{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:P6D7ZBALMJHX3CW4WAZTODHNXT","short_pith_number":"pith:P6D7ZBAL","canonical_record":{"source":{"id":"2307.05195","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-07-11T12:02:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"26cde1c8f168084c3b79f9cce4f29308aaa7535685549b618ea2aa1741d7b63b","abstract_canon_sha256":"c4bc49a861e5bedfd70c0bb9ceb819fd9fadc196c4154d727661bf2fd975329d"},"schema_version":"1.0"},"canonical_sha256":"7f87fc840b624f7d8adcb033370cedbcc8cfc85435ee8540ab481157c52316a1","source":{"kind":"arxiv","id":"2307.05195","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.05195","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"2307.05195v2","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.05195","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"P6D7ZBALMJHX","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"P6D7ZBALMJHX3CW4","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"P6D7ZBAL","created_at":"2026-07-05T10:14:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:P6D7ZBALMJHX3CW4WAZTODHNXT","target":"record","payload":{"canonical_record":{"source":{"id":"2307.05195","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-07-11T12:02:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"26cde1c8f168084c3b79f9cce4f29308aaa7535685549b618ea2aa1741d7b63b","abstract_canon_sha256":"c4bc49a861e5bedfd70c0bb9ceb819fd9fadc196c4154d727661bf2fd975329d"},"schema_version":"1.0"},"canonical_sha256":"7f87fc840b624f7d8adcb033370cedbcc8cfc85435ee8540ab481157c52316a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:21.906324Z","signature_b64":"sVJISYAEmxjVm2nYwalmzhoQHsbq3++lHZquQ6FWDNzVYUiBCk+PFY1eAm9sIkUdADp5rHJqugk7A4MGqLdrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f87fc840b624f7d8adcb033370cedbcc8cfc85435ee8540ab481157c52316a1","last_reissued_at":"2026-07-05T10:14:21.905838Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:21.905838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.05195","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDp/Bp6te2IqYCM5lv6RwwpjpcUVS1S6WQWx/yCut/Gdq0jGjHMxNjZ5wADn7w+gL6p9uRjO3UZA7aIk1woWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T17:50:06.168097Z"},"content_sha256":"da4ba1a652542c9e6571df30956f912071f1f72748b3b8993fdf65d7fceebae2","schema_version":"1.0","event_id":"sha256:da4ba1a652542c9e6571df30956f912071f1f72748b3b8993fdf65d7fceebae2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:P6D7ZBALMJHX3CW4WAZTODHNXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost simple groups as flag-transitive automorphism groups of 2-designs with {\\lambda} = 2","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Seyed Hassan Alavi","submitted_at":"2023-07-11T12:02:46Z","abstract_excerpt":"In this article, we study $2$-designs with $\\lambda=2$ admitting a flag-transitive almost simple automorphism group with socle a finite simple exceptional group of Lie type, and we prove that such a $2$-design does not exist. In conclusion, we present a classification of $2$-designs with $\\lambda=2$ admitting flag-transitive and point-primitive automorphism groups of almost simple type, which states that such a $2$-design belongs to an infinite family of $2$-designs with parameter set $((3^n-1)/2,3,2)$ and $X=PSL_n(3)$ for some $n\\geq 3$, or it is isomorphic to the $2$-design with parameter se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.05195","kind":"arxiv","version":2},"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/2307.05195/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XgjUww6fKRbErofPA61/jokqmmGFjOS8jL+/W+U2nWXT37qfV5Sy6L11uzX26dvibAOIoyHUe+GuQuzy7IFCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T17:50:06.168701Z"},"content_sha256":"4a09eedcbf14dc2383dc3fd5964623052fa48c506e90d6e821fa2b7cb7c144ba","schema_version":"1.0","event_id":"sha256:4a09eedcbf14dc2383dc3fd5964623052fa48c506e90d6e821fa2b7cb7c144ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6D7ZBALMJHX3CW4WAZTODHNXT/bundle.json","state_url":"https://pith.science/pith/P6D7ZBALMJHX3CW4WAZTODHNXