{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CCTNJDXNTLQS7LL7GTWNNBZE6P","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":"fc4248c058254b50487db00ed800404c51c7ab42d28df95458c79a79c413401f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-02-06T13:10:49Z","title_canon_sha256":"062f0c15de63860ffcc16756334cf7ffa6121c5c15239485fe28c46cd3095657"},"schema_version":"1.0","source":{"id":"1902.02154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02154","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02154v1","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02154","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"CCTNJDXNTLQS","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CCTNJDXNTLQS7LL7","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CCTNJDXN","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:01c2a3e9625538e94c952ea3ce4f44b01dd3663353984e962a1b7b5ed3c57461","target":"graph","created_at":"2026-05-17T23:54:37Z","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":"In the present paper, we introduce the new construction of quandles. For a group $G$ and its subset $A$ we construct a quandle $Q(G,A)$ which is called the $(G,A)$-quandle and study properties of this quandle. In particular, we prove that if $Q$ is a quandle such that the natural map $Q\\to G_Q$ from $Q$ to its enveloping group $G_Q$ is injective, then $Q$ is the $(G,A)$-quandle for an appropriate group $G$ and its subset $A$. Also we introduce the free product of quandles and study this construction for $(G,A)$-quandles. In addition, we classify all finite quandles with enveloping group $\\math","authors_text":"Timur Nasybullov, Valeriy Bardakov","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-02-06T13:10:49Z","title":"On embeddings of quandles into groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02154","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":"sha256:6be61b4eb88fe66f1ce5b61dd0d0db94c295526b0c9ca0d9f40ad446a12b8759","target":"record","created_at":"2026-05-17T23:54:37Z","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":"fc4248c058254b50487db00ed800404c51c7ab42d28df95458c79a79c413401f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-02-06T13:10:49Z","title_canon_sha256":"062f0c15de63860ffcc16756334cf7ffa6121c5c15239485fe28c46cd3095657"},"schema_version":"1.0","source":{"id":"1902.02154","kind":"arxiv","version":1}},"canonical_sha256":"10a6d48eed9ae12fad7f34ecd68724f3f834e0f14dd526ddc7a847f080fe9382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10a6d48eed9ae12fad7f34ecd68724f3f834e0f14dd526ddc7a847f080fe9382","first_computed_at":"2026-05-17T23:54:37.804798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:37.804798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I7R50HASjCzHxYu/RJakHtNalkyhllqIgnFHKqetNnFbXv8VF0kWlQ8dgHgzx5w8TFrsDILCXDXE2GWKirFCAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:37.805447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6be61b4eb88fe66f1ce5b61dd0d0db94c295526b0c9ca0d9f40ad446a12b8759","sha256:01c2a3e9625538e94c952ea3ce4f44b01dd3663353984e962a1b7b5ed3c57461"],"state_sha256":"e1c612377d217c2412ff87bcc9aca3dd2cb6a82712534b70462422e5adcdb15c"}