{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JMZOBGYJ6CFFC3LUAK3YTCQPEL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2658461d37a779cc668a184d5f8ae6aeaa20948310662f24e85806af36fc479a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-11-13T06:57:15Z","title_canon_sha256":"d2909f4cbfc690e132b9d384cb661637c4c62c44ec2f4714328255ba00208ebe"},"schema_version":"1.0","source":{"id":"1911.06175","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.06175","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"arxiv_version","alias_value":"1911.06175v2","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.06175","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"pith_short_12","alias_value":"JMZOBGYJ6CFF","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"pith_short_16","alias_value":"JMZOBGYJ6CFFC3LU","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"pith_short_8","alias_value":"JMZOBGYJ","created_at":"2026-07-05T01:25:35Z"}],"graph_snapshots":[{"event_id":"sha256:33fe98d60d25d969462ebb91cf6a20854456393311d0246be3e4b8766369850d","target":"graph","created_at":"2026-07-05T01:25:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.06175/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we investigate $2$-$(v,k,\\lambda)$ designs with $\\gcd(r,\\lambda)=1$ admitting flag-transitive automorphism groups $G$. We prove that if $G$ is an almost simple group, then such a design belongs to one of the seven infinite families of $2$-designs or it is one of the eleven well-known examples. We describe all these examples of designs. We, in particular, prove that if $\\mathcal{D}$ is a symmetric $(v,k,\\lambda)$ design with $\\gcd(k,\\lambda)=1$ admitting a flag-transitive automorphism group $G$, then either $G\\leq A\\Gamma L_{1}(q)$ for some odd prime power $q$, or $\\mathcal{D}$","authors_text":"Ashraf Daneshkhah, Fatemeh Mouseli, Seyed Hassan Alavi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-11-13T06:57:15Z","title":"A classification of flag-transitive block designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.06175","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cba2a6ab621bdc15fa8ab70d33a75e787ec5bbcf013392164d7a1f043b5a70b6","target":"record","created_at":"2026-07-05T01:25:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2658461d37a779cc668a184d5f8ae6aeaa20948310662f24e85806af36fc479a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-11-13T06:57:15Z","title_canon_sha256":"d2909f4cbfc690e132b9d384cb661637c4c62c44ec2f4714328255ba00208ebe"},"schema_version":"1.0","source":{"id":"1911.06175","kind":"arxiv","version":2}},"canonical_sha256":"4b32e09b09f08a516d7402b7898a0f22cd137da6be46d8929c16e3c930889bae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b32e09b09f08a516d7402b7898a0f22cd137da6be46d8929c16e3c930889bae","first_computed_at":"2026-07-05T01:25:35.667510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:25:35.667510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sNWB+exL5gfbX7DSDDIAxCljGktk/RWGKMirg4gOnk88LBYPEXBIYXzhQNbT3Jt6oiauvc0NDDEvzWEEBhm1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:25:35.667912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.06175","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cba2a6ab621bdc15fa8ab70d33a75e787ec5bbcf013392164d7a1f043b5a70b6","sha256:33fe98d60d25d969462ebb91cf6a20854456393311d0246be3e4b8766369850d"],"state_sha256":"2ec7601435b844baf62aec37d1f2967195fd2ec74d4b8d80186606970d7d8f5c"}