{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:IEVSAXXNIE35BY3G3CXZPCOIFK","short_pith_number":"pith:IEVSAXXN","canonical_record":{"source":{"id":"math/0503100","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2005-03-05T14:02:30Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9d26586bde61006148401e93a4a24a34a25c15b0c90a52f042b3439d3d31858f","abstract_canon_sha256":"4eee3db0acf2660f09fdd23e0fae08c74c6def6cd4f927cdacc3f355f46c60d5"},"schema_version":"1.0"},"canonical_sha256":"412b205eed4137d0e366d8af9789c82aa7b94f8e2694e31cb7eb76d061d6fffc","source":{"kind":"arxiv","id":"math/0503100","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0503100","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0503100v1","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0503100","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"IEVSAXXNIE35","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"IEVSAXXNIE35BY3G","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"IEVSAXXN","created_at":"2026-06-03T22:06:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:IEVSAXXNIE35BY3G3CXZPCOIFK","target":"record","payload":{"canonical_record":{"source":{"id":"math/0503100","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2005-03-05T14:02:30Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9d26586bde61006148401e93a4a24a34a25c15b0c90a52f042b3439d3d31858f","abstract_canon_sha256":"4eee3db0acf2660f09fdd23e0fae08c74c6def6cd4f927cdacc3f355f46c60d5"},"schema_version":"1.0"},"canonical_sha256":"412b205eed4137d0e366d8af9789c82aa7b94f8e2694e31cb7eb76d061d6fffc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:16.555519Z","signature_b64":"0DdydbqUPMrYl9pzuPZURuwWPXKlp8DFWJW/oznmFf7Pa4GWOXDmD0Aqz3gXyRpDAEAZIpftn839NNM0jmXrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"412b205eed4137d0e366d8af9789c82aa7b94f8e2694e31cb7eb76d061d6fffc","last_reissued_at":"2026-06-03T22:06:16.555090Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:16.555090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0503100","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T22:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EwtZyKFcsVnkXB1394h8uJY6Ec99XfU6X0zQX3RF5NL7rJ7swn0+C6Eq8FmJsC80vucMbKKQJb7wa8Mfl/osCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:25:18.559349Z"},"content_sha256":"2d084ab4cef682989851aceed2c5046e72113b9fd0e5b631d0c1bde581445c27","schema_version":"1.0","event_id":"sha256:2d084ab4cef682989851aceed2c5046e72113b9fd0e5b631d0c1bde581445c27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:IEVSAXXNIE35BY3G3CXZPCOIFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Model for Understanding Numerical Stability","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Folkmar Bornemann","submitted_at":"2005-03-05T14:02:30Z","abstract_excerpt":"We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore capable of correctly predicting stability or instability of an algorithm. By means of nontrivial examples, such as the componentwise backward stability analysis of Gaussian elimination with a single iterative refinement step, we demonstrate that the model even yields quantitative backward error bounds that show all the known problem-dependent terms (with the exc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503100","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0503100/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T22:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIAHnkXexdaNnjDbO+LC7pKgOU3hiFy4XM2JPabM16kBCdAsvcDc0wtfJ0O/ePFy6hHWBhoH+4JbfDixN/SnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:25:18.559790Z"},"content_sha256":"2b029e06f40616cd3ce70230a1d39c522282af34dd3874e900b7315185cbf826","schema_version":"1.0","event_id":"sha256:2b029e06f40616cd3ce70230a1d39c522282af34dd3874e900b7315185cbf826"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEVSAXXNIE35BY3G3CXZPCOIFK/bundle.json","state_url":"https://pith.science/pith/IEVSAXXNIE35BY3G3CXZPCOIFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEVSAXXNIE35BY3G3CXZPCOIFK/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":"2026-06-04T15:25:18Z","links":{"resolver":"https://pith.science/pith/IEVSAXXNIE35BY3G3CXZPCOIFK","bundle":"https://pith.science/pith/IEVSAXXNIE35BY3G3CXZPCOIFK/bundle.json","state":"https://pith.science/pith/IEVSAXXNIE35BY3G3CXZPCOIFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEVSAXXNIE35BY3G3CXZPCOIFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:IEVSAXXNIE35BY3G3CXZPCOIFK","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":"4eee3db0acf2660f09fdd23e0fae08c74c6def6cd4f927cdacc3f355f46c60d5","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-03-05T14:02:30Z","title_canon_sha256":"9d26586bde61006148401e93a4a24a34a25c15b0c90a52f042b3439d3d31858f"},"schema_version":"1.0","source":{"id":"math/0503100","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0503100","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0503100v1","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0503100","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"IEVSAXXNIE35","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"IEVSAXXNIE35BY3G","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"IEVSAXXN","created_at":"2026-06-03T22:06:16Z"}],"graph_snapshots":[{"event_id":"sha256:2b029e06f40616cd3ce70230a1d39c522282af34dd3874e900b7315185cbf826","target":"graph","created_at":"2026-06-03T22:06:16Z","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/math/0503100/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore capable of correctly predicting stability or instability of an algorithm. By means of nontrivial examples, such as the componentwise backward stability analysis of Gaussian elimination with a single iterative refinement step, we demonstrate that the model even yields quantitative backward error bounds that show all the known problem-dependent terms (with the exc","authors_text":"Folkmar Bornemann","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2005-03-05T14:02:30Z","title":"A Model for Understanding Numerical Stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503100","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":"sha256:2d084ab4cef682989851aceed2c5046e72113b9fd0e5b631d0c1bde581445c27","target":"record","created_at":"2026-06-03T22:06:16Z","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":"4eee3db0acf2660f09fdd23e0fae08c74c6def6cd4f927cdacc3f355f46c60d5","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-03-05T14:02:30Z","title_canon_sha256":"9d26586bde61006148401e93a4a24a34a25c15b0c90a52f042b3439d3d31858f"},"schema_version":"1.0","source":{"id":"math/0503100","kind":"arxiv","version":1}},"canonical_sha256":"412b205eed4137d0e366d8af9789c82aa7b94f8e2694e31cb7eb76d061d6fffc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"412b205eed4137d0e366d8af9789c82aa7b94f8e2694e31cb7eb76d061d6fffc","first_computed_at":"2026-06-03T22:06:16.555090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:16.555090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0DdydbqUPMrYl9pzuPZURuwWPXKlp8DFWJW/oznmFf7Pa4GWOXDmD0Aqz3gXyRpDAEAZIpftn839NNM0jmXrAg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:16.555519Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0503100","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d084ab4cef682989851aceed2c5046e72113b9fd0e5b631d0c1bde581445c27","sha256:2b029e06f40616cd3ce70230a1d39c522282af34dd3874e900b7315185cbf826"],"state_sha256":"fc4bbe796ba0b022f71946953b7421f955620546a8bb65966b4b8688c61c57f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGKortRViu5eVN2jIjJGb/BKfMzXYlE++iwEmoaZTt1n6D0jkp/yQFXk4WDwIXrLsNkDGMMg4NcF2OBFkjPcBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:25:18.562202Z","bundle_sha256":"8efab1e0b2425e333377778e957208707244a3be90cda6d1abf2b877f440f12d"}}