{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ANSG66DHXD7IISSC2RI3QTUML2","short_pith_number":"pith:ANSG66DH","schema_version":"1.0","canonical_sha256":"03646f7867b8fe844a42d451b84e8c5e98cdcf076553cb098496c0537ad4f2c1","source":{"kind":"arxiv","id":"1902.00376","version":1},"attestation_state":"computed","paper":{"title":"Matrices dropping rank in codimension one and critical loci in computer vision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristina Turrini, GianMario Besana, Marina Bertolini, Roberto Notari","submitted_at":"2019-02-01T14:47:43Z","abstract_excerpt":"Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable $4 \\times 3$ matrices, $N,$ of linear forms. Such loci are classified in this paper, in the case in which $N$ drops rank in codimension one, giving rise to reducible varieties. This leads to a complete classification of matrices of size $(n+1) \\times n$ for $n \\le 3,$ which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally."},"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":"1902.00376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-01T14:47:43Z","cross_cats_sorted":[],"title_canon_sha256":"1d306820b661c877e486e8a66e5bb59a2489fea54f6ef89e91ce9157e3a8b53a","abstract_canon_sha256":"00bfb26fed89ed704fbf1564361ef81d0d2d697d70d6f5d6b6d2e10d602fd86e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:57.613728Z","signature_b64":"byRImruSNWsJlMAR/L2xGNdkYU94B/zbTWoRHAc8NCH3Kouvkdi2Wnm0vi/dK3uNPv9M1OtYfSEQcHfuacVFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03646f7867b8fe844a42d451b84e8c5e98cdcf076553cb098496c0537ad4f2c1","last_reissued_at":"2026-05-17T23:54:57.613152Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:57.613152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrices dropping rank in codimension one and critical loci in computer vision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristina Turrini, GianMario Besana, Marina Bertolini, Roberto Notari","submitted_at":"2019-02-01T14:47:43Z","abstract_excerpt":"Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable $4 \\times 3$ matrices, $N,$ of linear forms. Such loci are classified in this paper, in the case in which $N$ drops rank in codimension one, giving rise to reducible varieties. This leads to a complete classification of matrices of size $(n+1) \\times n$ for $n \\le 3,$ which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00376","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.00376","created_at":"2026-05-17T23:54:57.613230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.00376v1","created_at":"2026-05-17T23:54:57.613230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00376","created_at":"2026-05-17T23:54:57.613230+00:00"},{"alias_kind":"pith_short_12","alias_value":"ANSG66DHXD7I","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"ANSG66DHXD7IISSC","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"ANSG66DH","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.10415","citing_title":"The Rank of Trifocal Grassmann Tensors","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2","json":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2.json","graph_json":"https://pith.science/api/pith-number/ANSG66DHXD7IISSC2RI3QTUML2/graph.json","events_json":"https://pith.science/api/pith-number/ANSG66DHXD7IISSC2RI3QTUML2/events.json","paper":"https://pith.science/paper/ANSG66DH"},"agent_actions":{"view_html":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2","download_json":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2.json","view_paper":"https://pith.science/paper/ANSG66DH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.00376&json=true","fetch_graph":"https://pith.science/api/pith-number/ANSG66DHXD7IISSC2RI3QTUML2/graph.json","fetch_events":"https://pith.science/api/pith-number/ANSG66DHXD7IISSC2RI3QTUML2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2/action/storage_attestation","attest_author":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2/action/author_attestation","sign_citation":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2/action/citation_signature","submit_replication":"https://pith.science/pith/ANSG66DHXD7IISSC2RI3QTUML2/action/replication_record"}},"created_at":"2026-05-17T23:54:57.613230+00:00","updated_at":"2026-05-17T23:54:57.613230+00:00"}