{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4K2V4ZIEHJZXOSPO3T6Y4U6ALK","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":"712cfd09cfebc3bdfe6cf1bafbf72e4ef516986de8646ccedf5e5c2d54e8294c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-19T10:27:32Z","title_canon_sha256":"9b22bdcec30eb7ed83162074ffa7763eebb17258512c331b39fba092aba3a056"},"schema_version":"1.0","source":{"id":"1412.6275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6275","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6275v1","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6275","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"4K2V4ZIEHJZX","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4K2V4ZIEHJZXOSPO","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4K2V4ZIE","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:522622bcd8164458b87775850c0c2df93a36a019bd2da2dad162b7fc1ae3e8a6","target":"graph","created_at":"2026-05-18T02:30:53Z","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 cover of a finite non-cyclic group $G$ is a family $\\mathcal{H}$ of proper subgroups of $G$ whose union equals $G$. A cover of $G$ is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover. We classify the finite non-cyclic groups all of whose irredundant covers are minimal.","authors_text":"Andrea Lucchini, Martino Garonzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-19T10:27:32Z","title":"Irredundant and minimal covers of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6275","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":"sha256:788a08999c9cb7d5d44f12de80dd1b044dc549ceb0dac77466e4efdd2f0c043e","target":"record","created_at":"2026-05-18T02:30:53Z","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":"712cfd09cfebc3bdfe6cf1bafbf72e4ef516986de8646ccedf5e5c2d54e8294c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-19T10:27:32Z","title_canon_sha256":"9b22bdcec30eb7ed83162074ffa7763eebb17258512c331b39fba092aba3a056"},"schema_version":"1.0","source":{"id":"1412.6275","kind":"arxiv","version":1}},"canonical_sha256":"e2b55e65043a737749eedcfd8e53c05a91518a8fc9c6d738ad5081f56cbc4afe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2b55e65043a737749eedcfd8e53c05a91518a8fc9c6d738ad5081f56cbc4afe","first_computed_at":"2026-05-18T02:30:53.918425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:53.918425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GB+iQykqUz8FYGUGX/u1Nom5KE48KECGFwXATgMpxXM0S8IQM31dBntIeW5m0Kuvq48SfTuFAyeqTbxv+MJtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:53.919060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:788a08999c9cb7d5d44f12de80dd1b044dc549ceb0dac77466e4efdd2f0c043e","sha256:522622bcd8164458b87775850c0c2df93a36a019bd2da2dad162b7fc1ae3e8a6"],"state_sha256":"c6f4501be18a0abd75710742fb3ba26df4dbebfa23301ae69b93abcc85a6da1b"}