{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DTRZD3YTFCVTHALHK7QRMIHM4H","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":"4b694bb2a3fcbf4896d0c832299e3f33b18fa3f63aad836007b4a2d71d9b463d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-04T01:19:28Z","title_canon_sha256":"0d5d7b98f80693a4d84c137b2596abe8713be84c40847ef04691965f9ce6ecda"},"schema_version":"1.0","source":{"id":"1607.00716","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00716","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00716v3","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00716","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"DTRZD3YTFCVT","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTRZD3YTFCVTHALH","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTRZD3YT","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:4dc62661729afd9ae4c1948fca606b557491c0b71c057369fd8759583071a122","target":"graph","created_at":"2026-05-18T00:49:42Z","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 exact/approximate non-orthogonal general joint block diagonalization ({\\sc nogjbd}) problem of a given real matrix set $\\mathcal{A}=\\{A_i\\}_{i=1}^m$ is to find a nonsingular matrix $W\\in\\mathbb{R}^{n\\times n}$ (diagonalizer) such that $W^T A_i W$ for $i=1,2,\\dots, m$ are all exactly/approximately block diagonal matrices with the same diagonal block structure and with as many diagonal blocks as possible. In this paper, we show that a solution to the exact/approximate {\\sc nogjbd} problem can be obtained by finding the exact/approximate solutions to the system of linear equations $A_iZ=Z^TA_","authors_text":"Chengyu Liu, Yunfeng Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-04T01:19:28Z","title":"An Algebraic Approach to Non-Orthogonal General Joint Block Diagonalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00716","kind":"arxiv","version":3},"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":"sha256:19c32585829d7a7d5ca43b206c66fcecd5cf37f4b63ffb791e0f44fc5a740660","target":"record","created_at":"2026-05-18T00:49:42Z","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":"4b694bb2a3fcbf4896d0c832299e3f33b18fa3f63aad836007b4a2d71d9b463d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-04T01:19:28Z","title_canon_sha256":"0d5d7b98f80693a4d84c137b2596abe8713be84c40847ef04691965f9ce6ecda"},"schema_version":"1.0","source":{"id":"1607.00716","kind":"arxiv","version":3}},"canonical_sha256":"1ce391ef1328ab33816757e11620ece1f4e239e8acd8c575606770d3d2a17324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ce391ef1328ab33816757e11620ece1f4e239e8acd8c575606770d3d2a17324","first_computed_at":"2026-05-18T00:49:42.291923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:42.291923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oBWH0WFXT73i7V/VipXMVNNFyUKNALi8LXCdBMrYjX3yDwzjfK74vzHw0cdKhMt5pm8qOfYBpaT89J1Li+spAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:42.292407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00716","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19c32585829d7a7d5ca43b206c66fcecd5cf37f4b63ffb791e0f44fc5a740660","sha256:4dc62661729afd9ae4c1948fca606b557491c0b71c057369fd8759583071a122"],"state_sha256":"e20628bf01ec360b15a1abc1f637a63b65a38d29795beb0067909f3a3f38eb89"}