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They proved the bound $v(d)\\leq d^{2d^2}$, and conjectured $v(d)\\leq d^{cd}$. We confirm it."},"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":"1503.07491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-25T18:55:08Z","cross_cats_sorted":[],"title_canon_sha256":"fb1995fd008d1c74b3b7bf404d6cffb28b0720f09c56572bc045a990c4579683","abstract_canon_sha256":"df9d945c7d7e623b605396a804fca5f45d2fd3b88272d89e646984612923b6e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:20.911437Z","signature_b64":"XL443WyFE3HhdBfc7I8Lt4zAyX/mkyQ3z6y4ZCscwrR9S2OjLJxxBCq2tMt9CeLt4JgsHInuUbgkn7aMuIICAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe722183fec815fd8bf30056e189104478f5ad7281878c7dcfb7ced85b4216ee","last_reissued_at":"2026-05-18T02:20:20.910653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:20.910653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of a conjecture of B\\'ar\\'any, Katchalski and Pach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Marton Naszodi","submitted_at":"2015-03-25T18:55:08Z","abstract_excerpt":"B\\'ar\\'any, Katchalski and Pach proved the following quantitative form of Helly's theorem. If the intersection of a family of convex sets in $\\mathbb{R}^d$ is of volume one, then the intersection of some subfamily of at most $2d$ members is of volume at most some constant $v(d)$. They proved the bound $v(d)\\leq d^{2d^2}$, and conjectured $v(d)\\leq d^{cd}$. 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