b5e7847c231a2b1499","abstract_canon_sha256":"132d47060180341a12ba24a8cbcb80e012f4fbd4bdf2c8cdbf68238ddb06c2c7"},"schema_version":"1.0"},"canonical_sha256":"486951b524ab3d8e85ff4f35e1b95b8407f4c583e07eab312253eb12b3c55efb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:38.633100Z","signature_b64":"/lj0jN0Bbr4iNDHK6fFjrv/2xpByB0zrvlIxu3hlyite6bzmiN6EKS3PiInyUfO74qQmDRytpI1MSbRJWeXTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"486951b524ab3d8e85ff4f35e1b95b8407f4c583e07eab312253eb12b3c55efb","last_reissued_at":"2026-05-18T01:49:38.632613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:38.632613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.0331","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icyzcPyPjHb8wiPgRmyNZV69lWDRqG6ltFP7Fr3SQ6H0iwhppElSKR2USuLpkohFGxJl2OF8QM7/LQfGy/lEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:00:17.423047Z"},"content_sha256":"69b63e697e9a184c390f76f0c84f1ffda783a68ea15bf3b2d44ca3c8a9732186","schema_version":"1.0","event_id":"sha256:69b63e697e9a184c390f76f0c84f1ffda783a68ea15bf3b2d44ca3c8a9732186"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JBUVDNJEVM6Y5BP7J426DOK3QQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new algorithm for complex non orthogonal joint diagonalization based on Shear and Givens rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"Adel Belouchrani, Ammar Mesloub, Karim Abeb-Meraim","submitted_at":"2013-06-03T09:00:28Z","abstract_excerpt":"This paper introduces a new algorithm to approximate non orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the JD problem and takes advantage from combining Givens and Shear rotations to attempt the approximate joint diagonalization (JD). It represents a non trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e. Complex JDi) using complex to real matrix transformation. Also, since several metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0331","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"omlgAhBGZ6UqqXIwGZlqZ0OhiN/w9cRjsaXOd25x6dYir1a1g3jhCs9+5hHgn44PJK/yKx3tS0TdcK/jW5QxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:00:17.423412Z"},"content_sha256":"c169658c128c1b577bdc2c37d70f7975122883f942cdfb7fccac5cea3fe56480","schema_version":"1.0","event_id":"sha256:c169658c128c1b577bdc2c37d70f7975122883f942cdfb7fccac5cea3fe56480"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JBUVDNJEVM6Y5BP7J426DOK3QQ/bundle.json","state_url":"https://pith.science/pith/JBUVDNJEVM6Y5BP7J426DOK3QQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JBUVDNJEVM6Y5BP7J426DOK3QQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T10:00:17Z","links":{"resolver":"https://pith.science/pith/JBUVDNJEVM6Y5BP7J426DOK3QQ","bundle":"https://pith.science/pith/JBUVDNJEVM6Y5BP7J426DOK3QQ/bundle.json","state":"https://pith.science/pith/JBUVDNJEVM6Y5BP7J426DOK3QQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JBUVDNJEVM6Y5BP7J426DOK3QQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JBUVDNJEVM6Y5BP7J426DOK3QQ","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":"132d47060180341a12ba24a8cbcb80e012f4fbd4bdf2c8cdbf68238ddb06c2c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-06-03T09:00:28Z","title_canon_sha256":"35515e46fb22edc8c97d35b3541acd2e0ffd4b13770162b5e7847c231a2b1499"},"schema_version":"1.0","source":{"id":"1306.0331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0331","created_at":"2026-05-18T01:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0331v1","created_at":"2026-05-18T01:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0331","created_at":"2026-05-18T01:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"JBUVDNJEVM6Y","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JBUVDNJEVM6Y5BP7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JBUVDNJE","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:c169658c128c1b577bdc2c37d70f7975122883f942cdfb7fccac5cea3fe56480","target":"graph","created_at":"2026-05-18T01:49:38Z","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":"This paper introduces a new algorithm to approximate non orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the JD problem and takes advantage from combining Givens and Shear rotations to attempt the approximate joint diagonalization (JD). It represents a non trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e. Complex JDi) using complex to real matrix transformation. Also, since several metho","authors_text":"Adel Belouchrani, Ammar Mesloub, Karim Abeb-Meraim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-06-03T09:00:28Z","title":"A new algorithm for complex non orthogonal joint diagonalization based on Shear and Givens rotations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0331","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":"sha256:69b63e697e9a184c390f76f0c84f1ffda783a68ea15bf3b2d44ca3c8a9732186","target":"record","created_at":"2026-05-18T01:49:38Z","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":"132d47060180341a12ba24a8cbcb80e012f4fbd4bdf2c8cdbf68238ddb06c2c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-06-03T09:00:28Z","title_canon_sha256":"35515e46fb22edc8c97d35b3541acd2e0ffd4b13770162b5e7847c231a2b1499"},"schema_version":"1.0","source":{"id":"1306.0331","kind":"arxiv","version":1}},"canonical_sha256":"486951b524ab3d8e85ff4f35e1b95b8407f4c583e07eab312253eb12b3c55efb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"486951b524ab3d8e85ff4f35e1b95b8407f4c583e07eab312253eb12b3c55efb","first_computed_at":"2026-05-18T01:49:38.632613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:38.632613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/lj0jN0Bbr4iNDHK6fFjrv/2xpByB0zrvlIxu3hlyite6bzmiN6EKS3PiInyUfO74qQmDRytpI1MSbRJWeXTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:38.633100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69b63e697e9a184c390f76f0c84f1ffda783a68ea15bf3b2d44ca3c8a9732186","sha256:c169658c128c1b577bdc2c37d70f7975122883f942cdfb7fccac5cea3fe56480"],"state_sha256":"27eb8b1937257d0b44f3d480848fc556dc1ddd55528d4542067e7a85d91d323c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8aDGxfQISh/nh9GTh+sPiCarDqIzJipQeiaJ4B6Czm1UX2cbdkFR0Axqoed0tpEDXVy6VMUCMQ7umGDHfRSmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:00:17.426763Z","bundle_sha256":"2da09ce642bc4292818edd93a4d2f7920b2180deba2ee1980b5806a396af68b3"}}