{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WDQEX4YQJ4ODK64ZVDJGD3BLI3","short_pith_number":"pith:WDQEX4YQ","canonical_record":{"source":{"id":"1412.3912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-12T07:59:16Z","cross_cats_sorted":[],"title_canon_sha256":"a0690e0c716bbd5a24eecbd594042dab2871d3b61011b000f54d59e020caf8e8","abstract_canon_sha256":"75ce4d53c4d74e4536d4f607f870ca359f8b78afe4c651cc8e4fdf6c3af07ee0"},"schema_version":"1.0"},"canonical_sha256":"b0e04bf3104f1c357b99a8d261ec2b46e8e8384278efcf8bb94a732135629966","source":{"kind":"arxiv","id":"1412.3912","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3912","created_at":"2026-05-18T02:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3912v1","created_at":"2026-05-18T02:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3912","created_at":"2026-05-18T02:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"WDQEX4YQJ4OD","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WDQEX4YQJ4ODK64Z","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WDQEX4YQ","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WDQEX4YQJ4ODK64ZVDJGD3BLI3","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-12T07:59:16Z","cross_cats_sorted":[],"title_canon_sha256":"a0690e0c716bbd5a24eecbd594042dab2871d3b61011b000f54d59e020caf8e8","abstract_canon_sha256":"75ce4d53c4d74e4536d4f607f870ca359f8b78afe4c651cc8e4fdf6c3af07ee0"},"schema_version":"1.0"},"canonical_sha256":"b0e04bf3104f1c357b99a8d261ec2b46e8e8384278efcf8bb94a732135629966","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:29.319139Z","signature_b64":"Ooxu1o18jN49TgW8Dz7THlY8CH5DLSr/S5tCynBp4wxHCy06Z5SboBxFnbFIRoLtvPNEpINFUNxkQzWvb5UOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0e04bf3104f1c357b99a8d261ec2b46e8e8384278efcf8bb94a732135629966","last_reissued_at":"2026-05-18T02:31:29.318573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:29.318573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3912","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"buVQJ3N5g9t06idOaSITXSigyBs4Mczd53FkdwQXuYpSAZEU445gg7WL6IQVCLprZRgCc/xPvUv4m4iHVn0MDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:45:17.936740Z"},"content_sha256":"0a89c3bad3ce7cccc8f19813d415e63656689bab39a74ac6610315273ca89434","schema_version":"1.0","event_id":"sha256:0a89c3bad3ce7cccc8f19813d415e63656689bab39a74ac6610315273ca89434"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WDQEX4YQJ4ODK64ZVDJGD3BLI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cheryl E. Praeger, Jan Saxl, Martin W. Liebeck","submitted_at":"2014-12-12T07:59:16Z","abstract_excerpt":"A linear group G on a finite vector space V, (that is, a subgroup of GL(V)) is called (1/2)-transitive if all the G-orbits on the set of nonzero vectors have the same size. We complete the classification of all the (1/2)-transitive linear groups. As a consequence we complete the determination of the finite (3/2)-transitive permutation groups -- the transitive groups for which a point-stabilizer has all its nontrivial orbits of the same size. We also determine the finite (k+1/2)-transitive permutation groups for integers k > 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3912","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GcXSnJhEw3aHHIPH0xxW9PUanUXFV/OWUCxuxKFdudCYP1RY8uFfv8W5hKOMMJZD76KMZMjDUn6rKjjNVjvtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:45:17.937084Z"},"content_sha256":"4b87463d6bf8ac3718489cb500554743f4bdb30328a73dd296733e3e1b4d35ee","schema_version":"1.0","event_id":"sha256:4b87463d6bf8ac3718489cb500554743f4bdb30328a73dd296733e3e1b4d35ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WDQEX4YQJ4ODK64ZVDJGD3BLI3/bundle.json","state_url":"https://pith.science/pith/WDQEX4YQJ4ODK64ZVDJGD3BLI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WDQEX4YQJ4ODK64ZVDJGD3BLI3/