{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N62BBEZIPZY72YOOEPXOTZQB3D","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":"05d21ce3ea62d4919c3b1974a3bac32ab0d17a48b9e48756923ac24f629aaacc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-04T13:33:52Z","title_canon_sha256":"9b935dfa797bfabd4243177500497f21d648234259867539a8708c71a95b643f"},"schema_version":"1.0","source":{"id":"1403.0785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0785","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0785v1","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0785","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"N62BBEZIPZY7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N62BBEZIPZY72YOO","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N62BBEZI","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:c7490759bed215fda3ba1c5a6f5708756f43a829f46b4bd895d7e80125e83c2a","target":"graph","created_at":"2026-05-18T02:57:15Z","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 finite simple graph is called a bi-Cayley graph over a group $H$ if it has a semiregular automorphism group, isomorphic to $H,$ which has two orbits on the vertex set. Cubic vertex-transitive bi-Cayley graphs over abelian groups have been classified recently by Feng and Zhou (Europ. J. Combin. 36 (2014), 679--693). In this paper we consider the latter class of graphs and select those in the class which are also arc-transitive. Furthermore, such a graph is called $0$-type when it is bipartite, and the bipartition classes are equal to the two orbits of the respective semiregular automorphism g","authors_text":"Hiroki Koike, Istv\\'an Kov\\'acs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-04T13:33:52Z","title":"Arc-transitive cubic abelian bi-Cayley graphs and BCI-graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0785","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:a21181319d489d17d69afb757ea416f8b2d8c621c2aea9d5bc908e61a4f0deb9","target":"record","created_at":"2026-05-18T02:57:15Z","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":"05d21ce3ea62d4919c3b1974a3bac32ab0d17a48b9e48756923ac24f629aaacc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-04T13:33:52Z","title_canon_sha256":"9b935dfa797bfabd4243177500497f21d648234259867539a8708c71a95b643f"},"schema_version":"1.0","source":{"id":"1403.0785","kind":"arxiv","version":1}},"canonical_sha256":"6fb41093287e71fd61ce23eee9e601d8f4935fe07dbd72e2d4f37ec4f88a934a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fb41093287e71fd61ce23eee9e601d8f4935fe07dbd72e2d4f37ec4f88a934a","first_computed_at":"2026-05-18T02:57:15.722955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:15.722955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1PE8um9eCOkzPM5/nt9G0Ytx08l3+c6HGPdClxzr5XnGJ9tbbecsJe78vPwW8n6Ns5HqqBt4Drj+QGNfqIWsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:15.723457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a21181319d489d17d69afb757ea416f8b2d8c621c2aea9d5bc908e61a4f0deb9","sha256:c7490759bed215fda3ba1c5a6f5708756f43a829f46b4bd895d7e80125e83c2a"],"state_sha256":"38522522289ba57b709c86aa077dfb059ef3695efc777da09a0539da55a70735"}