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We prove that there exists only one such pair $(\\mathcal{D}, G)$ in which $\\mathcal{D}$ is a $2$-$(176,8,2)$ design and $G=HS$, the Higman-Sims simple group."},"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":"1603.07405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-24T01:19:25Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e8fc414d2b25a41378359b8c5f6f42c0cf27ea0335fdfde5f04686b19580abe7","abstract_canon_sha256":"28428eaa80608e7efe4b955d0506f52e8ae5cd443d61cc926b0bf8fc3ea17c3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:21.046445Z","signature_b64":"fa8jInlKaFYQhL3mIcScbulgXMy4FNeChxS4jRzeU/ZVetDyXs3qKOHMA9KxNgR2rz46n3J+ahu5z5CRmAhABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cbe8c689e3689423749cdf86492ec1774266ec2e45188fb653f7d12f8f4f812","last_reissued_at":"2026-05-18T01:18:21.045809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:21.045809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Block-transitive and point-primitive $2$-$(v,k,2)$ designs with sporadic socle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Shenglin Zhou, Xiaohong Zhang","submitted_at":"2016-03-24T01:19:25Z","abstract_excerpt":"The purpose of this paper is to classify all pairs $(\\mathcal{D}, G)$, where $\\mathcal{D}$ is a non-trivial $2$-$(v, k, 2)$ design, and $G\\leq Aut(\\mathcal{D})$ acts transitively on the set of blocks of $\\mathcal{D}$ and primitively on the set of points of $\\mathcal{D}$ with sporadic socle. 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