{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JTHKO4M7PWF5UMYZF7T6DWZIWP","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":"48245f7648e486ab901fd47dda4681bbec126e7999fab3cd6525385adc8de985","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-28T07:57:30Z","title_canon_sha256":"a226e67e5cbee118dd37b4712ab61e255be7b1397f239f4718d052c92f35f840"},"schema_version":"1.0","source":{"id":"1208.5579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5579","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5579v1","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5579","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"JTHKO4M7PWF5","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JTHKO4M7PWF5UMYZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JTHKO4M7","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:cb86d96446056b5e175ca11b05928579620b1c289abfa487a8613a728b1774cf","target":"graph","created_at":"2026-05-18T03:46:58Z","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 continue some recent investigations of W. Dziobiak, J. Jezek, and M. Maroti. Let G=(G,\\cdot) be a commutative group. A semilattice over G is a semilattice enriched with G as a set of unary operations acting as semilattice automorphisms. We prove that the minimal quasivarieties of semilattices over a finite abelian group G are in one-to-one correspondence with the subgroups of G. If G is not finite, then we reduce the description of minimal quasivarieties to that of those minimal quasivarieties in which not every algebra has a zero element.","authors_text":"Ildik\\'o V. Nagy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-28T07:57:30Z","title":"Minimal quasivarieties of semilattices over commutative groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5579","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:c57e1e1680d47270d4777709354bf2f2ba78a5e68f4a2e848e90c0bbe36bb949","target":"record","created_at":"2026-05-18T03:46:58Z","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":"48245f7648e486ab901fd47dda4681bbec126e7999fab3cd6525385adc8de985","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-28T07:57:30Z","title_canon_sha256":"a226e67e5cbee118dd37b4712ab61e255be7b1397f239f4718d052c92f35f840"},"schema_version":"1.0","source":{"id":"1208.5579","kind":"arxiv","version":1}},"canonical_sha256":"4ccea7719f7d8bda33192fe7e1db28b3d6539b16f8ad0f431633a7c99c8c3a28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ccea7719f7d8bda33192fe7e1db28b3d6539b16f8ad0f431633a7c99c8c3a28","first_computed_at":"2026-05-18T03:46:58.308816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:58.308816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d4gwxc02fC5jvx+cR01oOI1mRa/TuEXJMmGuQ/3KOCRw/ityJHmab3uggWtNsjR67qe2dPsiSqY3vfcZnfoaDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:58.309470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c57e1e1680d47270d4777709354bf2f2ba78a5e68f4a2e848e90c0bbe36bb949","sha256:cb86d96446056b5e175ca11b05928579620b1c289abfa487a8613a728b1774cf"],"state_sha256":"2ff90031b721d89d1e630c596b156c1b58bd46646daac191fc7b2967a3286b9d"}