{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YPSOKVYJKHSODRP7KOCLIUZOW5","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":"1574330521d927b13f316e8d8e87c29e19836a584e7eaf9607c8407fb8afc203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-09T19:55:23Z","title_canon_sha256":"7088d5741a17275126e25fa817bad2aa0e23a9494461febe3a104bb4ab04244b"},"schema_version":"1.0","source":{"id":"1512.03021","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03021","created_at":"2026-05-18T00:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03021v3","created_at":"2026-05-18T00:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03021","created_at":"2026-05-18T00:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"YPSOKVYJKHSO","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YPSOKVYJKHSODRP7","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YPSOKVYJ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:df852908ee83fdea01a589624dec97a6ea92a409bffddd6d782adb6772029ffe","target":"graph","created_at":"2026-05-18T00:39:58Z","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":"The concept of configuration was first introduced to give a characterization for the amenability of groups. Then the concept of two-sided configuration was suggested to provide normality to study the group structures more efficiently. It has been interesting that for which groups, two-sided configuration equivalence would imply isomorphism. We introduce a class of groups, containing polycyclic and FC groups, which for them, the notions of two-sided configuration equivalence and isomorphism coincide.","authors_text":"Ali Rejali, Meisam Soleimani Malekan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-09T19:55:23Z","title":"Two-sided configuration equivalence and isomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03021","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":"sha256:186e42e3fa1b06b2c1262f676107a8870c049be003fd6621da6dbbd75d75846f","target":"record","created_at":"2026-05-18T00:39:58Z","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":"1574330521d927b13f316e8d8e87c29e19836a584e7eaf9607c8407fb8afc203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-09T19:55:23Z","title_canon_sha256":"7088d5741a17275126e25fa817bad2aa0e23a9494461febe3a104bb4ab04244b"},"schema_version":"1.0","source":{"id":"1512.03021","kind":"arxiv","version":3}},"canonical_sha256":"c3e4e5570951e4e1c5ff5384b4532eb7746a5e36fb53183932b80d9a2f204b1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3e4e5570951e4e1c5ff5384b4532eb7746a5e36fb53183932b80d9a2f204b1e","first_computed_at":"2026-05-18T00:39:58.597308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:58.597308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"svDy8ep8T09zE2ooZOWZ4aFQsQ5e6gg/XlaHss4kVv6nk5kocvp2bRzDUKRyOTRFWeivywVH2pC0WTjl/VjDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:58.598043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03021","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:186e42e3fa1b06b2c1262f676107a8870c049be003fd6621da6dbbd75d75846f","sha256:df852908ee83fdea01a589624dec97a6ea92a409bffddd6d782adb6772029ffe"],"state_sha256":"1cded63f15290a7052f13b52bff25e562561fdab85275c55a0d19920cb7d23ed"}