{"paper":{"title":"Large point-degrees in intersecting families of finite vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hao Li, Jicheng Ma","submitted_at":"2026-06-07T16:07:04Z","abstract_excerpt":"Let \\(V\\) be an \\(n\\)-dimensional vector space over the finite field \\(\\Fq\\), and let \\(\\Gr{V}{k}\\) denote the family of all \\(k\\)-dimensional subspaces of \\(V\\). A family \\(\\cF\\subseteq\\Gr{V}{k}\\) is called intersecting if \\(\\dim(F\\cap F')\\ge1\\) for all \\(F,F'\\in\\cF\\). For a point \\(P\\le V\\), let \\(d_P(\\cF)\\) denote the number of members of \\(\\cF\\) that contain \\(P\\), and order the point-degrees as \\(d_1(\\cF)\\ge d_2(\\cF)\\ge\\cdots\\ge d_{\\points{n}}(\\cF)\\), where \\(\\points{m}=(q^m-1)/(q-1)\\) is the number of points in an \\(m\\)-dimensional subspace. Recent work of Frankl and Wang~\\cite{FW2025} a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08709","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08709/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}