{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:D4O4YNDQPZKFYZ3O4LHXQTHTP4","short_pith_number":"pith:D4O4YNDQ","canonical_record":{"source":{"id":"1905.08321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-20T19:52:07Z","cross_cats_sorted":[],"title_canon_sha256":"7b2ba318d2cae81df5c8bafaf54fed4797610172bcbfa51965f239a3adcfef95","abstract_canon_sha256":"5b5c343de3b9405832a08786a4110036b41003902a05892ac630e46f7343e87b"},"schema_version":"1.0"},"canonical_sha256":"1f1dcc34707e545c676ee2cf784cf37f3b5da5f23a7f9a60bf265e593c851e1f","source":{"kind":"arxiv","id":"1905.08321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.08321","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"1905.08321v1","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08321","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"D4O4YNDQPZKF","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"D4O4YNDQPZKFYZ3O","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"D4O4YNDQ","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:D4O4YNDQPZKFYZ3O4LHXQTHTP4","target":"record","payload":{"canonical_record":{"source":{"id":"1905.08321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-20T19:52:07Z","cross_cats_sorted":[],"title_canon_sha256":"7b2ba318d2cae81df5c8bafaf54fed4797610172bcbfa51965f239a3adcfef95","abstract_canon_sha256":"5b5c343de3b9405832a08786a4110036b41003902a05892ac630e46f7343e87b"},"schema_version":"1.0"},"canonical_sha256":"1f1dcc34707e545c676ee2cf784cf37f3b5da5f23a7f9a60bf265e593c851e1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:43.659141Z","signature_b64":"yueOI7s/L00bt7BGlRUtBUW2iYNmEOlYjaJhOw59vfSaY3WDBtk2S45m1/RYAGNRXO9xIAyuCmBAY/7TXvl+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f1dcc34707e545c676ee2cf784cf37f3b5da5f23a7f9a60bf265e593c851e1f","last_reissued_at":"2026-05-17T23:45:43.658540Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:43.658540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.08321","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":"2026-05-17T23:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EB6kUm1RJShKA8ulb3ByUC7D1Iqg52lmdGcs0V6ISeHa135N3g+GZZhxErNV79o8gsm6Srrc3qgPCc1frByPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:34:14.681533Z"},"content_sha256":"cb3d5965ad457481d1a1aff9cbbb4110e558b59fc08fb81a19125d4e437c7314","schema_version":"1.0","event_id":"sha256:cb3d5965ad457481d1a1aff9cbbb4110e558b59fc08fb81a19125d4e437c7314"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:D4O4YNDQPZKFYZ3O4LHXQTHTP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On local analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Felipe Cucker, Teresa Krick","submitted_at":"2019-05-20T19:52:07Z","abstract_excerpt":"We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these condition numbers around a point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08321","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":""},"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":"2026-05-17T23:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"moPya99HMIx7viWbk4Kbv+0Eu1J2kXCIMTzBbLU909qfiibU8AiR4XBTQ86xBrE0mHoiPqhyDCUIYGRsxledAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:34:14.681883Z"},"content_sha256":"df289235e21232062b5a74636b0f0f3970c2101aaa3822421771dcb2fea836dd","schema_version":"1.0","event_id":"sha256:df289235e21232062b5a74636b0f0f3970c2101aaa3822421771dcb2fea836dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4O4YNDQPZKFYZ3O4LHXQTHTP4/bundle.json","state_url":"https://pith.science/pith/D4O4YNDQPZKFYZ3O4LHXQTHTP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4O4YNDQPZKFYZ3O4LHXQTHTP4/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":"2026-06-02T04:34:14Z","links":{"resolver":"https://pith.science/pith/D4O4YNDQPZKFYZ3O4LHXQTHTP4","bundle":"https://pith.science/pith/D4O4YNDQPZKFYZ3O4LHXQTHTP4/bundle.json","state":"https://pith.science/pith/D4O4YNDQPZKFYZ3O4LHXQTHTP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4O4YNDQPZKFYZ3O4LHXQTHTP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:D4O4YNDQPZKFYZ3O4LHXQTHTP4","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":"5b5c343de3b9405832a08786a4110036b41003902a05892ac630e46f7343e87b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-20T19:52:07Z","title_canon_sha256":"7b2ba318d2cae81df5c8bafaf54fed4797610172bcbfa51965f239a3adcfef95"},"schema_version":"1.0","source":{"id":"1905.08321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.08321","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"1905.08321v1","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08321","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"D4O4YNDQPZKF","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"D4O4YNDQPZKFYZ3O","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"D4O4YNDQ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:df289235e21232062b5a74636b0f0f3970c2101aaa3822421771dcb2fea836dd","target":"graph","created_at":"2026-05-17T23:45:43Z","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":"We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these condition numbers around a point.","authors_text":"Felipe Cucker, Teresa Krick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-20T19:52:07Z","title":"On local analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08321","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:cb3d5965ad457481d1a1aff9cbbb4110e558b59fc08fb81a19125d4e437c7314","target":"record","created_at":"2026-05-17T23:45:43Z","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":"5b5c343de3b9405832a08786a4110036b41003902a05892ac630e46f7343e87b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-20T19:52:07Z","title_canon_sha256":"7b2ba318d2cae81df5c8bafaf54fed4797610172bcbfa51965f239a3adcfef95"},"schema_version":"1.0","source":{"id":"1905.08321","kind":"arxiv","version":1}},"canonical_sha256":"1f1dcc34707e545c676ee2cf784cf37f3b5da5f23a7f9a60bf265e593c851e1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f1dcc34707e545c676ee2cf784cf37f3b5da5f23a7f9a60bf265e593c851e1f","first_computed_at":"2026-05-17T23:45:43.658540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:43.658540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yueOI7s/L00bt7BGlRUtBUW2iYNmEOlYjaJhOw59vfSaY3WDBtk2S45m1/RYAGNRXO9xIAyuCmBAY/7TXvl+BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:43.659141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.08321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb3d5965ad457481d1a1aff9cbbb4110e558b59fc08fb81a19125d4e437c7314","sha256:df289235e21232062b5a74636b0f0f3970c2101aaa3822421771dcb2fea836dd"],"state_sha256":"f65dbba30e7d4426553ab1564e567bb0d488e7f1d73d64cb5b9150e19a481234"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EqY3DsoqXAGhWKOTnG5P+Iu9h1X/070Q6xVQIfz+2YzGbUOptL75Xto0wOMd3AMr7g9wqRlX6hxYEqIwdZvfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:34:14.684214Z","bundle_sha256":"3702b1a4877c76281af4315d501e9024db67cf7532820183e67d65b3a0fd74e4"}}