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6D7ZBALMJHX3CW4WAZTODHNXT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-21T17:50:06Z","links":{"resolver":"https://pith.science/pith/P6D7ZBALMJHX3CW4WAZTODHNXT","bundle":"https://pith.science/pith/P6D7ZBALMJHX3CW4WAZTODHNXT/bundle.json","state":"https://pith.science/pith/P6D7ZBALMJHX3CW4WAZTODHNXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6D7ZBALMJHX3CW4WAZTODHNXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:P6D7ZBALMJHX3CW4WAZTODHNXT","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":"c4bc49a861e5bedfd70c0bb9ceb819fd9fadc196c4154d727661bf2fd975329d","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-07-11T12:02:46Z","title_canon_sha256":"26cde1c8f168084c3b79f9cce4f29308aaa7535685549b618ea2aa1741d7b63b"},"schema_version":"1.0","source":{"id":"2307.05195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.05195","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"2307.05195v2","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.05195","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"P6D7ZBALMJHX","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"P6D7ZBALMJHX3CW4","created_at":"2026-07-05T10:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"P6D7ZBAL","created_at":"2026-07-05T10:14:21Z"}],"graph_snapshots":[{"event_id":"sha256:4a09eedcbf14dc2383dc3fd5964623052fa48c506e90d6e821fa2b7cb7c144ba","target":"graph","created_at":"2026-07-05T10:14:21Z","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/2307.05195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we study $2$-designs with $\\lambda=2$ admitting a flag-transitive almost simple automorphism group with socle a finite simple exceptional group of Lie type, and we prove that such a $2$-design does not exist. In conclusion, we present a classification of $2$-designs with $\\lambda=2$ admitting flag-transitive and point-primitive automorphism groups of almost simple type, which states that such a $2$-design belongs to an infinite family of $2$-designs with parameter set $((3^n-1)/2,3,2)$ and $X=PSL_n(3)$ for some $n\\geq 3$, or it is isomorphic to the $2$-design with parameter se","authors_text":"Seyed Hassan Alavi","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-07-11T12:02:46Z","title":"Almost simple groups as flag-transitive automorphism groups of 2-designs with {\\lambda} = 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.05195","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:da4ba1a652542c9e6571df30956f912071f1f72748b3b8993fdf65d7fceebae2","target":"record","created_at":"2026-07-05T10:14:21Z","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":"c4bc49a861e5bedfd70c0bb9ceb819fd9fadc196c4154d727661bf2fd975329d","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-07-11T12:02:46Z","title_canon_sha256":"26cde1c8f168084c3b79f9cce4f29308aaa7535685549b618ea2aa1741d7b63b"},"schema_version":"1.0","source":{"id":"2307.05195","kind":"arxiv","version":2}},"canonical_sha256":"7f87fc840b624f7d8adcb033370cedbcc8cfc85435ee8540ab481157c52316a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f87fc840b624f7d8adcb033370cedbcc8cfc85435ee8540ab481157c52316a1","first_computed_at":"2026-07-05T10:14:21.905838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:14:21.905838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sVJISYAEmxjVm2nYwalmzhoQHsbq3++lHZquQ6FWDNzVYUiBCk+PFY1eAm9sIkUdADp5rHJqugk7A4MGqLdrDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:14:21.906324Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.05195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da4ba1a652542c9e6571df30956f912071f1f72748b3b8993fdf65d7fceebae2","sha256:4a09eedcbf14dc2383dc3fd5964623052fa48c506e90d6e821fa2b7cb7c144ba"],"state_sha256":"02649dc42d0a0509ace70d1b86a14e93b8812b1ae19ce6bd5dddefd7155f3564"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjhmKS4vOlbd+SHURk/wlmvigZw8KcL02ONMNBy9O2JPZvT+Zz+uFBvZGEPuGLZXcxR/oEl1ZYO9HdAJ1NTwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T17:50:06.173804Z","bundle_sha256":"57c8a4e5b1a238a795ae42e0ac02b1a56ab30ab55dece28fe49e174be00c7b5f"}}