{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IZDTSKBMDYP6ZRRATJAZNIZYVO","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":"14747f056be91fefc7dde29f6586357f9bef127d04ffd03f78668a00e20c78df","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-12-18T17:21:44Z","title_canon_sha256":"6378b4f34facea93b7e7f91e02b57cc1076b5202ff867552522d63620a160fcf"},"schema_version":"1.0","source":{"id":"1612.05954","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05954","created_at":"2026-05-18T00:35:43Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05954v2","created_at":"2026-05-18T00:35:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05954","created_at":"2026-05-18T00:35:43Z"},{"alias_kind":"pith_short_12","alias_value":"IZDTSKBMDYP6","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IZDTSKBMDYP6ZRRA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IZDTSKBM","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:a88d2380137f280ac6c9f7d1f45e22eae59ec8cf5096c43ceb1a8e17765c089f","target":"graph","created_at":"2026-05-18T00:35:43Z","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 show that the conjugacy problem in a wreath product $A \\wr B$ is uniform-$\\mathsf{TC}^0$-Turing-reducible to the conjugacy problem in the factors $A$ and $B$ and the power problem in $B$. If $B$ is torsion free, the power problem for $B$ can be replaced by the slightly weaker cyclic submonoid membership problem for $B$. Moreover, if $A$ is abelian, the cyclic subgroup membership problem suffices, which itself is uniform-$\\mathsf{AC}^0$-many-one-reducible to the conjugacy problem in $A \\wr B$.\n  Furthermore, under certain natural conditions, we give a uniform $\\mathsf{TC}^0$ Turing reduction","authors_text":"Alexei Miasnikov, Armin Wei{\\ss}, Svetla Vassileva","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-12-18T17:21:44Z","title":"The conjugacy problem in free solvable groups and wreath product of abelian groups is in TC$^0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05954","kind":"arxiv","version":2},"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":"sha256:63b68d69f71110bdf071a48361e116fa2e0ddeea71ea99d883af7e4ed6182ec9","target":"record","created_at":"2026-05-18T00:35:43Z","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":"14747f056be91fefc7dde29f6586357f9bef127d04ffd03f78668a00e20c78df","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-12-18T17:21:44Z","title_canon_sha256":"6378b4f34facea93b7e7f91e02b57cc1076b5202ff867552522d63620a160fcf"},"schema_version":"1.0","source":{"id":"1612.05954","kind":"arxiv","version":2}},"canonical_sha256":"464739282c1e1fecc6209a4196a338abbddfc5f021dc600758c9e8b30238b178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"464739282c1e1fecc6209a4196a338abbddfc5f021dc600758c9e8b30238b178","first_computed_at":"2026-05-18T00:35:43.792219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:43.792219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UnaOcAkCnf4xXnDQFOMSrVR5u3iel6Pk8lDAWhISutyjBqSsjG5S9v+DJgFQ82n8Hb5ATr3GW+mGKHqP9P1YDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:43.792764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05954","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b68d69f71110bdf071a48361e116fa2e0ddeea71ea99d883af7e4ed6182ec9","sha256:a88d2380137f280ac6c9f7d1f45e22eae59ec8cf5096c43ceb1a8e17765c089f"],"state_sha256":"db94e1fca3eea85c003f9bc94db87a07c6a46335c531e4d31eea0f7d25047c3e"}