{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:VVAINQVBKLQPWLNK6CH7AHRB64","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":"bbae8b23d5a5e562c3c8c62b85367008daf418e9d20513c7f3b54578f09263e4","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-06-29T14:47:35Z","title_canon_sha256":"42a317cba60520aefedc30d93f55d929999a042ca5415521871368bbbe575530"},"schema_version":"1.0","source":{"id":"math/0606764","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606764","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606764v3","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606764","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"pith_short_12","alias_value":"VVAINQVBKLQP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"VVAINQVBKLQPWLNK","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"VVAINQVB","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:e57c825f50ee8cba96b5790536d332f49a94de03b7ef01e195aa2070a4a9ea64","target":"graph","created_at":"2026-05-18T03:56:24Z","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 study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of Burnside-Frobenius theorem) and some related properties. We give examples of groups with and without this property and study its behavior under some extensions. An affirmative answer to the twisted Dehn conjugacy problem for polycyclic-by-finite group is obtained. Some problems for the further study are indicated.","authors_text":"Alexander Fel'shtyn, Evgenij Troitsky","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-06-29T14:47:35Z","title":"Twisted conjugacy separable groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606764","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":"sha256:304339effb924298e279a8af89f32da0d09f0031e1ff101a55c51e66022aca4f","target":"record","created_at":"2026-05-18T03:56:24Z","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":"bbae8b23d5a5e562c3c8c62b85367008daf418e9d20513c7f3b54578f09263e4","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2006-06-29T14:47:35Z","title_canon_sha256":"42a317cba60520aefedc30d93f55d929999a042ca5415521871368bbbe575530"},"schema_version":"1.0","source":{"id":"math/0606764","kind":"arxiv","version":3}},"canonical_sha256":"ad4086c2a152e0fb2daaf08ff01e21f728a6b60656d9b1d917d0d481befa0949","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad4086c2a152e0fb2daaf08ff01e21f728a6b60656d9b1d917d0d481befa0949","first_computed_at":"2026-05-18T03:56:24.738769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:24.738769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oRiAU4gu5xLordJ0Y/8CxlzJWYJqO6CDhD2qjIzrThWGyXkHSgB538bYn02Ek3fCVoR+75V+49GvoyBLRAt3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:24.739559Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606764","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:304339effb924298e279a8af89f32da0d09f0031e1ff101a55c51e66022aca4f","sha256:e57c825f50ee8cba96b5790536d332f49a94de03b7ef01e195aa2070a4a9ea64"],"state_sha256":"2ee0398d48a2c6b158f4db33671b464fc7e94e7f7a03beefd5a86f491793be9d"}