{"paper":{"title":"Characterising hyperbolic hyperplanes of a non-singular quadric in $PG(4,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice M.W. Hui, Jeroen Schillewaert, S.G. Barwick, Wen-Ai Jackson","submitted_at":"2019-06-04T02:43:04Z","abstract_excerpt":"Let $H$ be a non-empty set of hyperplanes in $PG(4,q)$, $q$ even, such that every point of $PG(4,q)$ lies in either $0$, $\\frac12q^3$ or $\\frac12(q^3+q^2)$ hyperplanes of $ H$, and every plane of $PG(4,q)$ lies in $0$ or at least $\\frac12q$ hyperplanes of $H$. Then $H$ is the set of all hyperplanes which meet a given non-singular quadric $Q(4,q)$ in a hyperbolic quadric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04932","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"}