{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:P4A4L2KXBCZGTOLPBPRVRQKMI4","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":"b46610b7f218e92dcbc90c89a6c7387dd9f8d5f73b1848675fec50fb2ee1f239","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-12T06:43:48Z","title_canon_sha256":"a5aa894a84141bdc716f84326069f6a0149ebc40d1512ba472d22421b31e4e60"},"schema_version":"1.0","source":{"id":"2410.09389","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.09389","created_at":"2026-07-05T11:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"2410.09389v4","created_at":"2026-07-05T11:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.09389","created_at":"2026-07-05T11:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"P4A4L2KXBCZG","created_at":"2026-07-05T11:55:14Z"},{"alias_kind":"pith_short_16","alias_value":"P4A4L2KXBCZGTOLP","created_at":"2026-07-05T11:55:14Z"},{"alias_kind":"pith_short_8","alias_value":"P4A4L2KX","created_at":"2026-07-05T11:55:14Z"}],"graph_snapshots":[{"event_id":"sha256:f1dc16f88080bc8608a47dfaf7154ade4ec5644fe2c419d232f99f902006822a","target":"graph","created_at":"2026-07-05T11:55:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.09389/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work is about an improved error analysis of CholeskyQR with the randomized model for the tall-skinny $X \\in \\mathbb{R}^{m\\times n}$. Due to the structure of CholeskyQR, we utilize the randomized model in the first step of CholeskyQR with a weak assumption. We receive a better sufficient condition of $\\kappa_{2}(X)$ and a tighter upper bound of residual for CholeskyQR2, together with a probabilistic shifted item $s$ for Shifted CholeskyQR3 based on $\\norm{X}_{F}$ after improved error analysis. Numerical experiments demonstrate the effectiveness of our new theoretical results. The probabili","authors_text":"Haoran Guan, Yuwei Fan","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-12T06:43:48Z","title":"An improved error analysis of CholeskyQR with the randomized model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.09389","kind":"arxiv","version":4},"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:e6b5c90567a93a60a798557da840e748ce94d04313b76a921debcb882ec571c2","target":"record","created_at":"2026-07-05T11:55:14Z","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":"b46610b7f218e92dcbc90c89a6c7387dd9f8d5f73b1848675fec50fb2ee1f239","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-12T06:43:48Z","title_canon_sha256":"a5aa894a84141bdc716f84326069f6a0149ebc40d1512ba472d22421b31e4e60"},"schema_version":"1.0","source":{"id":"2410.09389","kind":"arxiv","version":4}},"canonical_sha256":"7f01c5e95708b269b96f0be358c14c4712e180ce30ecd109b6e9896cc01f3627","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f01c5e95708b269b96f0be358c14c4712e180ce30ecd109b6e9896cc01f3627","first_computed_at":"2026-07-05T11:55:14.911957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:14.911957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mxCHGEJUeJXbqI0ozj647Xj/JhutkYGGBDKv2JsZ4/qGt0XCTWbLPwRskT9J0/am8gitcybwvUo/ImuRhs4LBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:14.912463Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.09389","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6b5c90567a93a60a798557da840e748ce94d04313b76a921debcb882ec571c2","sha256:f1dc16f88080bc8608a47dfaf7154ade4ec5644fe2c419d232f99f902006822a"],"state_sha256":"7c842f0114e01ab8225518cc37e8bc990ad90be1f057d1061cc0054dd4af2d44"}