{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OQ4Q7M6Z2JIRSTYR5KDJEI3C45","short_pith_number":"pith:OQ4Q7M6Z","schema_version":"1.0","canonical_sha256":"74390fb3d9d251194f11ea86922362e778ea0454a1a4a860694d375a6aed6489","source":{"kind":"arxiv","id":"1309.2005","version":1},"attestation_state":"computed","paper":{"title":"Characterizations of finite classical polar spaces by intersection numbers with hyperplanes and speces of codimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jeroen Schillewaert, Stefaan De Winter","submitted_at":"2013-09-08T20:24:28Z","abstract_excerpt":"In this article we show that non-singular quadrics and non-singular Hermitian varieties are completely characterized by their intersection numbers with respect to hyperplanes and spaces of codimension 2. This strongly generalizes a result by Ferri and Tallini \\cite{FT} and also provides necessary and sufficient conditions for quasi-quadrics (respectively their Hermitian analogues) to be non-singular quadrics (respectively Hermitian varieties).} \\section{Introduction} When Segre \\cite{Segre} proved his celebrated characterization of conics (\"every set of $q+1$ points in $\\mathrm{PG}(2,q)$, $q$ "},"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":"1309.2005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-08T20:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"c6dfa0026ea53f5d8d426d3834c6ed34208a4fdb5b320d490883f0caf8b853df","abstract_canon_sha256":"b36acc5134721fe11ea1e706b652bde85ad419497379d4aca0d3af2ef6503399"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:56.797636Z","signature_b64":"OkQomq996XqJAHrPrVuBHbbi63thtCiXrqhzFXRBBCf+dERYIGepfKRojRQyEyST7wQsA9XHMfRx9mSh9pL0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74390fb3d9d251194f11ea86922362e778ea0454a1a4a860694d375a6aed6489","last_reissued_at":"2026-05-18T03:13:56.797027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:56.797027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of finite classical polar spaces by intersection numbers with hyperplanes and speces of codimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jeroen Schillewaert, Stefaan De Winter","submitted_at":"2013-09-08T20:24:28Z","abstract_excerpt":"In this article we show that non-singular quadrics and non-singular Hermitian varieties are completely characterized by their intersection numbers with respect to hyperplanes and spaces of codimension 2. This strongly generalizes a result by Ferri and Tallini \\cite{FT} and also provides necessary and sufficient conditions for quasi-quadrics (respectively their Hermitian analogues) to be non-singular quadrics (respectively Hermitian varieties).} \\section{Introduction} When Segre \\cite{Segre} proved his celebrated characterization of conics (\"every set of $q+1$ points in $\\mathrm{PG}(2,q)$, $q$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2005","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":"1309.2005","created_at":"2026-05-18T03:13:56.797106+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.2005v1","created_at":"2026-05-18T03:13:56.797106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2005","created_at":"2026-05-18T03:13:56.797106+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQ4Q7M6Z2JIR","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQ4Q7M6Z2JIRSTYR","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQ4Q7M6Z","created_at":"2026-05-18T12:27:54.935989+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/OQ4Q7M6Z2JIRSTYR5KDJEI3C45","json":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45.json","graph_json":"https://pith.science/api/pith-number/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/graph.json","events_json":"https://pith.science/api/pith-number/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/events.json","paper":"https://pith.science/paper/OQ4Q7M6Z"},"agent_actions":{"view_html":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45","download_json":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45.json","view_paper":"https://pith.science/paper/OQ4Q7M6Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.2005&json=true","fetch_graph":"https://pith.science/api/pith-number/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/graph.json","fetch_events":"https://pith.science/api/pith-number/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/action/storage_attestation","attest_author":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/action/author_attestation","sign_citation":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/action/citation_signature","submit_replication":"https://pith.science/pith/OQ4Q7M6Z2JIRSTYR5KDJEI3C45/action/replication_record"}},"created_at":"2026-05-18T03:13:56.797106+00:00","updated_at":"2026-05-18T03:13:56.797106+00:00"}