{"paper":{"title":"The Suda-Tanaka-Tokushige conjecture for $\\mathbf{p}$-biased intersecting families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lihua Feng, Yongjiang Wu","submitted_at":"2026-06-25T01:54:41Z","abstract_excerpt":"In 2017, Suda, Tanaka and Tokushige conjectured that if $1>p_1\\ge\\cdots\\ge p_n>0$ with $p_3\\le \\frac{1}{2}$, then every intersecting family $\\mathcal A\\subseteq 2^{[n]}$ satisfies $\\mu_{\\mathbf{p}}(\\mathcal A)\\le p_1$, where $\\mu_{\\mathbf{p}}$ is the non-uniform product measure defined by $\\mu_{\\mathbf{p}}(\\mathcal{A})=\\sum_{A\\in\\mathcal{A}} \\prod_{i\\in A} p_i \\prod_{j\\in [n]\\setminus A}(1-p_j)$. In addition, if $p_1 > p_3$ or $p_1 < \\frac{1}{2}$, then equality holds if and only if $\\mathcal{A}$ is a star centered at some $i \\in [n]$ with $p_i = p_1$. In this paper, we prove this conjecture in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26521","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/2606.26521/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"}