{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J57IKJIUAKTXSBGFFH53CDK4JS","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":"5d914aa69fc5a468e61357830aac8f575a09d642ec6443e231560e26cccadcea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-08T17:42:51Z","title_canon_sha256":"37c667a9cb27097635ee523102131b922e7140606eafe06b1d2325a8780add37"},"schema_version":"1.0","source":{"id":"1307.2186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2186","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2186v1","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2186","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"J57IKJIUAKTX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J57IKJIUAKTXSBGF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J57IKJIU","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:d870880ca33878e1834d7dee9cbcfe5525e23b9da92aa9b7c9814e18c84dd0b8","target":"graph","created_at":"2026-05-18T01:10:33Z","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":"This paper is concerned with the reduction of a unitary matrix U to CMV-like shape. A Lanczos--type algorithm is presented which carries out the reduction by computing the block tridiagonal form of the Hermitian part of U, i.e., of the matrix U+U^H. By elaborating on the Lanczos approach we also propose an alternative algorithm using elementary matrices which is numerically stable. If U is rank--structured then the same property holds for its Hermitian part and, therefore, the block tridiagonalization process can be performed using the rank--structured matrix technology with reduced complexity","authors_text":"Gianna M. Del Corso, Luca Gemignani, Roberto Bevilacqua","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-08T17:42:51Z","title":"Compression of unitary rank--structured matrices to CMV-like shape with an application to polynomial rootfinding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2186","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:b7f545c937dcfc8fc79633cd877a34ba75d1ffd92b0c675728c7eb0275afb146","target":"record","created_at":"2026-05-18T01:10:33Z","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":"5d914aa69fc5a468e61357830aac8f575a09d642ec6443e231560e26cccadcea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-08T17:42:51Z","title_canon_sha256":"37c667a9cb27097635ee523102131b922e7140606eafe06b1d2325a8780add37"},"schema_version":"1.0","source":{"id":"1307.2186","kind":"arxiv","version":1}},"canonical_sha256":"4f7e85251402a77904c529fbb10d5c4cafdb1a1734af40bbe44fac54b7777ca3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f7e85251402a77904c529fbb10d5c4cafdb1a1734af40bbe44fac54b7777ca3","first_computed_at":"2026-05-18T01:10:33.793959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:33.793959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hEThLpjk9Dc0dx5ug7arp8FIcvzFHa2zXi8a2cYG+DphDSluNeknuBVbjpIB1G8mvFsj4jPi0spYYbtEJ7iZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:33.794658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7f545c937dcfc8fc79633cd877a34ba75d1ffd92b0c675728c7eb0275afb146","sha256:d870880ca33878e1834d7dee9cbcfe5525e23b9da92aa9b7c9814e18c84dd0b8"],"state_sha256":"2f9b7d7b25cd94dd7198ad8fc4493eec37dde9c870a008514cacdb786621e5e3"}