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(i) If $10\\geq \\lambda \\geq 5$, then except $(G,G_x,G_B,k,\\lambda)=(PSL(2,761),{E_{761}}\\rtimes {C_{380}},S_4,24,7)$ or $(PSL(2,512),{E_{512}}\\rtimes {C_{511}},{D_{18}},18,8)$ undecided, $\\cal D$ is a $4$-$(24,8,5)$, $4$-$(9,8,5)$, $4$-$(8,6,6)$, $4$-$(10,9,6)$, $4$-$(9,"},"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":"1908.00760","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-02T08:52:20Z","cross_cats_sorted":[],"title_canon_sha256":"bd4fbad2c401150f6bb2097211faeea4ffb3efc31e240d364bc47a3e48962b69","abstract_canon_sha256":"ac84d829788b9a82f8f6229351d90593612e9ed0afd25a3e6f765d437f31f86f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:14:20.515555Z","signature_b64":"NgA8NqlKOt2pjjPxA1DYX4C8SKpJK9OMU1yJ55pEcTAOpt/kRyI1WyblonKzUnOUwbUAwEpUrzsZolS/0azrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b31c22b6abe1a6da2484d3595678f47ae0d2f3013b92c380017e2e642d67cfa","last_reissued_at":"2026-07-05T00:14:20.515135Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:14:20.515135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flag-transitive $4$-designs and $PSL(2,q)$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huili Dong","submitted_at":"2019-08-02T08:52:20Z","abstract_excerpt":"This paper considers flag-transitive $4$-$(q+1,k,\\lambda)$ designs with $\\lambda\\geq5$ and $q+1>k>4$. 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(i) If $10\\geq \\lambda \\geq 5$, then except $(G,G_x,G_B,k,\\lambda)=(PSL(2,761),{E_{761}}\\rtimes {C_{380}},S_4,24,7)$ or $(PSL(2,512),{E_{512}}\\rtimes {C_{511}},{D_{18}},18,8)$ undecided, $\\cal D$ is a $4$-$(24,8,5)$, $4$-$(9,8,5)$, $4$-$(8,6,6)$, $4$-$(10,9,6)$, $4$-$(9,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00760","kind":"arxiv","version":3},"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/1908.00760/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.00760","created_at":"2026-07-05T00:14:20.515208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.00760v3","created_at":"2026-07-05T00:14:20.515208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00760","created_at":"2026-07-05T00:14:20.515208+00:00"},{"alias_kind":"pith_short_12","alias_value":"BMY4EK3KXYNG","created_at":"2026-07-05T00:14:20.515208+00:00"},{"alias_kind":"pith_short_16","alias_value":"BMY4EK3KXYNG3ISI","created_at":"2026-07-05T00:14:20.515208+00:00"},{"alias_kind":"pith_short_8","alias_value":"BMY4EK3K","created_at":"2026-07-05T00:14:20.515208+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6","json":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6.json","graph_json":"https://pith.science/api/pith-number/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/graph.json","events_json":"https://pith.science/api/pith-number/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/events.json","paper":"https://pith.science/paper/BMY4EK3K"},"agent_actions":{"view_html":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6","download_json":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6.json","view_paper":"https://pith.science/paper/BMY4EK3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.00760&json=true","fetch_graph":"https://pith.science/api/pith-number/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/graph.json","fetch_events":"https://pith.science/api/pith-number/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/action/storage_attestation","attest_author":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/action/author_attestation","sign_citation":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/action/citation_signature","submit_replication":"https://pith.science/pith/BMY4EK3KXYNG3ISIJU2ZKZ4PI6/action/replication_record"}},"created_at":"2026-07-05T00:14:20.515208+00:00","updated_at":"2026-07-05T00:14:20.515208+00:00"}