{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RWFLGCQB3JND74BASLB6PZIVPF","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":"087e39ca26d9538ff94d801c8858178525ab10c0ec6cf98d8af4ff523cb6ef15","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-30T20:49:22Z","title_canon_sha256":"127a6e6c52fa64c318193ff2a5e7e2fd07b10856b44b5c4a78d18b57c38d779e"},"schema_version":"1.0","source":{"id":"1312.0150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0150","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0150v1","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0150","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"pith_short_12","alias_value":"RWFLGCQB3JND","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RWFLGCQB3JND74BA","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RWFLGCQB","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c4038fcd80768abdb39de4a7e4c72a368c0cbe0c454068f63b44c790e302ec3d","target":"graph","created_at":"2026-05-18T02:44:31Z","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":"Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of two, left and a right, Cantero-Morales-Velazquez block moment matrices, which are constructed using a quasi-definite matrix measure. A block Gauss-Borel factorization problem of these moment matrices leads to two sets of biorthogonal matrix orthogonal Laurent polynomials and matrix Szeg\\H{o} polynomials, which can be expressed in terms of Schur complements of bordered truncations of the block moment matrix. The corresponding block extensi","authors_text":"Gerardo Ariznabarreta, Manuel Manas","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-30T20:49:22Z","title":"Matrix Orthogonal Laurent Polynomials on the Unit Circle and Toda Type Integrable Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0150","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":"sha256:2c738f89ced41618f2c8bf2544b5b457408f9449834cf6297cb0a7350487a82b","target":"record","created_at":"2026-05-18T02:44:31Z","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":"087e39ca26d9538ff94d801c8858178525ab10c0ec6cf98d8af4ff523cb6ef15","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-30T20:49:22Z","title_canon_sha256":"127a6e6c52fa64c318193ff2a5e7e2fd07b10856b44b5c4a78d18b57c38d779e"},"schema_version":"1.0","source":{"id":"1312.0150","kind":"arxiv","version":1}},"canonical_sha256":"8d8ab30a01da5a3ff02092c3e7e5157975142ee5f063e9ad430ea7cfb7d1f35e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d8ab30a01da5a3ff02092c3e7e5157975142ee5f063e9ad430ea7cfb7d1f35e","first_computed_at":"2026-05-18T02:44:31.642422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:31.642422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VyOX/uovELMsTh4odA2JBlsmPezV2YbEfEjXjnwAw7AVaRfG26JuMFbsgBq7+LXqkypY+LCvoULq6BSwmGA0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:31.642879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c738f89ced41618f2c8bf2544b5b457408f9449834cf6297cb0a7350487a82b","sha256:c4038fcd80768abdb39de4a7e4c72a368c0cbe0c454068f63b44c790e302ec3d"],"state_sha256":"ac9ffc899e8af1e675d9b3417cd31f3c307c2a50d460383d57b9c36e46f910df"}