{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KTGQ3ZYNFYMQF4JYC7YJQOMCYH","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":"f8b6acab6430e67b9b0a8291a2e7f7b9c843d65ff26fc70903b38d20f6728c0c","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-08T09:19:31Z","title_canon_sha256":"2c48c290510af569e736de71deab9103db90e428cc2693e2a66eb008de656ff8"},"schema_version":"1.0","source":{"id":"1211.1797","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1797","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1797v3","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1797","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"KTGQ3ZYNFYMQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KTGQ3ZYNFYMQF4JY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KTGQ3ZYN","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:f60c1a0f297ab5b5f439c960440359a47dc9294faf7bbb157df5254ac3bd80d4","target":"graph","created_at":"2026-05-18T02:39:24Z","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 deduce a simple representation and the invariant factor decompositions of the subgroups of the group $\\Bbb{Z}_m \\times \\Bbb{Z}_n$, where $m$ and $n$ are arbitrary positive integers. We obtain formulas for the total number of subgroups and the number of subgroups of a given order.","authors_text":"Christoph Wiesmeyr, L\\'aszl\\'o T\\'oth, Mario Hampejs, Nicki Holighaus","cross_cats":["math.CO","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-08T09:19:31Z","title":"Representing and counting the subgroups of the group Z_m x Z_n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1797","kind":"arxiv","version":3},"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":"sha256:8646c25dce54af33dd420bbd74c912c115d212dce8b3fec997f65003621e394e","target":"record","created_at":"2026-05-18T02:39:24Z","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":"f8b6acab6430e67b9b0a8291a2e7f7b9c843d65ff26fc70903b38d20f6728c0c","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-08T09:19:31Z","title_canon_sha256":"2c48c290510af569e736de71deab9103db90e428cc2693e2a66eb008de656ff8"},"schema_version":"1.0","source":{"id":"1211.1797","kind":"arxiv","version":3}},"canonical_sha256":"54cd0de70d2e1902f13817f0983982c1c80275470d06300ab439795acd17a411","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54cd0de70d2e1902f13817f0983982c1c80275470d06300ab439795acd17a411","first_computed_at":"2026-05-18T02:39:24.273373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:24.273373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3hjeupwxqqf6dC7RHcUQkMH97lB0IYF2h7QsBTTMb03OpkTE1gKISjD1NmJ1n0SlN7wiSutxYm4Xe/djBfGUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:24.273717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1797","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8646c25dce54af33dd420bbd74c912c115d212dce8b3fec997f65003621e394e","sha256:f60c1a0f297ab5b5f439c960440359a47dc9294faf7bbb157df5254ac3bd80d4"],"state_sha256":"0da42f7c9d6d5cabb0b3982ad92ccdf0349f2e7b196d201159860c80eff386de"}