{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GZKQBW34YGRF5SLA2OOU56ACQ5","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":"cff258115fbee70f622c5240950015c2dd0034ff45725340859190738efc6876","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-18T06:08:31Z","title_canon_sha256":"1903e743a68ec07d581f6240474dd59fa778b670c0b0097b0098aefa6ae4ed62"},"schema_version":"1.0","source":{"id":"1603.05773","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05773","created_at":"2026-05-18T01:11:31Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05773v2","created_at":"2026-05-18T01:11:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05773","created_at":"2026-05-18T01:11:31Z"},{"alias_kind":"pith_short_12","alias_value":"GZKQBW34YGRF","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GZKQBW34YGRF5SLA","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GZKQBW34","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:811c82607f16e7e00a2ffa17a7b9a193d6cd91642e968cc03e2f134eb6edda0c","target":"graph","created_at":"2026-05-18T01:11:31Z","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 present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework provides an extension of the classical linearization theory for polynomials expressed in non-monomial bases and allows to represent polynomials expressed in product families, that is as a linear combination of elements of the form $\\phi_i(\\lambda) \\psi_j(\\lambda)$, where $\\{ \\phi_i(\\lambda) \\}$ and $\\{ \\psi_j(\\lambda) \\}$ can either be polynomial bases or polynomia","authors_text":"Leonardo Robol, Paul Van Dooren, Raf Vandebril","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-18T06:08:31Z","title":"A framework for structured linearizations of matrix polynomials in various bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05773","kind":"arxiv","version":2},"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":"sha256:092b2c57b2c4afc84e41125ea01c4e0bf0beed7ea7e9763608273c4289950e66","target":"record","created_at":"2026-05-18T01:11:31Z","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":"cff258115fbee70f622c5240950015c2dd0034ff45725340859190738efc6876","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-18T06:08:31Z","title_canon_sha256":"1903e743a68ec07d581f6240474dd59fa778b670c0b0097b0098aefa6ae4ed62"},"schema_version":"1.0","source":{"id":"1603.05773","kind":"arxiv","version":2}},"canonical_sha256":"365500db7cc1a25ec960d39d4ef80287522b45d5df8513ae98d3481eaec8f7ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"365500db7cc1a25ec960d39d4ef80287522b45d5df8513ae98d3481eaec8f7ef","first_computed_at":"2026-05-18T01:11:31.337837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:31.337837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ipc0g4Mfhuq90kYx3tLQMw4w3mjajnsyblFRajWiW49Szu6meUIli84iSgotbac/x0OFJ3LNm5tPdcEZOKUSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:31.338257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05773","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:092b2c57b2c4afc84e41125ea01c4e0bf0beed7ea7e9763608273c4289950e66","sha256:811c82607f16e7e00a2ffa17a7b9a193d6cd91642e968cc03e2f134eb6edda0c"],"state_sha256":"ab511fddbd53b1bdd0b6a529860a7f2a6314259c0bd5b714f2ca39342cc5cc87"}