{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ILLTPTHFXK7UEDEXPOQDMQV2UD","short_pith_number":"pith:ILLTPTHF","schema_version":"1.0","canonical_sha256":"42d737cce5babf420c977ba03642baa0e5ca4e2dcf2a63c43bb189be3976c1b6","source":{"kind":"arxiv","id":"2310.02719","version":2},"attestation_state":"computed","paper":{"title":"Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.CV","authors_text":"Benjamin Kimia, Hongyi Fan, Joe Kileel","submitted_at":"2023-10-04T10:45:55Z","abstract_excerpt":"In this paper, we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact that relative pose estimation, based on standard 5-point or 7-point Random Sample Consensus (RANSAC) algorithms, can fail even when no outliers are present and there is enough data to support a hypothesis. We argue that these cases arise due to the intrinsic instability of the 5- and 7-point minimal problems. We apply our framework to characterize the instabi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.02719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2023-10-04T10:45:55Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"fea604da8e0ec0954095e448530daf2d3caf4bc6c99c02ed0996acce98b7ec7f","abstract_canon_sha256":"82348409b6e4ff52266a3ad859c386955d2d46ba14c2ad3b91089a1df1588d96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:00:57.682135Z","signature_b64":"UWrsCTX2p6wzH5za2P4j+6LUJGyUZgopkDpU1BYWut7ct0Ct9pxOnFhzhnaLmZAqPa0/IT8ezoQGkBE/9+uSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42d737cce5babf420c977ba03642baa0e5ca4e2dcf2a63c43bb189be3976c1b6","last_reissued_at":"2026-07-05T11:00:57.681669Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:00:57.681669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.CV","authors_text":"Benjamin Kimia, Hongyi Fan, Joe Kileel","submitted_at":"2023-10-04T10:45:55Z","abstract_excerpt":"In this paper, we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact that relative pose estimation, based on standard 5-point or 7-point Random Sample Consensus (RANSAC) algorithms, can fail even when no outliers are present and there is enough data to support a hypothesis. We argue that these cases arise due to the intrinsic instability of the 5- and 7-point minimal problems. We apply our framework to characterize the instabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.02719","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.02719/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2310.02719","created_at":"2026-07-05T11:00:57.681729+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.02719v2","created_at":"2026-07-05T11:00:57.681729+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.02719","created_at":"2026-07-05T11:00:57.681729+00:00"},{"alias_kind":"pith_short_12","alias_value":"ILLTPTHFXK7U","created_at":"2026-07-05T11:00:57.681729+00:00"},{"alias_kind":"pith_short_16","alias_value":"ILLTPTHFXK7UEDEX","created_at":"2026-07-05T11:00:57.681729+00:00"},{"alias_kind":"pith_short_8","alias_value":"ILLTPTHF","created_at":"2026-07-05T11:00:57.681729+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.10407","citing_title":"Numerically Computing Galois Groups of Minimal Problems","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD","json":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD.json","graph_json":"https://pith.science/api/pith-number/ILLTPTHFXK7UEDEXPOQDMQV2UD/graph.json","events_json":"https://pith.science/api/pith-number/ILLTPTHFXK7UEDEXPOQDMQV2UD/events.json","paper":"https://pith.science/paper/ILLTPTHF"},"agent_actions":{"view_html":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD","download_json":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD.json","view_paper":"https://pith.science/paper/ILLTPTHF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.02719&json=true","fetch_graph":"https://pith.science/api/pith-number/ILLTPTHFXK7UEDEXPOQDMQV2UD/graph.json","fetch_events":"https://pith.science/api/pith-number/ILLTPTHFXK7UEDEXPOQDMQV2UD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD/action/storage_attestation","attest_author":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD/action/author_attestation","sign_citation":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD/action/citation_signature","submit_replication":"https://pith.science/pith/ILLTPTHFXK7UEDEXPOQDMQV2UD/action/replication_record"}},"created_at":"2026-07-05T11:00:57.681729+00:00","updated_at":"2026-07-05T11:00:57.681729+00:00"}