{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O5DAD6MI64RC2U5RHVHKSPHJI6","short_pith_number":"pith:O5DAD6MI","canonical_record":{"source":{"id":"1401.5606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T10:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"bba0fa253c0c4a3c385506532f2a39516c9152d097d9cd73b0f5918edc9f4872","abstract_canon_sha256":"35ac5dae3286a461911947011258224f52ea241fe7e81a0b0d2c148fbe202206"},"schema_version":"1.0"},"canonical_sha256":"774601f988f7222d53b13d4ea93ce94791f76d58e9e9af4802a08fb4d0d9a8ac","source":{"kind":"arxiv","id":"1401.5606","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5606","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5606v2","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5606","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"O5DAD6MI64RC","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O5DAD6MI64RC2U5R","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O5DAD6MI","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O5DAD6MI64RC2U5RHVHKSPHJI6","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T10:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"bba0fa253c0c4a3c385506532f2a39516c9152d097d9cd73b0f5918edc9f4872","abstract_canon_sha256":"35ac5dae3286a461911947011258224f52ea241fe7e81a0b0d2c148fbe202206"},"schema_version":"1.0"},"canonical_sha256":"774601f988f7222d53b13d4ea93ce94791f76d58e9e9af4802a08fb4d0d9a8ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:54.071303Z","signature_b64":"koi5uCadKDpFEIYsf96AXP7DsHOZAavxyRgcgb01yJitPLX/22FEiJQkxiudqfUJ2YamsDP95ML8KSBcdyF3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"774601f988f7222d53b13d4ea93ce94791f76d58e9e9af4802a08fb4d0d9a8ac","last_reissued_at":"2026-05-18T02:40:54.070829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:54.070829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5606","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BS0Y7JGvAFHTzDfncIWdP64aCyJmmoWnQNoCwW6m8N95ux8xqJ5itpGlAUOxrRAMkn1PU/rP0Iq4Lkj2NMBvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:00:01.579358Z"},"content_sha256":"f4aefd3438eae7ccb6071c789c8c5af7082d8ce559800d2d226b82b4cd6962c1","schema_version":"1.0","event_id":"sha256:f4aefd3438eae7ccb6071c789c8c5af7082d8ce559800d2d226b82b4cd6962c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O5DAD6MI64RC2U5RHVHKSPHJI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Implicit QR for Companion-like Pencils","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Luca Gemignani, Paola Boito, Yuli Eidelman","submitted_at":"2014-01-22T10:05:55Z","abstract_excerpt":"A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized eigenvalues of certain NxN rank structured matrix pencils using O(N^2) ops and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5606","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XmKaclvYNGy1GEorcNlxvplORIW56AIB56G4MgzcPQxTzlma8PsKKpxs344mFXaA22OjGRAmKzuFUQwzsHgxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:00:01.579713Z"},"content_sha256":"9c1f50f911b1f93ffd2ccc82e6239c57d651b27888406eda2c25ba348d6958c2","schema_version":"1.0","event_id":"sha256:9c1f50f911b1f93ffd2ccc82e6239c57d651b27888406eda2c25ba348d6958c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O5DAD6MI64RC2U5RHVHKSPHJI6/bundle.json","state_url":"https://pith.science/pith/O5DAD6MI64RC2U5RHVHKSPHJI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O5DAD6MI64RC2U5RHVHKSPHJI6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T04:00:01Z","links":{"resolver":"https://pith.science/pith/O5DAD6MI64RC2U5RHVHKSPHJI6","bundle":"https://pith.science/pith/O5DAD6MI64RC2U5RHVHKSPHJI6/bundle.json","state":"https://pith.science/pith/O5DAD6MI64RC2U5RHVHKSPHJI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O5DAD6MI64RC2U5RHVHKSPHJI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O5DAD6MI64RC2U5RHVHKSPHJI6","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":"35ac5dae3286a461911947011258224f52ea241fe7e81a0b0d2c148fbe202206","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T10:05:55Z","title_canon_sha256":"bba0fa253c0c4a3c385506532f2a39516c9152d097d9cd73b0f5918edc9f4872"},"schema_version":"1.0","source":{"id":"1401.5606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5606","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5606v2","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5606","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"O5DAD6MI64RC","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O5DAD6MI64RC2U5R","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O5DAD6MI","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:9c1f50f911b1f93ffd2ccc82e6239c57d651b27888406eda2c25ba348d6958c2","target":"graph","created_at":"2026-05-18T02:40:54Z","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":"A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized eigenvalues of certain NxN rank structured matrix pencils using O(N^2) ops and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.","authors_text":"Luca Gemignani, Paola Boito, Yuli Eidelman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T10:05:55Z","title":"Implicit QR for Companion-like Pencils"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5606","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:f4aefd3438eae7ccb6071c789c8c5af7082d8ce559800d2d226b82b4cd6962c1","target":"record","created_at":"2026-05-18T02:40:54Z","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":"35ac5dae3286a461911947011258224f52ea241fe7e81a0b0d2c148fbe202206","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-22T10:05:55Z","title_canon_sha256":"bba0fa253c0c4a3c385506532f2a39516c9152d097d9cd73b0f5918edc9f4872"},"schema_version":"1.0","source":{"id":"1401.5606","kind":"arxiv","version":2}},"canonical_sha256":"774601f988f7222d53b13d4ea93ce94791f76d58e9e9af4802a08fb4d0d9a8ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"774601f988f7222d53b13d4ea93ce94791f76d58e9e9af4802a08fb4d0d9a8ac","first_computed_at":"2026-05-18T02:40:54.070829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:54.070829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"koi5uCadKDpFEIYsf96AXP7DsHOZAavxyRgcgb01yJitPLX/22FEiJQkxiudqfUJ2YamsDP95ML8KSBcdyF3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:54.071303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4aefd3438eae7ccb6071c789c8c5af7082d8ce559800d2d226b82b4cd6962c1","sha256:9c1f50f911b1f93ffd2ccc82e6239c57d651b27888406eda2c25ba348d6958c2"],"state_sha256":"ecc4cf666642893e281876ed7b6d160c951fc40314781e4bf3c80b5dd1852ffd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gsXSa8e+son0mLDMXMo3CTs8Lh/eYvenUL6NWUA2qu8kypE0rMOXEnx4rA6sQ81sQXw+/vOBq6XyVjAPSTrRDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:00:01.581691Z","bundle_sha256":"821142f89b007298fdf5f9aa65b150b667c41f171b643597358342400e1f85c9"}}