{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VYTLBDKYCCYBHPDVTXTZGLJZN7","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":"a95e57e4e4ec7d0da172920eb19cb109b5ad7d21e333fd5b4187770bfb40c599","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-05T10:29:30Z","title_canon_sha256":"3fe03a6c7558fc5513a2df1459eb6718af426b4c26c4f36a5b7b6f3b562bbb81"},"schema_version":"1.0","source":{"id":"1510.01316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01316","created_at":"2026-05-18T01:30:57Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01316v1","created_at":"2026-05-18T01:30:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01316","created_at":"2026-05-18T01:30:57Z"},{"alias_kind":"pith_short_12","alias_value":"VYTLBDKYCCYB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VYTLBDKYCCYBHPDV","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VYTLBDKY","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:5225e528301bb09d6a569064ee1fa230a8779190b231f938634bf1df81bb2e0a","target":"graph","created_at":"2026-05-18T01:30:57Z","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 new subclass of AG-groupoids, so called, cyclic associative Abel-Grassman groupoids or CA-AG-groupoid is studied. These have been enumerated up to order $6$. A test for the verification of cyclic associativity for an arbitrary AG-groupoid has been introduced. Various properties of CA-AG-groupoids have been studied. Relationship among CA-AG-groupoids and other subclasses of AG-groupoids is investigated. It is shown that the subclass of CA-AG-groupoid is different from that of the AG{*}-groupoid as well as AG{*}{*}-groupoids.","authors_text":"Imtiaz Ahmad, Muhammad Iqbal, Muhammad Irfan Ali, Muhammad Shah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-05T10:29:30Z","title":"On cyclic associative Abel-Grassman groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01316","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:ce6790866f7bdfef83702060865c4001aa40d164fa3103a0287ce8619359be5d","target":"record","created_at":"2026-05-18T01:30:57Z","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":"a95e57e4e4ec7d0da172920eb19cb109b5ad7d21e333fd5b4187770bfb40c599","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-05T10:29:30Z","title_canon_sha256":"3fe03a6c7558fc5513a2df1459eb6718af426b4c26c4f36a5b7b6f3b562bbb81"},"schema_version":"1.0","source":{"id":"1510.01316","kind":"arxiv","version":1}},"canonical_sha256":"ae26b08d5810b013bc759de7932d396fca80e70908b04af7c44c6896b166c53b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae26b08d5810b013bc759de7932d396fca80e70908b04af7c44c6896b166c53b","first_computed_at":"2026-05-18T01:30:57.205629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:57.205629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aukPt3Hm2tD1IngLGnb1VZ7QmuQDjO2DCzcqkKyrAsp6X8aMpjre+5453/fO4OoArc77+uAM7uk7DZPAixb1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:57.206275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce6790866f7bdfef83702060865c4001aa40d164fa3103a0287ce8619359be5d","sha256:5225e528301bb09d6a569064ee1fa230a8779190b231f938634bf1df81bb2e0a"],"state_sha256":"41ca924aebcd4821925c4eedd5e25c1b53a80a1f35b78a0f1c8c10a8ccb62b0d"}