{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LRHGHF3DZHVSNLI3QJMFTG6WAH","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":"afe0411d07214dc6c54c9d137f257521556207f36bdea517cb83d4a8bab94982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-16T12:08:01Z","title_canon_sha256":"176d4728057e771fe1ab0ecc24f53e5ef026bb3c08fc92d8a6926186faa1c715"},"schema_version":"1.0","source":{"id":"1404.4218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4218","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4218v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4218","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"LRHGHF3DZHVS","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LRHGHF3DZHVSNLI3","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LRHGHF3D","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:2aa472ead5b7da0ab5a78c0f35f0c76f068438308991109d371dc6b9945dd5f9","target":"graph","created_at":"2026-05-18T02:54:05Z","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":"Given a group G and a G-module A, we show how to determine up to isomorphism the extensions E of A by G so that A embeds as smallest non-trivial term of the derived series or of the lower central series into E.","authors_text":"Andreas Distler, Bettina Eick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-16T12:08:01Z","title":"Group extensions with special properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4218","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":"sha256:8182df41a121f3591683691c7ab855246fca9bd97ca419f91226d98b84f693de","target":"record","created_at":"2026-05-18T02:54:05Z","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":"afe0411d07214dc6c54c9d137f257521556207f36bdea517cb83d4a8bab94982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-16T12:08:01Z","title_canon_sha256":"176d4728057e771fe1ab0ecc24f53e5ef026bb3c08fc92d8a6926186faa1c715"},"schema_version":"1.0","source":{"id":"1404.4218","kind":"arxiv","version":1}},"canonical_sha256":"5c4e639763c9eb26ad1b8258599bd601df34a3613cd563bc57505ad597a2f936","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c4e639763c9eb26ad1b8258599bd601df34a3613cd563bc57505ad597a2f936","first_computed_at":"2026-05-18T02:54:05.902806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:05.902806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dhRdJywuEexXb4ouiAvy9bBP+JgibwKORBDe+bXbBF8YAZmIF0F/KwgDBzrul9X8aRWt7Syoo97tvKZtYJK1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:05.903489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8182df41a121f3591683691c7ab855246fca9bd97ca419f91226d98b84f693de","sha256:2aa472ead5b7da0ab5a78c0f35f0c76f068438308991109d371dc6b9945dd5f9"],"state_sha256":"c7d9aed76c52c483edd50df567842fea65db56c3b5dc5fc2ff728ad4f4057814"}