{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VRATVXT3KRO2MMCI656EXTZI2F","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":"a22142075cfde657e9ed082a23ddc0fd5b394b474c6e507fdc47debba552f38f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T16:55:49Z","title_canon_sha256":"a68d01316b56ef35f5470b7e03c466cea438a1c841869ab98a9da3fcf095babc"},"schema_version":"1.0","source":{"id":"1805.11580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11580","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11580v1","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11580","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"pith_short_12","alias_value":"VRATVXT3KRO2","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VRATVXT3KRO2MMCI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VRATVXT3","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:f3607d178244933e9de67c136f30f5e077446bf5b087113d6f94952e2125c84b","target":"graph","created_at":"2026-05-18T00:14:41Z","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":"We show how to construct linearizations of matrix polynomials $z\\mathbf{a}(z)\\mathbf{d}_0 + \\mathbf{c}_0$, $\\mathbf{a}(z)\\mathbf{b}(z)$, $\\mathbf{a}(z) + \\mathbf{b}(z)$ (when $\\mathrm{deg}\\left(\\mathbf{b}(z)\\right) < \\mathrm{deg}\\left(\\mathbf{a}(z)\\right)$), and $z\\mathbf{a}(z)\\mathbf{d}_0\\mathbf{b}(z) + \\mathbf{c_0}$ from linearizations of the component parts, $\\mathbf{a}(z)$ and $\\mathbf{b}(z)$. This allows the extension to matrix polynomials of a new companion matrix construction.","authors_text":"Eunice Y. S. Chan, J. Rafael Sendra, Juana Sendra, Laureano Gonzalez-Vega, Robert M. Corless","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T16:55:49Z","title":"Algebraic Linearizations of Matrix Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11580","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":"sha256:41ee8c8ab54cc8ef745352582f1eb352f6ae9e2f103fe562d1417d35d2ae8c87","target":"record","created_at":"2026-05-18T00:14:41Z","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":"a22142075cfde657e9ed082a23ddc0fd5b394b474c6e507fdc47debba552f38f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-29T16:55:49Z","title_canon_sha256":"a68d01316b56ef35f5470b7e03c466cea438a1c841869ab98a9da3fcf095babc"},"schema_version":"1.0","source":{"id":"1805.11580","kind":"arxiv","version":1}},"canonical_sha256":"ac413ade7b545da63048f77c4bcf28d1468e7bfcd0a698710a035b8664fa4595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac413ade7b545da63048f77c4bcf28d1468e7bfcd0a698710a035b8664fa4595","first_computed_at":"2026-05-18T00:14:41.981406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:41.981406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a3L8J+Tzjf68X3pxtdLNPalLtFF6mAGmohMUStiXGVCjzRo62DFptgC0mG837tepTDMRbOo76jdrqKD1rOirAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:41.982055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41ee8c8ab54cc8ef745352582f1eb352f6ae9e2f103fe562d1417d35d2ae8c87","sha256:f3607d178244933e9de67c136f30f5e077446bf5b087113d6f94952e2125c84b"],"state_sha256":"093f0e94b5b2f0023cf7f8e271bc9cd8bfe5928cdde1d6e64a4d08c1b8601dac"}