{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AIGYSKIUPF6RDNWPWZYUZZMQ3G","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":"0f0720f1b0e3cd507bd3468c5228f242849689ceabcbe2ad5c6f276669830da9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-02T02:37:50Z","title_canon_sha256":"119c166e0c91f977dff0865832d996719fc4592bb21e5f52100c140bd0a081f4"},"schema_version":"1.0","source":{"id":"1703.00591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00591","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00591v1","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00591","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"pith_short_12","alias_value":"AIGYSKIUPF6R","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AIGYSKIUPF6RDNWP","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AIGYSKIU","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:ea513b5b2d6d398aa8528a659f3bd2eb87fed1ec9959af22d71bb557b9137394","target":"graph","created_at":"2026-05-18T00:49:41Z","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":"The matrix joint block diagonalization problem (JBDP) of a given matrix set $\\mathcal{A}=\\{A_i\\}_{i=1}^m$ is about finding a nonsingular matrix $W$ such that all $W^{T} A_i W$ are block diagonal. It includes the matrix joint diagonalization problem (JBD) as a special case for which all $W^{T} A_i W$ are required diagonal. Generically, such a matrix $W$ may not exist, but there are practically applications such as multidimensional independent component analysis (MICA) for which it does exist under the ideal situation, i.e., no noise is presented. However, in practice noises do get in and, as a ","authors_text":"Reng-cang Li, Yunfeng Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-02T02:37:50Z","title":"Perturbation Analysis for Matrix Joint Block Diagonalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00591","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":"sha256:5c65cc865e029cef213fde6e60feb302638899a68c1ccc23418b1adccbe8b18a","target":"record","created_at":"2026-05-18T00:49:41Z","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":"0f0720f1b0e3cd507bd3468c5228f242849689ceabcbe2ad5c6f276669830da9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-02T02:37:50Z","title_canon_sha256":"119c166e0c91f977dff0865832d996719fc4592bb21e5f52100c140bd0a081f4"},"schema_version":"1.0","source":{"id":"1703.00591","kind":"arxiv","version":1}},"canonical_sha256":"020d892914797d11b6cfb6714ce590d992dd5428d7a0f7e959a21a4792415d5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"020d892914797d11b6cfb6714ce590d992dd5428d7a0f7e959a21a4792415d5d","first_computed_at":"2026-05-18T00:49:41.279079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:41.279079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nN9n9vifShPgU7DEOiZ6QkjmmNHozdRp8t6xE5SEzCHznNuUbGQFiYzwijNm725HCEBSYvbR/Lcp9oO8zZ+5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:41.279555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c65cc865e029cef213fde6e60feb302638899a68c1ccc23418b1adccbe8b18a","sha256:ea513b5b2d6d398aa8528a659f3bd2eb87fed1ec9959af22d71bb557b9137394"],"state_sha256":"6c7455334c7b80c49e329320f1ab249174912d5ae51d49af49cb9a795fc341d0"}