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":"2026-06-03T07:45:17Z","links":{"resolver":"https://pith.science/pith/WDQEX4YQJ4ODK64ZVDJGD3BLI3","bundle":"https://pith.science/pith/WDQEX4YQJ4ODK64ZVDJGD3BLI3/bundle.json","state":"https://pith.science/pith/WDQEX4YQJ4ODK64ZVDJGD3BLI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WDQEX4YQJ4ODK64ZVDJGD3BLI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WDQEX4YQJ4ODK64ZVDJGD3BLI3","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":"75ce4d53c4d74e4536d4f607f870ca359f8b78afe4c651cc8e4fdf6c3af07ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-12T07:59:16Z","title_canon_sha256":"a0690e0c716bbd5a24eecbd594042dab2871d3b61011b000f54d59e020caf8e8"},"schema_version":"1.0","source":{"id":"1412.3912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3912","created_at":"2026-05-18T02:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3912v1","created_at":"2026-05-18T02:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3912","created_at":"2026-05-18T02:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"WDQEX4YQJ4OD","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WDQEX4YQJ4ODK64Z","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WDQEX4YQ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:4b87463d6bf8ac3718489cb500554743f4bdb30328a73dd296733e3e1b4d35ee","target":"graph","created_at":"2026-05-18T02:31:29Z","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"},"paper":{"abstract_excerpt":"A linear group G on a finite vector space V, (that is, a subgroup of GL(V)) is called (1/2)-transitive if all the G-orbits on the set of nonzero vectors have the same size. We complete the classification of all the (1/2)-transitive linear groups. As a consequence we complete the determination of the finite (3/2)-transitive permutation groups -- the transitive groups for which a point-stabilizer has all its nontrivial orbits of the same size. We also determine the finite (k+1/2)-transitive permutation groups for integers k > 1.","authors_text":"Cheryl E. Praeger, Jan Saxl, Martin W. Liebeck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-12T07:59:16Z","title":"The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3912","kind":"arxiv","version":1},"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":"sha256:0a89c3bad3ce7cccc8f19813d415e63656689bab39a74ac6610315273ca89434","target":"record","created_at":"2026-05-18T02:31:29Z","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":"75ce4d53c4d74e4536d4f607f870ca359f8b78afe4c651cc8e4fdf6c3af07ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-12T07:59:16Z","title_canon_sha256":"a0690e0c716bbd5a24eecbd594042dab2871d3b61011b000f54d59e020caf8e8"},"schema_version":"1.0","source":{"id":"1412.3912","kind":"arxiv","version":1}},"canonical_sha256":"b0e04bf3104f1c357b99a8d261ec2b46e8e8384278efcf8bb94a732135629966","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0e04bf3104f1c357b99a8d261ec2b46e8e8384278efcf8bb94a732135629966","first_computed_at":"2026-05-18T02:31:29.318573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:29.318573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ooxu1o18jN49TgW8Dz7THlY8CH5DLSr/S5tCynBp4wxHCy06Z5SboBxFnbFIRoLtvPNEpINFUNxkQzWvb5UOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:29.319139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a89c3bad3ce7cccc8f19813d415e63656689bab39a74ac6610315273ca89434","sha256:4b87463d6bf8ac3718489cb500554743f4bdb30328a73dd296733e3e1b4d35ee"],"state_sha256":"20639344f1dc491823aa214cd5b1df7c016774959925b61e915049c0736bd2ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wtACQgptkNQAm3ToOXqETqwk5XXOwM5fBTF8VAsKh3Q6h41yJVSXw/LDHmNVOvdxS5mrkhuj6tSfrS2mzT4EBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:45:17.938965Z","bundle_sha256":"9352bec032fda3d244a253713741631131743be324fc2b803c84b4c62320cbff"}}