{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:F3N5DRQFB2EFLJHC5M6GFIIXD4","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":"4e42540276272ffc6afd652ee8267e42a54c57f280b8de226f9d4ad94a4137e5","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-18T18:32:41Z","title_canon_sha256":"b20cb5042988ee1102ae3c65de6726db95ee64c42dbb45be47b555b57ca8f2ee"},"schema_version":"1.0","source":{"id":"0812.3613","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3613","created_at":"2026-06-03T23:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3613v2","created_at":"2026-06-03T23:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3613","created_at":"2026-06-03T23:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"F3N5DRQFB2EF","created_at":"2026-06-03T23:06:09Z"},{"alias_kind":"pith_short_16","alias_value":"F3N5DRQFB2EFLJHC","created_at":"2026-06-03T23:06:09Z"},{"alias_kind":"pith_short_8","alias_value":"F3N5DRQF","created_at":"2026-06-03T23:06:09Z"}],"graph_snapshots":[{"event_id":"sha256:432991c8b839dc6d797d816f91fbee8126daac8b51f0a05d6a44d7c19344dcf5","target":"graph","created_at":"2026-06-03T23:06:09Z","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/0812.3613/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compare Stochastic and Worst-case condition numbers and loss of precision for general computational problems. We show an upper bound for the ratio of Worst-case condition number to the Stochastic condition number of order O(sqrt m). We show an upper bound for the difference between the Worst-case loss of precision and the Stochastic loss of precision of order O(ln m). The results hold if the perturbations are measured norm-wise or componentwise.","authors_text":"Dennis Cheung, Lisa H.Y. Zhou","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-18T18:32:41Z","title":"Stochastic Vs Worst-case Condition Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3613","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:ec0eabb9eedd969f62c09e80f77eecaa3f6a5e8db2143f5a016845b4710322fd","target":"record","created_at":"2026-06-03T23:06:09Z","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":"4e42540276272ffc6afd652ee8267e42a54c57f280b8de226f9d4ad94a4137e5","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-12-18T18:32:41Z","title_canon_sha256":"b20cb5042988ee1102ae3c65de6726db95ee64c42dbb45be47b555b57ca8f2ee"},"schema_version":"1.0","source":{"id":"0812.3613","kind":"arxiv","version":2}},"canonical_sha256":"2edbd1c6050e8855a4e2eb3c62a1171f1f882af5eb49fc7b07dbd605a0cffd9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2edbd1c6050e8855a4e2eb3c62a1171f1f882af5eb49fc7b07dbd605a0cffd9c","first_computed_at":"2026-06-03T23:06:09.937279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:09.937279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oT17ZLx8HU47kSPeWEZgcYPtacy/1AFNtqbZRTgssRZoIyUkeT3ASICpFFKOXnfytfdKsRbzBRAQu+OprnZJDQ==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:09.937631Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3613","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec0eabb9eedd969f62c09e80f77eecaa3f6a5e8db2143f5a016845b4710322fd","sha256:432991c8b839dc6d797d816f91fbee8126daac8b51f0a05d6a44d7c19344dcf5"],"state_sha256":"602e243a5f132eabbe2a9f7c80bafebe77a72f990d5f2e77631ff0d24c6d5ca6"}