{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KGF2756QMJFBQZ2MFWJNOMZZNJ","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":"a9d4bf1af2ee09868a483ce14676e2da9df20ed8caaafe14790c80d7fc80394a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-22T08:44:08Z","title_canon_sha256":"080d131baa8629a4aaaf8d9ab2a05746e29cd0b8a146c9f880140d723c180589"},"schema_version":"1.0","source":{"id":"1501.05423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05423","created_at":"2026-05-18T02:28:54Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05423v1","created_at":"2026-05-18T02:28:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05423","created_at":"2026-05-18T02:28:54Z"},{"alias_kind":"pith_short_12","alias_value":"KGF2756QMJFB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KGF2756QMJFBQZ2M","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KGF2756Q","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:dd5949182432736fb488c0063ee257fe76f0c39f4859e95716669e72fa8f89d4","target":"graph","created_at":"2026-05-18T02:28:54Z","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":"We present a survey of our recent research on varieties, generated by wreath products of groups. In particular, the full classification of all cases, when the (cartesian or direct) wreath product of any abelian groups $A$ and $B$ generates the product variety $\\var{A} \\var{B}$, is given. The analog of this is given for sets of abelian groups. We also present new, unpublished research on cases when the similar question is considered for non-abelian, finite groups.","authors_text":"Vahagn H. Mikaelian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-22T08:44:08Z","title":"Varieties generated by wreath products of abelian and nilpotent groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05423","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:bccded14e70876216f07490a33e2a16c8b1e2a8f8fb7b779a425ddd7a3bc7565","target":"record","created_at":"2026-05-18T02:28:54Z","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":"a9d4bf1af2ee09868a483ce14676e2da9df20ed8caaafe14790c80d7fc80394a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-22T08:44:08Z","title_canon_sha256":"080d131baa8629a4aaaf8d9ab2a05746e29cd0b8a146c9f880140d723c180589"},"schema_version":"1.0","source":{"id":"1501.05423","kind":"arxiv","version":1}},"canonical_sha256":"518baff7d0624a18674c2d92d733396a5ed0f038034d898fb2354316abc8b960","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"518baff7d0624a18674c2d92d733396a5ed0f038034d898fb2354316abc8b960","first_computed_at":"2026-05-18T02:28:54.653468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:54.653468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p5HUYKyaM1R6tca74gt+zXmFynvac/NYE0wzQG0ZQQssM3O7FPGvBjojKp3xmDFyssUPvCryozBno1JgZLnjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:54.653811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bccded14e70876216f07490a33e2a16c8b1e2a8f8fb7b779a425ddd7a3bc7565","sha256:dd5949182432736fb488c0063ee257fe76f0c39f4859e95716669e72fa8f89d4"],"state_sha256":"b64a8476fc458ad278b8a290c96d5abad3423c0e38bcaf7499b83615dfbeaf4b"}