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We disprove the conjecture for large $k$, and s"},"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":"1802.01825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-06T07:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"dbe81f008d571bee49727e4dd62bbe5b095c0c38b1819c4c67e187f422e13aba","abstract_canon_sha256":"cd014bd660f02e79aeb73ee742b6dddf8258af1b6598b4f3d8a45fc73802439f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:21.179790Z","signature_b64":"LKtyde0VTWLGaoN9Dj+lmmahfOO/1xVT0LesqIwiYnDTeM+8AW8alSvTeBYY2L58x+h5hcZTauIz08mIzEBADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8e68c1988c8f320ce3331e411a2e85c560922feb71a28574285b1b81c1b7cb5","last_reissued_at":"2026-05-18T00:24:21.179333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:21.179333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transversals in Uniform Linear Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anders Yeo, Michael A. 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