{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FAT5MLGHO66LS2SKC246DDQKUC","short_pith_number":"pith:FAT5MLGH","schema_version":"1.0","canonical_sha256":"2827d62cc777bcb96a4a16b9e18e0aa0aeb1116a638bc0a046a861223d0023ad","source":{"kind":"arxiv","id":"1209.4938","version":2},"attestation_state":"computed","paper":{"title":"Polar varieties, Bertini's theorems and number of points of singular complete intersections over a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antonio Cafure, Guillermo Matera, Melina Privitelli","submitted_at":"2012-09-21T23:50:21Z","abstract_excerpt":"Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimension r and singular locus of dimension at most s, and let \\pi:V-->P^{s+1} be a \"generic\" linear mapping. We obtain an effective version of the Bertini smoothness theorem concerning \\pi, namely an explicit upper bound of the degree of a proper Zariski closed subset of P^{s+1} which contains all the points defining singular fibers of \\pi. For this purpose we make essential use of the concept of polar variety associated"},"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":"1209.4938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-21T23:50:21Z","cross_cats_sorted":[],"title_canon_sha256":"06feda12902b77bc76e4f1cce988b7eb305211aee35fc6eb8293ae6856c541f2","abstract_canon_sha256":"86a230baa5f6c126c5dd3e67358b9d3334ec5767313abade8fdc0cb0de50756a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:45.542246Z","signature_b64":"5pxN3BFow1MKzFJAsT2/bF3Q/wxLi2RtoGAO3Cy7cCjhAddyYFOjHKz04/z5U8W4/3RNwuYdxVdUVIzBzr7aBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2827d62cc777bcb96a4a16b9e18e0aa0aeb1116a638bc0a046a861223d0023ad","last_reissued_at":"2026-05-18T03:21:45.541488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:45.541488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polar varieties, Bertini's theorems and number of points of singular complete intersections over a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antonio Cafure, Guillermo Matera, Melina Privitelli","submitted_at":"2012-09-21T23:50:21Z","abstract_excerpt":"Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimension r and singular locus of dimension at most s, and let \\pi:V-->P^{s+1} be a \"generic\" linear mapping. We obtain an effective version of the Bertini smoothness theorem concerning \\pi, namely an explicit upper bound of the degree of a proper Zariski closed subset of P^{s+1} which contains all the points defining singular fibers of \\pi. For this purpose we make essential use of the concept of polar variety associated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4938","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":""},"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":"1209.4938","created_at":"2026-05-18T03:21:45.541618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4938v2","created_at":"2026-05-18T03:21:45.541618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4938","created_at":"2026-05-18T03:21:45.541618+00:00"},{"alias_kind":"pith_short_12","alias_value":"FAT5MLGHO66L","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"FAT5MLGHO66LS2SK","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"FAT5MLGH","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC","json":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC.json","graph_json":"https://pith.science/api/pith-number/FAT5MLGHO66LS2SKC246DDQKUC/graph.json","events_json":"https://pith.science/api/pith-number/FAT5MLGHO66LS2SKC246DDQKUC/events.json","paper":"https://pith.science/paper/FAT5MLGH"},"agent_actions":{"view_html":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC","download_json":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC.json","view_paper":"https://pith.science/paper/FAT5MLGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4938&json=true","fetch_graph":"https://pith.science/api/pith-number/FAT5MLGHO66LS2SKC246DDQKUC/graph.json","fetch_events":"https://pith.science/api/pith-number/FAT5MLGHO66LS2SKC246DDQKUC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC/action/storage_attestation","attest_author":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC/action/author_attestation","sign_citation":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC/action/citation_signature","submit_replication":"https://pith.science/pith/FAT5MLGHO66LS2SKC246DDQKUC/action/replication_record"}},"created_at":"2026-05-18T03:21:45.541618+00:00","updated_at":"2026-05-18T03:21:45.541618+00:00"}