{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UMJATIQWJPIWQVGH3C2LJLTNR2","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":"948c7afa4d8cff3841b736aab215f7ae40c2dd4d67f1b6ff804444465c577858","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-04T14:58:44Z","title_canon_sha256":"6b3bcc518361636622547f799b7d82d7e63f1cfa0d34fba7be218e93dd1caa4b"},"schema_version":"1.0","source":{"id":"1608.01567","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01567","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01567v2","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01567","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"UMJATIQWJPIW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UMJATIQWJPIWQVGH","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UMJATIQW","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:b8e20ab19fb15503e2c8c273bfa8c344e7d403507fb1ab3991acaa06107bee45","target":"graph","created_at":"2026-05-18T00:52:44Z","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":"It was recently observed that the singular values of the off-diagonal blocks of the matrix sequences generated by the Cyclic Reduction algorithm decay exponentially. This property was used to solve, with a higher efficiency, certain quadratic matrix equations encountered in the analysis of queueing models. In this paper, we provide a sharp theoretical bound to the basis of this exponential decay together with a tool for its estimation based on a rational interpolation problem. Applications to solving $n\\times n$ block tridiagonal block Toeplitz systems with $n\\times n$ semiseparable blocks and","authors_text":"Dario Andrea Bini, Leonardo Robol, Stefano Massei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-04T14:58:44Z","title":"On the decay of the off-diagonal singular values in cyclic reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01567","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":"sha256:1d56f95e5745499a11cb592185eb3616a08f08ad280b1a648d7f077c0562ac26","target":"record","created_at":"2026-05-18T00:52:44Z","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":"948c7afa4d8cff3841b736aab215f7ae40c2dd4d67f1b6ff804444465c577858","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-04T14:58:44Z","title_canon_sha256":"6b3bcc518361636622547f799b7d82d7e63f1cfa0d34fba7be218e93dd1caa4b"},"schema_version":"1.0","source":{"id":"1608.01567","kind":"arxiv","version":2}},"canonical_sha256":"a31209a2164bd16854c7d8b4b4ae6d8ea63d18139badfe81cca749d855454d73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a31209a2164bd16854c7d8b4b4ae6d8ea63d18139badfe81cca749d855454d73","first_computed_at":"2026-05-18T00:52:44.168873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:44.168873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"skOHLbiWPce8zVrgEX2toWbk/mct8XYz8Y+hhX7ckzDLdfb9jiTObhDAy+mKBkeKeUOUkf8NMm17u9JZm6UtCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:44.169365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01567","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d56f95e5745499a11cb592185eb3616a08f08ad280b1a648d7f077c0562ac26","sha256:b8e20ab19fb15503e2c8c273bfa8c344e7d403507fb1ab3991acaa06107bee45"],"state_sha256":"5e115813ace15d480ac3df9056350a479618e1baccd6ceadd5eb82e00bda6be5"}