{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AAQU4A3QYPIN5JLOLVL33ZY7IO","short_pith_number":"pith:AAQU4A3Q","schema_version":"1.0","canonical_sha256":"00214e0370c3d0dea56e5d57bde71f43be59227c81ee6b00c77a478c8a083638","source":{"kind":"arxiv","id":"1610.00570","version":1},"attestation_state":"computed","paper":{"title":"Relative $m$-ovoids of elliptic quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Cossidente, F. Pavese","submitted_at":"2016-10-03T14:37:04Z","abstract_excerpt":"Let ${\\cal Q}^-(2n+1,q)$ be an elliptic quadric of ${\\rm PG}(2n+1,q)$. A relative $m$-ovoid of ${\\cal Q}^-(2n+1,q)$ (with respect to a parablic section ${\\cal Q} := {\\cal Q}(2n,q) \\subset {\\cal Q}^-(2n+1,q)$) is a subset $\\cal R$ of points of ${\\cal Q}^-(2n+1,q)\\setminus {\\cal Q}$ such that every generator of ${\\cal Q}^-(2n+1,q)$ not contained in $\\cal Q$ meets $\\cal R$ in precisely $m$ points. A relative $m$-ovoid having the same size as its complement (in ${\\cal Q}^-(2n+1,q) \\setminus {\\cal Q}$) is called a relative hemisystem. We show that a nontrivial relative $m$-ovoid of ${\\cal Q}^-(2n+1"},"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":"1610.00570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-03T14:37:04Z","cross_cats_sorted":[],"title_canon_sha256":"a54cd54f88584e2ff67f9b42ee284d76285575762d67ae4fdc1dccd514c880b3","abstract_canon_sha256":"a9b41161d9ddefe0ff015f7c9da6a28e60ee16cde63cc3fa96677f48933943eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:25.230638Z","signature_b64":"YJH0IqVKjxOq2QfN7tuL3C8DUNBfwBmtSFcRFjGoXqZiwbghWiZZie70EVvTgDGVwmoS394IGulREPTJ07qUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00214e0370c3d0dea56e5d57bde71f43be59227c81ee6b00c77a478c8a083638","last_reissued_at":"2026-05-18T01:03:25.229988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:25.229988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative $m$-ovoids of elliptic quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Cossidente, F. Pavese","submitted_at":"2016-10-03T14:37:04Z","abstract_excerpt":"Let ${\\cal Q}^-(2n+1,q)$ be an elliptic quadric of ${\\rm PG}(2n+1,q)$. A relative $m$-ovoid of ${\\cal Q}^-(2n+1,q)$ (with respect to a parablic section ${\\cal Q} := {\\cal Q}(2n,q) \\subset {\\cal Q}^-(2n+1,q)$) is a subset $\\cal R$ of points of ${\\cal Q}^-(2n+1,q)\\setminus {\\cal Q}$ such that every generator of ${\\cal Q}^-(2n+1,q)$ not contained in $\\cal Q$ meets $\\cal R$ in precisely $m$ points. A relative $m$-ovoid having the same size as its complement (in ${\\cal Q}^-(2n+1,q) \\setminus {\\cal Q}$) is called a relative hemisystem. We show that a nontrivial relative $m$-ovoid of ${\\cal Q}^-(2n+1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00570","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":"1610.00570","created_at":"2026-05-18T01:03:25.230080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00570v1","created_at":"2026-05-18T01:03:25.230080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00570","created_at":"2026-05-18T01:03:25.230080+00:00"},{"alias_kind":"pith_short_12","alias_value":"AAQU4A3QYPIN","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"AAQU4A3QYPIN5JLO","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"AAQU4A3Q","created_at":"2026-05-18T12:30:04.600751+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/AAQU4A3QYPIN5JLOLVL33ZY7IO","json":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO.json","graph_json":"https://pith.science/api/pith-number/AAQU4A3QYPIN5JLOLVL33ZY7IO/graph.json","events_json":"https://pith.science/api/pith-number/AAQU4A3QYPIN5JLOLVL33ZY7IO/events.json","paper":"https://pith.science/paper/AAQU4A3Q"},"agent_actions":{"view_html":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO","download_json":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO.json","view_paper":"https://pith.science/paper/AAQU4A3Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00570&json=true","fetch_graph":"https://pith.science/api/pith-number/AAQU4A3QYPIN5JLOLVL33ZY7IO/graph.json","fetch_events":"https://pith.science/api/pith-number/AAQU4A3QYPIN5JLOLVL33ZY7IO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO/action/storage_attestation","attest_author":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO/action/author_attestation","sign_citation":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO/action/citation_signature","submit_replication":"https://pith.science/pith/AAQU4A3QYPIN5JLOLVL33ZY7IO/action/replication_record"}},"created_at":"2026-05-18T01:03:25.230080+00:00","updated_at":"2026-05-18T01:03:25.230080+00:00"}