{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A6LVSO6OB6KA2NK6FHJ5HLNE4Q","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":"59bca1ea518044526406b906191d05c33cd4e249d9d06fb4c6b9fdfc80320fc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-17T16:01:28Z","title_canon_sha256":"eeb38614b8f5ec665abe1496bf8499bfd362951260cee42d505734bf41658e0f"},"schema_version":"1.0","source":{"id":"1808.05913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05913","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05913v1","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05913","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"A6LVSO6OB6KA","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A6LVSO6OB6KA2NK6","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A6LVSO6O","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:6d17f2dc89d6682415355531de853e88f3b76fc277a29dea812dca5344f1f344","target":"graph","created_at":"2026-05-18T00:07:51Z","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":"P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker's canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren's algorithm to square complex matrices with respect to consimilarity transformations and to pairs of m-by-n complex matrices.","authors_text":"Tetiana Klymchuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-17T16:01:28Z","title":"Regularizing algorithm for mixed matrix pencils"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05913","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":"sha256:4e2dd99e61e0caedf4d216ff98e89aa885a8a2984146df29c95e29a0c5b3ee70","target":"record","created_at":"2026-05-18T00:07:51Z","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":"59bca1ea518044526406b906191d05c33cd4e249d9d06fb4c6b9fdfc80320fc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-17T16:01:28Z","title_canon_sha256":"eeb38614b8f5ec665abe1496bf8499bfd362951260cee42d505734bf41658e0f"},"schema_version":"1.0","source":{"id":"1808.05913","kind":"arxiv","version":1}},"canonical_sha256":"0797593bce0f940d355e29d3d3ada4e405566455ef7603cecdbee90d32a2bdff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0797593bce0f940d355e29d3d3ada4e405566455ef7603cecdbee90d32a2bdff","first_computed_at":"2026-05-18T00:07:51.670408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:51.670408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T9ywBilMMAkEEu1vDjmzsfjefvgPVI1eg8X9OqYrwNZFGRuNuXmvQ2gSQz8/D+mnSaUAFZTfaTSolHp97PhrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:51.671180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.05913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e2dd99e61e0caedf4d216ff98e89aa885a8a2984146df29c95e29a0c5b3ee70","sha256:6d17f2dc89d6682415355531de853e88f3b76fc277a29dea812dca5344f1f344"],"state_sha256":"299a74a961a719e7a72c69f34fb4572bdef5a117c1feb9227ca4aabd80ad38e2"}